RS Aggarwal solution class 8 chapter 10 Profit and Loss Exercise 10A

Exercise 10A

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Q1 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 1:

Find the gain or loss percent when:
(i) CP = Rs 620 and SP = Rs 713
(ii) CP = Rs 675 and SP = Rs 630
(iii) CP = Rs 345 and SP = Rs 372.60
(iv) CP = Rs 80 and SP = Rs 76.80

Answer 1:

$$\begin{gathered} \left(\mathrm{i}\right) \\ \mathrm{CP}=\mathrm{Rs}. 620 \\ \mathrm{SP}=\mathrm{Rs}. 713 \\ \mathrm{Since} \mathrm{SP}> \mathrm{CP}, \mathrm{there} \mathrm{is} \mathrm{a} \mathrm{gain}. \\ \mathrm{Gain} =713 - 620 = \mathrm{Rs}. 93 \\ \mathrm{Gain} \mathrm{percentage}=(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100)\% \\ =(\frac{93}{620}\times 100)\% \\ =15\% \end{gathered}$$

(ii)
$$\begin{gathered} \mathrm{CP}=\mathrm{Rs} 675 \\ \mathrm{SP}=\mathrm{Rs} 630 \\ \mathrm{Since} \mathrm{SP}< \mathrm{CP}, \mathrm{there} \mathrm{is} \mathrm{a} \mathrm{loss}. \\ \mathrm{Loss}=675 - 630 = \mathrm{Rs}. 45 \\ \mathrm{Loss} \mathrm{percentage} =(\frac{\mathrm{Loss}}{\mathrm{CP}}\times 100)\% \\ =(\frac{45}{675}\times 100)\% \\ =6\frac{2}{3}\% \end{gathered}$$

(iii)
$$\begin{gathered} \mathrm{CP}=\mathrm{Rs}. 345 \\ \mathrm{SP}=\mathrm{Rs}. 372.60 \\ \mathrm{Since} \mathrm{SP}> \mathrm{CP}, \mathrm{there} \mathrm{is} \mathrm{a} \mathrm{gain}. \\ \mathrm{Gain}=372.60 - 345 = \mathrm{Rs}. 27.6 \\ \mathrm{Gain} \mathrm{percentage}=(\frac{\mathrm{gain}}{\mathrm{CP}} \times 100)\% \\ =(\frac{27.6}{345}\times 100)\% \\ =\left(\frac{2760}{345}\right)\% \\ =8\% \end{gathered}$$

(iv)
$$\begin{gathered} \mathrm{CP}=\mathrm{Rs} 80 \\ \mathrm{SP}=\mathrm{Rs} 76.80 \\ \mathrm{Since} \mathrm{SP}< \mathrm{CP}, \mathrm{there} \mathrm{is} \mathrm{a} \mathrm{loss}. \\ \mathrm{Loss} =80 - 76.80 = \mathrm{Rs}. 3.2 \\ \mathrm{Loss} \mathrm{percentage}=(\frac{\mathrm{loss}}{\mathrm{CP}} \times 100)\% \\ =(\frac{3.2}{80}\times 100)\% \\ =(\frac{32}{80}\times 100)\% \\ =4\% \end{gathered}$$

Q2 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 2:

Find the selling price when:
(i) CP = Rs 1650 and gain% = 4%
(ii) CP = Rs 915 and gain% = $6\frac{2}{3}\%$
(iii) CP = Rs 875 and loss% = 12%
(iv) CP = Rs 645 and loss% = $13\frac{1}{3}\%$

Answer 2:

(i)
$$\begin{gathered} \mathrm{CP}=\mathrm{Rs}. 1650 \\ \mathrm{Gain} \mathrm{percentage}=4\% \\ \mathrm{SP}=\frac{(100+\mathrm{gain} \%)}{100}\times \mathrm{CP} \\ =\frac{(100+4)}{100}\times 1650 \\ =\frac{104\times 1650}{100} \\ =\mathrm{Rs}. 1716 \end{gathered}$$

(ii)
$$\begin{gathered} \mathrm{CP}=\mathrm{Rs}. 915 \\ \mathrm{Gain} \mathrm{percentage}=6\frac{2}{3}\%=\frac{20}{3}\% \\ \mathrm{SP}=\frac{(100+\mathrm{gain} \%)}{100}\times \mathrm{CP} \\ =\frac{(100+{\displaystyle \frac{20}{3}})}{100}\times 915 \\ =\frac{\left({\displaystyle \frac{320}{3}}\right)}{100}\times 915 \\ =\left(\frac{320}{3}\right)\times \left(\frac{1}{100}\right)\times 915 \\ =\mathrm{Rs}. 976 \end{gathered}$$

(iii)
$$\begin{gathered} \mathrm{CP}=\mathrm{Rs}. 875 \\ \mathrm{Loss} \mathrm{percentage}=12\% \\ \mathrm{SP}=\frac{(100-\mathrm{loss} \%)}{100}\times \mathrm{CP} \\ =\frac{(100-12)}{100}\times 875 \\ =\frac{77000}{100} \\ =\mathrm{Rs}. 770 \end{gathered}$$

(iv)

$$\begin{gathered} \mathrm{CP}=\mathrm{Rs}. 645 \\ \mathrm{Loss} \mathrm{percentage}=13\frac{1}{3}\%=\frac{40}{3}\% \\ \mathrm{SP}=\frac{(100-\mathrm{loss} \%)}{100}\times \mathrm{CP} \\ =\frac{(100-{\displaystyle \frac{40}{3}})}{100}\times 645 \\ =\frac{\left({\displaystyle \frac{300-40}{3}}\right)}{100}\times 645 \\ =\left(\frac{260}{3}\right)\times \left(\frac{1}{100}\right)\times 645 \\ =\mathrm{Rs}. 559 \end{gathered}$$

Q3 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 3:

Find the cost price when:
(i) SP = Rs 1596 and gain% = 12%
(ii) SP = Rs 2431 and loss% = $6\frac{1}{2}\%$
(iii) SP = Rs 657.60 and loss% = 4%
(iv) SP = Rs 34.40 and gain% = $7\frac{1}{2}\%$

Answer 3:

$$\begin{gathered} \left(\mathrm{i}\right) \\ \mathrm{SP}=\mathrm{Rs}. 1596 \\ \mathrm{Gain} \mathrm{percentage}=12\% \\ \mathrm{CP}=\frac{100}{(100+\mathrm{gain} \%)}\times \mathrm{SP} \\ =\frac{100}{(100+12)}\times 1596 \\ =\mathrm{Rs}. 1425 \end{gathered}$$

(ii)

$$\begin{gathered} \mathrm{SP}=\mathrm{Rs}. 2431 \\ \mathrm{Loss} \mathrm{percentage}=6\frac{1}{2}\%=\frac{13}{2}\% \\ \mathrm{CP}=\frac{100}{(100-\mathrm{loss} \%)}\times \mathrm{SP} \\ =\frac{100}{(100-{\displaystyle \frac{13}{2}})}\times 2431 \\ =\frac{100\times 2}{187}\times 2431 \\ =\mathrm{Rs}. 2600 \end{gathered}$$

(iii)
$$\begin{gathered} \mathrm{SP}=\mathrm{Rs}. 657.60 \\ \mathrm{Loss} \mathrm{percentage}=4\% \\ \mathrm{CP}=\frac{100}{(100-\mathrm{loss} \%)}\times \mathrm{SP} \\ =\frac{100}{(100-4)}\times 657.60 \\ =\mathrm{Rs}. 685 \end{gathered}$$

(iv)
$$\begin{gathered} \mathrm{SP}=\mathrm{Rs}. 34.40 \\ \mathrm{Gain} \mathrm{percentage}=7\frac{1}{2}\%=\frac{15}{2}\% \\ \mathrm{CP}=\frac{100}{(100+\mathrm{gain} \%)}\times \mathrm{SP} \\ =\frac{100}{(100+{\displaystyle \frac{15}{2}})}\times 34.40 \\ =\frac{100\times 2}{215}\times 34.40 \\ =\mathrm{Rs}. 32 \end{gathered}$$

Q4 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 4:

Manjit bought an iron safe for ₹ 12160 and paid ₹ 340 for its transportation. Then, he sold it for ₹ 12875. Find his gain per cent

Answer 4:

CP of the iron safe = ₹12,160
Money spent on transportation = ₹340
Total CP = ₹12,160 + ₹340 = ₹12,500
SP of the iron safe = ₹12,875
Profit = SP − CP = ₹12,875 − ₹12,500 = ₹375
∴ Profit% = $\frac{\mathrm{Profit}}{\mathrm{CP}}\times 100\%$$=\frac{375}{12500}\times 100\%=3\%$
 

Q5 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 5:

Robin purchased an old car for Rs 73500. He spent Rs 10300 on repairs and paid Rs 2600 for its insurance. Then he sold it to a mechanic for Rs 84240. What was his percentage gain or loss?

Answer 5:

$$\begin{gathered} \mathrm{CP} \mathrm{of} \mathrm{the} \mathrm{car}=\mathrm{Rs}. 73500 \\ \mathrm{Repairs}=\mathrm{Rs}. 10300 \\ \mathrm{Insurance}=\mathrm{Rs}. 2600 \\ \mathrm{Total} \mathrm{CP}=73500+10300+2600=\mathrm{Rs}.86400 \\ \mathrm{SP}=\mathrm{Rs}. 84240 \\ \mathrm{Since} \mathrm{SP}<\mathrm{CP}, \mathrm{Robin} \mathrm{has} \mathrm{a} \mathrm{loss}. \\ \mathrm{Loss}=86400-84240 \\ =\mathrm{Rs}. 2160 \\ \mathrm{Loss} \mathrm{percentage}=(\frac{\mathrm{loss}}{\mathrm{total} \mathrm{CP}}\times 100)\% \\ =(\frac{2160}{86400}\times 100)\% \\ =2\frac{1}{2}\% \end{gathered}$$

Q6 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 6:

Hari bought 20 kg of rice at ₹ 36 per kg and 25 kg of rice at ₹ 32 per kg. He mixed the two varieties and sold the mixture at ₹ 38 per kg. Find his gain per cent in the whole transaction.

Answer 6:

Total cost of rice of 1st variety = ₹36/kg × 20 kg = ₹720
Total cost of rice of 2nd variety = ₹32/kg × 25 kg = ₹800
Total cost of the two rice varieties = ₹720 + ₹800 = ₹1,520
Total quantity of the two rice varieties = 20 kg + 25 kg = 45 kg
Selling price of the mixture of two rice = ₹38/kg × 45 kg = ₹1,710
Gain = SP − CP = ₹1,710 − ₹1,520 = ₹190
Gain% = $\frac{\mathrm{Gain}}{\mathrm{CP}}\times 100\%=\frac{190}{1520}\times 100\%=12\frac{1}{2}\%$

Q7 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 7:

Coffee costing Rs 250 per kg was mixed with chicory costing Rs 75 per kg in the ratio 5 : 2 for a  certain blend. If the mixture was sold at Rs 230 per kg, find the gain or loss per cent.

Answer 7:

$$\begin{gathered} \mathrm{Let} 5 \mathrm{kg} \mathrm{of} \mathrm{coffee} \mathrm{be} \mathrm{mixed} \mathrm{with} 2 \mathrm{kg} \mathrm{of} \mathrm{chicory}. \\ \mathrm{CP} \mathrm{of} \mathrm{the} \mathrm{mixture}=\mathrm{Rs} (250\times 5+75\times 2) \\ =\mathrm{Rs} (1250+150) \\ =\mathrm{Rs}. 1400 \\ \mathrm{SP} \mathrm{of} \mathrm{the} \mathrm{mixture}=\mathrm{Rs} (7\times 230)=\mathrm{Rs}. 1610 \\ \mathrm{Since} \mathrm{SP}>\mathrm{CP}, \mathrm{there} \mathrm{is} \mathrm{a} \mathrm{gain}. \\ \mathrm{Now}, \mathrm{gain}=\mathrm{Rs} (1610-1400) \\ =\mathrm{Rs}. 210 \\ \mathrm{Gain} \mathrm{percentage}=(\frac{\mathrm{gain}}{\mathrm{total} \mathrm{CP}}\times 100)\% \\ =(\frac{210}{1400}\times 100)\% \\ =15\% \end{gathered}$$

Q8 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 8:

If the selling price of 16 water bottles is equal to the cost price of 17 water bottles, find the gain per cent earned by the dealer.

Answer 8:

$$\begin{gathered} \mathrm{Let} \mathrm{Rs} x \mathrm{be} \mathrm{the} \mathrm{SP} \mathrm{of} \mathrm{each} \mathrm{bottle} \mathrm{and} \mathrm{Rs} y \mathrm{be} \mathrm{the} \mathrm{CP} \mathrm{of} \mathrm{each} \mathrm{bottle}. \\ \mathrm{SP} \mathrm{of} 16 \mathrm{bottles} = \mathrm{CP} \mathrm{of} 17 \mathrm{bottles} \\ \Rightarrow 16\mathrm{x}=17\mathrm{y} \\ \Rightarrow \frac{\mathrm{x}}{\mathrm{y}}=\frac{17}{16} \\ \mathrm{Gain} \mathrm{per} \mathrm{bottle}=\mathrm{SP}-\mathrm{CP} \\ =\mathrm{Rs} (\mathrm{x}-\mathrm{y}) \\ \therefore \mathrm{Gain} \mathrm{percentage}=(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100)\% \\ =(\frac{\mathrm{x}-\mathrm{y}}{\mathrm{y}}\times 100)\% \\ =\left\{\right(\frac{\mathrm{x}}{\mathrm{y}}-1)\times 100\}\% \\ =\left\{\right(\frac{17}{16}-1)\times 100\}\% \\ =(\frac{1}{16}\times 100)\% \\ =6\frac{1}{4}\% \end{gathered}$$

Q9 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 9:

The cost price of 12 candles is equal to the selling price of 15 candles. Find the loss per cent.

Answer 9:

$$\begin{gathered} \mathrm{Let} \mathrm{Rs} x \mathrm{be} \mathrm{the} \mathrm{CP} \mathrm{of} \mathrm{one} \mathrm{candle} \mathrm{and} \mathrm{Rs}. y \mathrm{be} \mathrm{the} \mathrm{SP} \mathrm{of} \mathrm{one} \mathrm{candle}. \\ \mathrm{Now}, \mathrm{CP} \mathrm{of} 12 \mathrm{candles}=\mathrm{SP} \mathrm{of} 15 \mathrm{candles} \\ \Rightarrow 12x=15y \\ \Rightarrow \frac{y}{x}=\frac{12}{15} \\ \mathrm{Loss} = \mathrm{CP}-\mathrm{SP} \\ =\mathrm{Rs} (x-y) \\ \therefore \mathrm{Loss} \mathrm{percentage}=(\frac{\mathrm{loss}}{\mathrm{CP}}\times 100)\% \\ =\left\{\right(\frac{x-y}{x})\times 100\}\% \\ =\left\{\right(1-\frac{y}{x})\times 100\}\% \\ =\left\{\right(1-\frac{12}{15})\times 100\}\% \\ =(\frac{3}{15}\times 100)\% \\ =20\% \end{gathered}$$

Q10 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 10:

By selling 130 cassettes, a man gains an amount equal to the selling price of 5 cassettes. Find the gain per cent.

Answer 10:

It is given that,
Gain = SP of 5 cassettes                 .....(1)
Gain = SP of 130 cassettes − CP of 130 cassettes
⇒ SP of 5 cassettes = SP of 130 cassettes − CP of 130 cassettes               [From (1)]
⇒ CP of 130 cassettes = SP of 125 cassettes          .....(2)
Let the CP of 1 cassettte be ₹x.
∴ CP of 125 cassettes = ₹125x
CP of 130 cassettes = ₹130x
SP of 125 cassettes = CP of 130 cassettes                    [From (2)]
⇒ SP of 125 cassettes = ₹130x
Now, gain% $=\frac{\mathrm{SP}-\mathrm{CP}}{\mathrm{CP}}\times 100\%=\frac{\left(130x-125x\right)}{125x}\times 100\%$$=\frac{5x}{125x}\times 100\%=4\%$
Thus, the gain percent is 4%.  

Q11 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 11:

By selling 45 lemons, a vendor loses a sum equal to the selling price of 3 lemons. Find his loss per cent.

Answer 11:

$$\begin{gathered} \mathrm{Let} \mathrm{Rs} x \mathrm{be} \mathrm{the} \mathrm{SP} \mathrm{of} \mathrm{one} \mathrm{lemon}. \\ \mathrm{SP} \mathrm{of} 45 \mathrm{lemons}=\mathrm{Rs}. 45x \\ \mathrm{Loss}=\mathrm{SP} \mathrm{of} 3 \mathrm{lemons}=\mathrm{Rs}. 3x \\ \mathrm{But} \mathrm{loss}=\mathrm{CP}-\mathrm{SP} \\ \mathrm{CP}=\mathrm{loss}+\mathrm{SP} \\ =3x+45x \\ =\mathrm{Rs}. 48x \\ \therefore \mathrm{Loss} \mathrm{percentage}=(\frac{\mathrm{loss}}{\mathrm{CP}}\times 100)\% \\ =(\frac{3x}{48x}\times 100)\% \\ =6\frac{1}{4}\% \end{gathered}$$

Q12 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 12:

Oranges are bought at 6 for ₹ 20 and sold at 4 for ₹ 18. Find the gain or loss per cent.

Answer 12:

LCM of 6 and 4 = 12
Let the number of oranges bought be 12.
CP of 6 oranges = ₹20
So, CP of 1 orange = $\frac{20}{6}=₹\frac{10}{3}$
CP of 12 orange = $12\times \frac{10}{3}=₹40$
SP of 4 oranges = ₹18
SP of 1 orange = $\frac{18}{4}=₹\frac{9}{2}$
SP of 12 oranges = $12\times \frac{9}{2}=₹54$
Here, SP of 12 oranges > CP of 12 oranges.
Profit = SP − CP = ₹54 − ₹40 = ₹14
∴ Profit% = $\frac{\mathrm{Profit}}{\mathrm{CP}}\times 100\%=\frac{14}{40}\times 100\%=35\%$

Q13 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 13:

A vendor purchased bananas at ₹ 40 per dozen and sold them at 10 for ₹ 36. Find his gain or loss per cent.

Answer 13:

LCM of 12 and 10 = 60
Let the number of banana bought be 60.
CP of 12 banana = ₹40
∴ CP of 1 banana = $\frac{40}{12}=₹\frac{10}{3}$
⇒ CP of 60 bananas = $60\times \frac{10}{3}=₹200$
SP of 10 bananas = ₹36
∴ SP of 1 banana = $\frac{36}{10}=₹\frac{18}{5}$
⇒ SP of 60 bananas = $60\times \frac{18}{5}=₹216$
Here, SP of 60 bananas > CP of 60 bananas.
Profit = SP − CP = ₹216 − ₹200 = ₹16
∴ Profit% = $\frac{\mathrm{Profit}}{\mathrm{CP}}\times 100\%=\frac{16}{200}\times 100=8\%$

Q14 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 14:

A man bought apples at 10 for ₹ 75 and sold them at ₹ 75 per dozen. Find his loss per cent.

Answer 14:

LCM of 10 and 12 = 60
Let the number of apples bought be 60.
CP of 10 oranges = ₹75
∴ CP of 1 orange = $₹\frac{75}{10}$
⇒ CP of 60 orange = $60\times \frac{75}{10}=₹450$
SP of 12 oranges = ₹75
∴ SP of 1 orange = $₹\frac{75}{12}$
⇒ SP of 60 oranges = $60\times \frac{75}{12}=₹375$
Here, CP of 60 oranges > SP of 60 oranges.
Loss = CP − SP = ₹450 − ₹375 = ₹75
∴ Loss% = $\frac{\mathrm{Loss}}{\mathrm{CP}}\times 100\%=\frac{75}{450}\times 100\%=16\frac{2}{3}\%$

Q15 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 15:

A man purchased some eggs at 3 for ₹ 16 and sold them at 5 for ₹ 36. Thus, he gained ₹ 168 in all. How many eggs did he purchase?

Answer 15:

Let the number of eggs purchased be x.
CP of 3 eggs = ₹16
∴ CP of 1 egg = $₹\frac{16}{3}$
⇒ CP of x eggs = $₹\frac{16}{3}x$
SP of 5 eggs = ₹36
∴ SP of 1 egg = $₹\frac{36}{5}$
⇒ SP of x eggs = $₹\frac{36}{5}x$
Gain = SP − CP = ₹168
$$\begin{gathered} \therefore \frac{36}{5}x-\frac{16}{3}x=168 \\ \Rightarrow \frac{28}{15}x=168 \\ \Rightarrow x=\frac{168\times 15}{28} \\ \Rightarrow x=90 \end{gathered}$$
Hence, the man purchased 90 eggs.

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Q16 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 16:

A dealer sold a camera for Rs 1080 gaining $\frac{1}{8}$ of its cost price. Find (i) the cost price of the camera, and (ii) the gain per cent earned by the dealer.

Answer 16:

$$\begin{gathered} \mathrm{SP} \mathrm{of} \mathrm{the} \mathrm{camera}=\mathrm{Rs}. 1080 \\ \mathrm{Let} \mathrm{Rs} x \mathrm{be} \mathrm{the} \mathrm{CP}. \\ \mathrm{Gain}=\mathrm{Rs}. \frac{1}{8}x ...\left(\mathrm{i}\right) \\ \mathrm{Also}, \mathrm{gain}=\mathrm{SP}-\mathrm{CP} \\ =\mathrm{Rs}. (1080 -x) ...\left(\mathrm{ii}\right) \\ \mathrm{From} \left(\mathrm{i}\right) \mathrm{and} \left(\mathrm{ii}\right), \mathrm{we} \mathrm{have}: \\ \frac{1}{8}x=1080 -x \\ \Rightarrow x=8640-8x \\ \Rightarrow 9x=8640 \\ \Rightarrow \mathrm{x}=960 \\ \therefore \mathrm{CP}=\mathrm{Rs}. 960 \\ \mathrm{Now}, \mathrm{gain} =\frac{1}{8}\mathrm{x} \\ =\frac{960}{8} \\ =\mathrm{Rs}. 120 \\ \therefore \mathrm{Gain} \mathrm{percentage}=(\frac{120}{960}\times 100)\% \\ =12\frac{1}{2}\% \end{gathered}$$

Q17 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 17:

Meenakshi sells a pen for Rs 54 and loses $\frac{1}{10}$ of her outlay. Find (i) the cost price of the pen, and (ii) the loss per cent.

Answer 17:

$$\begin{gathered} \mathrm{SP} \mathrm{of} \mathrm{the} \mathrm{pen}=\mathrm{Rs}. 54 \\ \mathrm{Let} \mathrm{Rs} x \mathrm{be} \mathrm{the} \mathrm{CP} \mathrm{of} \mathrm{the} \mathrm{pen}. \\ \mathrm{Loss}=\mathrm{Rs}. \frac{x}{10} \\ \mathrm{SP}=\mathrm{CP}-\mathrm{Loss} \\ =x-\frac{x}{10} \\ =\mathrm{Rs}. \frac{9x}{10} \\ \mathrm{Now}, \mathrm{we} \mathrm{have}\frac{9\mathrm{x}}{10}=54 \\ \Rightarrow x=54\times \frac{10}{9} \\ \Rightarrow \mathrm{x}=60 \\ \therefore \mathrm{CP} \mathrm{of} \mathrm{the} \mathrm{pen}=\mathrm{Rs}. 60 \\ \mathrm{Now}, \mathrm{loss}=\frac{\mathrm{x}}{10} \\ =\frac{60}{10} \\ =\mathrm{Rs}. 6 \\ \therefore \mathrm{Loss} \mathrm{percentage}=(\frac{\mathrm{loss}}{\mathrm{CP}}\times 100)\% \\ =(\frac{6}{60}\times 100)\% \\ =10\% \end{gathered}$$

Q18 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 18:

A dealer gets ₹ 940 more if instead of selling a table at a loss of 10%, it is sold at a gain of 10%. Find the cost price of the table.

Answer 18:

Let the cost price be ₹x.
Loss = 10% of ₹x = $\frac{10}{100}x=₹\frac{x}{10}$
SP in case of loss = CP − Loss = $x-\frac{x}{10}=₹\frac{9x}{10}$
Gain =10% of ₹x = $\frac{10}{100}x=₹\frac{x}{10}$
SP in case of profit = CP + Profit = $x+\frac{x}{10}=₹\frac{11x}{10}$
It is given that dealer gets ₹940 more if sold at a profit of 10% instead of loss of 10%.
∴ SP in case of profit − SP in case of loss = ₹940
$$\begin{gathered} \Rightarrow \frac{11x}{10}-\frac{9x}{10}=940 \\ \Rightarrow \frac{2x}{10}=940 \\ \Rightarrow x=4700 \end{gathered}$$
Hence, the cost price of the table is ₹4,700.

Q19 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 19:

A dealer gets Rs 56 less if instead of selling a chair at a gain of 15%, it is sold at a gain of 8%. Find the cost price of the chair.

Answer 19:

$$\begin{gathered} \mathrm{Let} Rs x be the \mathrm{CP}. \\ {\mathrm{Gain}}_1 \mathrm{percentage}=\left(\frac{{\mathrm{gain}}_1}{\mathrm{CP}}\times 100\right)\% \\ \Rightarrow 15=\frac{{\mathrm{gain}}_1}{x}\times 100 \\ \Rightarrow {\mathrm{Gain}}_1=\mathrm{Rs} \frac{15x}{100} \\ \mathrm{Again}, {\mathrm{gain}}_2 \mathrm{percentage}=\left(\frac{{\mathrm{gain}}_2}{\mathrm{CP}}\times 100\right)\% \\ \Rightarrow 8=\frac{{\mathrm{gain}}_2}{x}\times 100 \\ \Rightarrow {\mathrm{Gain}}_2=\mathrm{Rs} \frac{8x}{100} \\ \mathrm{According} \mathrm{to} \mathrm{the} \mathrm{question}, \mathrm{we} \mathrm{have}: \\ {\mathrm{Gain}}_1-{\mathrm{gain}}_{ 2}= 56 \\ \Rightarrow \frac{15\mathrm{x}}{100} - \frac{8\mathrm{x}}{100}=56 \\ \Rightarrow \frac{7\mathrm{x}}{100}=56 \\ \Rightarrow 7x=5600 \\ \Rightarrow x=800 \\ \mathrm{Hence}, \mathrm{the} \mathrm{CP} \mathrm{of} \mathrm{the} \mathrm{chair} \mathrm{is} \mathrm{Rs} 800. \end{gathered}$$

Q20 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 20:

A cycle was sold at a gain of 10%. Had it been sold for ₹ 260 more, the gain would have been 14%. Find the cost price of the cycle.

Answer 20:

Let the CP be ₹x.
SP when gain is 10% = $x+\frac{10}{100}x=₹\frac{110}{100}x$
SP when gain is 14% = $x+\frac{14}{100}x=₹\frac{114}{100}x$
Difference in SP = SP when gain is 14% − SP when gain is 10% = ₹260
$$\begin{gathered} \therefore \frac{114x}{100}-\frac{110x}{100}=260 \\ \Rightarrow \frac{4x}{100}=260 \\ \Rightarrow x=6500 \end{gathered}$$
Hence, the CP of the cycle is ₹6,500.

Q21 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 21:

Sonu buys 40 kg of wheat at ₹ 12.50 per kg and 30 kg of wheat at ₹ 14 per kg. At what rate per kg should he sell the mixture to gain 5% on the whole?

Answer 21:

40 kg of wheat is bought for ₹12.50/kg.
∴ CP of 40 kg of wheat = 40 × 12.50 = ₹500
30 kg of wheat is bought for ₹14/kg.
∴ CP of 30 kg of wheat = 30 × 14 = ₹420
Total CP = ₹500 + ₹420 = ₹920
Profit = 5% of CP = 5% of ₹920 = $\frac{5}{100}\times 920=₹46$
Let the SP be ₹x.
Profit = SP − CP
⇒ x − 920 = 46
⇒ x = ₹966
SP of 70 kg wheat = ₹966
∴ SP of 1 kg wheat = $\frac{966}{70}=₹13.80$
Thus, the selling price of the mixture is ₹13.80/kg.

Q22 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 22:

Wasim bought two cricket bats for ₹ 840 and ₹ 360 respectively. He sells the first bat at a gain of 15% and the second one at a loss of 5%. Find his gain or loss per cent in the whole transaction.

Answer 22:

CP of the first bat = ₹840
Profit% on the first bat = 15%
∴ Profit = 15% of ₹840 = $\frac{15}{100}\times 840=₹126$
SP of the first bat = ₹840 + ₹126 = ₹966
CP of the second bat = ₹360
Loss = 5% of ₹360 = $\frac{5}{100}\times 360=₹18$
SP of the second bat = ₹360 − ₹18 = ₹342
Total CP of two bats = CP of first bat + CP of second bat = ₹840 + ₹360 = ₹1,200
Total SP of two bats = SP of first bat + SP of second bat = ₹966 + ₹342 = ₹1,308
Here, Total SP of two bats > Total CP of two bats.
Gain = Total SP of two bats − Total CP of two bats = ₹1,308 − ₹1,200 = ₹108
∴ Gain% in the whole transaction$=\frac{\mathrm{Gain}}{\mathrm{Total} \mathrm{CP} \mathrm{of} \mathrm{two} \mathrm{bats}}\times 100\%$$=\frac{108}{1200}\times 100=9\%$

Q23 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 23:

Hema bought two pairs of jeans for ₹ 1450 each. She sold one of them at a gain of 8% and the other at a loss of 4%. Find her gain or loss per cent in the whole transaction.

Answer 23:

CP of first jeans = ₹1,450
Profit = 8% of CP = $\frac{8}{100}\times 1450=₹116$
SP of first jeans = ₹1,450 + ₹116 = ₹1,566
CP of second jeans = ₹1,450
Loss = 4% of CP = $\frac{4}{100}\times 1450=₹58$
SP of second jeans = ₹1450 − ₹58 = ₹1,392
Total CP of two jeans = CP of first jeans + CP of second jeans = ₹1,450 + ₹1,450 = ₹2,900
Total SP of two jeans = SP of first jeans + SP of second jeans = ₹1,566 + ₹1,392 = ₹2,958
Here, Total SP of two jeans > Total CP of two jeans.
Gain = Total SP of two jeans − Total CP of two jeans = ₹2,958 − ₹2,900 = ₹58
∴ Gain% = $\frac{\mathrm{Gain}}{\mathrm{Total} \mathrm{CP} \mathrm{of} \mathrm{two} \mathrm{jeans}}\times 100\%=\frac{58}{2900}\times 100\%=2\%$

Q24 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 24:

A grocer purchased 200 kg of rice at Rs 25 per kg. He sold 80 kg of it at a gain of 10% and 40 kg at a loss of 4%. At what rate per kg should he sell the remainder to gain 8% on his total investment?

Answer 24:

CP of 1 kg of rice = Rs 25
C.P of 200 kg rice= $\mathrm{Rs} (200\times 25)=\mathrm{Rs} 5000$
CP of 80 kg of rice=$\mathrm{Rs} (25\times 80)=\mathrm{Rs} 2000$

CP of 40 kg of rice =$\mathrm{Rs} (25\times 40)=\mathrm{Rs} 1000$
 
$$\begin{gathered} \mathrm{SP} \mathrm{of} 80 \mathrm{kg} \mathrm{of} \mathrm{rice} = \frac{100+\mathrm{gain}\%}{100}\times \mathrm{CP} \\ =\mathrm{Rs} \frac{110}{100}\times 2000 \\ =\mathrm{Rs} 2200 \end{gathered}$$

$$\begin{gathered} \mathrm{SP} \mathrm{of} 40 \mathrm{kg} \mathrm{rice}=\frac{100-\mathrm{loss}\%}{100}\times \mathrm{CP} \\ =\mathrm{Rs} \frac{96}{100}\times 1000 \\ =\mathrm{Rs} 960 \end{gathered}$$

 $$\begin{gathered} \mathrm{SP} \mathrm{of} 200 \mathrm{kg} \mathrm{rice}=\frac{100+\mathrm{gain}\%}{100}\times \mathrm{CP} \\ =\mathrm{Rs} \frac{108}{100}\times 5000 \\ =\mathrm{Rs} 5400 \end{gathered}$$

Remaining quantity of rice = (200 − 80 + 40) kg = 80 kg

​SP of the remaining rice (80 kg) = Rs (5400 − 2200 − 960)
                                                        = Rs 2240

$\therefore \mathrm{Rate} \mathrm{per} \mathrm{kg} = \mathrm{Rs} \frac{2240}{80}= \mathrm{Rs} 28$

Q25 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 25:

If the selling price of a TV set is equal to $\frac{6}{5}$ of its cost price, find the gain per cent.

Answer 25:

Let the CP of the TV set be ₹x.
SP of the TV set = $\frac{6}{5}\mathrm{CP}=₹\frac{6}{5}x$
Gain = SP of the TV set − CP of the TV set = $\frac{6}{5}x-x=₹\frac{x}{5}$
Gain% = $\frac{\mathrm{Gain}}{\mathrm{CP}}\times 100\%=\frac{{\displaystyle \frac{x}{5}}}{x}\times 100\%=\frac{100}{5}\%=20\%$

Q26 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 26:

If the selling price of a flower vase is $\frac{5}{6}$ of its cost price, find the loss per cent.

Answer 26:

Let the CP of the flower vase set be ₹x.
SP of the flower vase = $\frac{5}{6}\mathrm{CP}=₹\frac{5}{6}x$
Loss = CP − SP = $x-\frac{5}{6}x=₹\frac{x}{6}$
Loss% = $\frac{\mathrm{Loss}}{\mathrm{CP}}\times 100\%=\frac{{\displaystyle \frac{x}{6}}}{x}\times 100\%=\frac{100}{6}\%=\frac{50}{3}\%=16\frac{2}{3}\%$

Q27 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 27:

By selling a bouquet for Rs 322, a florist gains 15%. At what price should he sell it to gain 25%?

Answer 27:

SP of the bouquet = Rs 322
Gain percentage = 15%
$$\begin{gathered} \mathrm{CP} \mathrm{of} \mathrm{the} \mathrm{bouquet} =\left(\frac{100}{100+\mathrm{gain}\%}\right)\times \mathrm{SP} \\ =\mathrm{Rs} \left(\frac{100}{100+15}\right)\times 322 \\ =\mathrm{Rs} \frac{100}{115}\times 322 \\ =\mathrm{Rs} 280 \end{gathered}$$

Now, CP = Rs 128 and desired gain percentage = 25%

$$\begin{gathered} \therefore \mathrm{Desired} \mathrm{S}\mathrm{P}=\left(\frac{100+\mathrm{gain}\%}{100}\right)\times \mathrm{CP} \\ =\mathrm{Rs} \frac{125}{100}\times 280 \\ =\mathrm{Rs} 350 \end{gathered}$$

​Hence, the selling price to obtain the desired gain must be Rs 350.

Q28 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 28:

By selling an umbrella for ₹ 336, a shopkeeper loses 4%. At what price must he sell it to gain 4%?

Answer 28:

Let the CP of the umbrella be ₹x.
SP of the umbrella = ₹336
Loss = 4% of ₹x = $₹\frac{4}{100}x$
CP − Loss = SP
$$\begin{gathered} \Rightarrow x-\frac{4}{100}x=336 \\ \Rightarrow \frac{96}{100}x=336 \\ \Rightarrow x=₹350 \end{gathered}$$
∴ CP of the umbrella = ₹350
Now, for gain of 4%,
SP = CP + Gain
$$\begin{gathered} \Rightarrow \mathrm{SP}=350+\frac{4}{100}\times 350 \\ \Rightarrow \mathrm{SP}=350+14 \\ \Rightarrow \mathrm{SP}=₹364 \end{gathered}$$
Hence, in order to gain 4%, the umbrella should be sold for ₹364.

Q29 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 29:

A radio is sold for Rs 3120 at a loss of 4%. What will be the gain or loss per cent if it is sold for Rs 3445?

Answer 29:

Let the original price be $x$.
SP = Rs 3120
Now, SP = CP − loss
​$$\begin{gathered} \Rightarrow 3120=x-\frac{4}{{\displaystyle \frac{100}{x}}} \\ \Rightarrow 3120=x-\frac{x}{25} \\ \Rightarrow 3120=\frac{24x}{25} \\ \Rightarrow \frac{3120\times 25}{24}=x \\ \Rightarrow x=3250 \end{gathered}$$

So, the cost price is Rs 3250.

If it is sold for Rs 3445, then its a gain because SP > CP.
Now, gain = SP − CP
= Rs (3445 − 3250)
= Rs 195
$$\begin{gathered} \therefore Gain percentage=\left(\frac{gain}{CP}\times 100\right)\% \\ =\left(\frac{195}{3250}\times 100\right)\% \\ =6\% \end{gathered}$$

Hence, gain percent = 6%

Q30 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 30:

Luxmi sold two sarees for ₹ 1980 each. On one, she lost 10%, while on the other she gained 10%. Find her gain or loss per cent in the whole transaction.

Answer 30:

SP of first saree = ₹1,980
Loss = 10%
Let the CP of first saree be ₹x.
CP = Loss + SP
$$\begin{gathered} \Rightarrow \frac{10}{100}\times x+1980=x \\ \Rightarrow x-\frac{{\displaystyle 10}}{{\displaystyle 100}}x=1980 \\ \Rightarrow \frac{90}{100}x=1980 \\ \Rightarrow x=2200 \end{gathered}$$
∴ CP of first saree = ₹2,200
SP of second saree = ₹1,980
Gain = 10%
Let the CP of second saree be ₹y.
CP = SP − Gain
$$\begin{gathered} \Rightarrow 1980-\frac{10}{100}\times y=y \\ \Rightarrow 1980-\frac{y}{10}=y \\ \Rightarrow y+\frac{y}{10}=1980 \\ \Rightarrow \frac{11y}{10}=1980 \\ \Rightarrow y=1800 \end{gathered}$$
∴ CP of second saree = ₹1,800
Total CP of two sarees = CP of first saree + CP of second saree = ₹2,200 + ₹1,800 = ₹4,000
Total SP of two sarees = SP of first saree + SP of second saree = ₹1,980 + ₹1,980 = ₹3,960
Here, Total CP of two sarees > Total SP of two sarees
Loss = Total CP of two sarees − Total SP of two sarees = ₹4,000 − ₹3,960 = ₹40
∴ Loss% in the whole transaction$=\frac{\mathrm{Loss}}{\mathrm{Total} \mathrm{CP} \mathrm{of} \mathrm{two} \mathrm{sarees}}\times 100\%=\frac{40}{4000}\times 100\%=1\%$

Q31 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 31:

A shopkeeper sold two fans for ​₹ 1140 each. On one he gains 14%, while on the other he loses 5%. Calculate his gain or loss per cent in the whole transaction.

Answer 31:

SP of first fan = ₹1,140
Gain = 14%
Let the CP of first fan be ₹x.
CP = SP − Gain
$$\begin{gathered} \Rightarrow x=1140-\frac{14}{100}x \\ \Rightarrow x+\frac{14}{100}x=1140 \\ \Rightarrow \frac{114}{100}x=1140 \\ \Rightarrow x=1000 \end{gathered}$$
∴ CP of first fan = ₹1,000
SP of second fan = ₹1,140
Loss = 5%
Let the CP of second fan be ₹y.
CP = Loss + SP
$$\begin{gathered} \Rightarrow y=\frac{5}{100}y+1140 \\ \Rightarrow y-\frac{5}{100}y=1140 \\ \Rightarrow \frac{95}{100}y=1140 \\ \Rightarrow y=1200 \end{gathered}$$
∴ CP of second fan = ₹1,200
Total CP of two fans = CP of first fan + CP of second fan = ₹1,000 + ₹1,200 = ₹2,200
Total SP of two fans = SP of first fan + SP of second fan = ₹1,140 + ₹1,140 = ₹2,280
Here, Total SP of two fans > Total CP of two fans
Gain = Total SP of two fans − Total CP of two fans = ₹2,280 − ₹2,200 = ₹80
∴ Gain% on whole transaction$=\frac{\mathrm{Gain}}{\mathrm{Total} \mathrm{CP} \mathrm{of} \mathrm{two} \mathrm{fans}}\times 100\%=\frac{80}{2200}\times 100\%=3.64\%$

Q32 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 32:

Vinod sold a watch to Arun at a gain of 12% and Arun had to sell it to Manoj at a loss of 5%. If manoj paid ₹ 3990 for it, how much did vinod pay for the watch?

Answer 32:

Let the CP of the watch for Vinod be ₹x.
SP = Gain + CP
$$\begin{gathered} =12\% \mathrm{of} \mathrm{CP}+x \\ =\frac{12}{100}x+x \\ =₹\frac{112}{100}x \end{gathered}$$
Now,
SP of the water for Vinod will be the CP of the watch for Arun.
SP of the watch for Arun
= CP − Loss
$$\begin{gathered} =\frac{112}{100}x-5\% \mathrm{of} \frac{112}{100}x \\ =\frac{112}{100}x-\frac{5}{100}\left(\frac{112}{100}x\right) \\ =\frac{112}{100}x\left(1-\frac{5}{100}\right) \\ =₹\frac{112}{100}x\left(\frac{95}{100}\right) \end{gathered}$$
SP of the watch for Arun will be the CP of the watch for Manoj.
But, CP of the watch for Manoj = ₹3,990
So,
$\frac{112}{100}x\left(\frac{95}{100}\right)=3990$
$\Rightarrow x=\frac{3990\times 100\times 100}{112\times 95}=3750$
Thus, Vinod paid ₹3,750 for the watch.

Q33 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 33:

Ahmed buys a plot of land for ₹ 480000. He sells $\frac{2}{5}$ of it at a loss of 6%. At what gain per cent should he sell the remaining part of the plot to gain 10% on the whole?

Answer 33:

CP of the plot of land = ₹4,80,000
CP of $\frac{2}{5}$th of the land = $\frac{2}{5}\times 480000=₹1,92,000$
Loss on $\frac{2}{5}$th of the land = 6%
SP of $\frac{2}{5}$th of the land = CP − Loss
$$\begin{gathered} =192000-\frac{6}{100}\times 192000 \\ =₹1,80,480 \end{gathered}$$
CP of $\frac{3}{5}$th of the land = 480000 − 192000 = ₹2,88,000
Total gain% = 10%
Total gain = $\frac{10}{100}\times 480000=₹48,000$
Total SP = CP + Gain = ₹4,80,000 + ₹48,000 = ₹5,28,000
SP of $\frac{3}{5}$th of the land = ₹5,28,000 − ₹1,80,480 = ₹3,47,520
Gain on $\frac{3}{5}$th of the land = SP of $\frac{3}{5}$th land − CP of $\frac{3}{5}$th land
= ₹3,47,520 − ₹2,88,000
= ₹59,520
Gain% on seling the remaining part of the plot = $\frac{\mathrm{Gain}}{\mathrm{CP} \mathrm{of} {\displaystyle \frac{3}{5}}\mathrm{th} \mathrm{land}}\times 100\%=\frac{59520}{288000}\times 100\%=20\frac{2}{3}\%$

Q34 | Ex-10A | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 34:

A grocer bought sugar worth Rs 4500. He sold one-third of it at a gain of 10%. At what gain per cent must the remaining sugar be sold to have a gain of 12% on the whole?

Answer 34:

CP of sugar = Rs 4500
Profit on one-third of the sugar = 10%

CP of one-third of the sugar = Rs $\frac{4500}{3}=\mathrm{Rs}. 1500$

 $$\begin{gathered} \mathrm{SP} \mathrm{of} \mathrm{one}-\mathrm{third} \mathrm{of} \mathrm{the} \mathrm{sugar} =\frac{100+\mathrm{gain}\%}{100}\times \mathrm{CP} \\ =\mathrm{Rs} \frac{110}{100}\times 1500 \\ =\mathrm{Rs} 1650 \end{gathered}$$

Now, profit= Rs (1650 − 1500) = Rs 150

At a profit of 12%, we have:
$$\begin{gathered} \mathrm{SP} \mathrm{of} \mathrm{sugar} =\frac{100+\mathrm{gain}\%}{100}\times \mathrm{CP} \\ =\mathrm{Rs} \frac{112}{100}\times 4500 \\ =\mathrm{Rs} 5040 \end{gathered}$$

∴ Gain= Rs (5040 − 4500) = Rs 5400

Profit on the remaining amount of sugar = Rs (540 − 150) = Rs 390
CP of the remaining sugar = Rs (4500 − 1500) = Rs 3000

 $$\begin{gathered} \mathrm{Gain} \mathrm{percentage}=\left(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100\right)\% \\ =\left(\frac{390}{3000}\times 100\right)\% \\ =13\% \end{gathered}$$

Therefore, the profit on the remaining amount of sugar is 13%.