RS Aggarwal solution class 8 chapter 10 Profit and Loss Test Paper 10

Test Paper 10

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Q1 | Test Paper 10 | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss

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Question 1:

By selling a flower pot for Rs 322, a man gains 15%. At what price should he sell it to gain 20%?

Answer 1:

$$\begin{gathered} \mathrm{SP}=\mathrm{Rs} 322 \\ \mathrm{Gain} \mathrm{percentage}=15\% \\ \therefore \mathrm{CP}=\left\{\frac{100}{\left(100+\mathrm{gain}\%\right)}\times \mathrm{SP}\right\} \end{gathered}$$
       $$\begin{gathered} =\mathrm{Rs}.\left\{\frac{100}{\left(100+15\right)}\times 322\right\} \\ =\mathrm{Rs}.\left(\frac{100}{115}\times 322\right) \\ =\mathrm{Rs}.280 \end{gathered}$$
$\mathrm{Now}, \mathrm{desired} \mathrm{SP}=\left\{\frac{\left(100+\mathrm{gain}\%\right)}{100}\times \mathrm{CP}\right\}$
                     $$\begin{gathered} =\mathrm{Rs}.\left\{\frac{\left(100+20\right)}{100}\times 280\right\} \\ =\mathrm{Rs}.\left(\frac{120}{100}\times 280\right) \\ =\mathrm{Rs}.336 \end{gathered}$$

∴ The desired selling price is Rs 336.

Q2 | Test Paper 10 | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss

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Question 2:

If the cost price of 12 pens is equal to the selling price of 16 pens, find the loss per cent.

Answer 2:

$$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{CP} \mathrm{of} \mathrm{each} \mathrm{pen} \mathrm{be} \mathrm{Rs} x. \\ \mathrm{CP} \mathrm{of} 16 \mathrm{pens}=\mathrm{Rs} 16x \\ \mathrm{SP} \mathrm{of} 16 \mathrm{pens}=\mathrm{CP} \mathrm{of} 12 \mathrm{pens}=\mathrm{Rs} 12x \\ \mathrm{i}.\mathrm{e}., \mathrm{CP}>\mathrm{SP} \\ \mathrm{Now}, \mathrm{loss}=\mathrm{CP}-\mathrm{SP} \\ =(16x-12x) \\ =Rs.4x \\ \therefore \mathrm{Loss} \mathrm{percentage}=\frac{\mathrm{loss}}{\mathrm{CP}}\times 100 \\ =\frac{4x}{16x}\times 100 \\ =25\% \end{gathered}$$
                        

Q3 | Test Paper 10 | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss

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Question 3:

A dealer gets Rs 30 less if instead of selling a chair at a gain of 12% he sells it at a gain of 8%. Find the cost price of the chair.

Answer 3:

​$$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{CP} \mathrm{be} \mathrm{Rs} x. \\ \mathrm{Then}, \mathrm{we} \mathrm{have}: \\ \left(12\% \mathrm{of} \mathrm{x}\right)-\left(8\% \mathrm{of} \mathrm{x}\right)=30 \\ \Rightarrow \left(\mathrm{x}\times \frac{12}{100}\right)-\left(\mathrm{x}\times \frac{8}{100}\right)=30 \\ \Rightarrow \left(\frac{12\mathrm{x}}{100}-\frac{8x}{100}\right)=30 \\ \Rightarrow \frac{4x}{100}=30 \\ \Rightarrow x=\left(30\times \frac{100}{4}\right) \\ =750 \end{gathered}$$
$\therefore \mathrm{The} \mathrm{cost} \mathrm{price} \mathrm{of} \mathrm{the} \mathrm{chair} \mathrm{is} \mathrm{Rs} 750.$

Q4 | Test Paper 10 | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss

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Question 4:

A trader marks his goods at 30% above cost price and allows a discount of 10%. What is his gain per cent?

Answer 4:

$$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{CP} \mathrm{be} \mathrm{Rs} 100. \\ \mathrm{Then}, \mathrm{marked} \mathrm{price}=\mathrm{Rs} 130 \\ \mathrm{Discount}=10\% \mathrm{of} \mathrm{MP} \end{gathered}$$
           
             $$\begin{gathered} =\left(10\% \mathrm{of} \mathrm{Rs}.130\right) \\ =\mathrm{Rs}.\left(130\times \frac{10}{100}\right) \\ =\mathrm{Rs}.13 \end{gathered}$$

$$\begin{gathered} \mathrm{Now}, \mathrm{SP}=\left(\mathrm{MP}\right)-\left(\mathrm{discount}\right) \\ =\mathrm{Rs}.\left(130-13\right) \\ =\mathrm{Rs}.117 \\ \therefore \mathrm{Gain} \mathrm{percentage}=\left(117-100\right)\% \\ =17\% \end{gathered}$$
$\therefore \mathrm{The} \mathrm{gain} \mathrm{percentage} \mathrm{of} \mathrm{the} \mathrm{trader} \mathrm{is} 17\%.$

Q5 | Test Paper 10 | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss

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Question 5:

Find the single discount equivalent to two successive discounts of 20% and 10%.

Answer 5:

$$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{marked} \mathrm{price} \mathrm{be} \mathrm{Rs} 100. \\ \mathrm{Then}, \mathrm{first} \mathrm{discount} \mathrm{on} \mathrm{it} =\mathrm{Rs} 20 \\ \mathrm{Price} \mathrm{after} \mathrm{the} \mathrm{first} \mathrm{discount}=\mathrm{Rs} \left(100-20\right) \end{gathered}$$
                                          $=Rs.80$
$\mathrm{Second} \mathrm{discount} \mathrm{on} \mathrm{it}=10\% \mathrm{of} \mathrm{Rs} 80$
                             $$\begin{gathered} =\mathrm{Rs} \left(80\times \frac{10}{100}\right) \\ =\mathrm{Rs} 8 \end{gathered}$$

$\mathrm{Price} \mathrm{after} \mathrm{the} \mathrm{second} \mathrm{discount}=\mathrm{Rs}.\left(80-8\right)$
                                             $=\mathrm{Rs}.72$
$$\begin{gathered} \mathrm{Net} \mathrm{selling} \mathrm{price}=\mathrm{Rs}.72 \\ \mathrm{Single} \mathrm{discount} \mathrm{equivalent} \mathrm{to} \mathrm{given} \mathrm{successive} \mathrm{discounts}=\left(100-72\right)\% \end{gathered}$$
                                                                             $=28\%$
$\therefore \mathrm{The} \mathrm{single} \mathrm{discount} \mathrm{equivalent} \mathrm{to} \mathrm{given} \mathrm{successive} \mathrm{discounts} \mathrm{is} 28\%.$

Q6 | Test Paper 10 | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss

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Question 6:

Rajan bought a watch for Rs 1870 including VAT at 10%. Find the original price of the watch.

Answer 6:

​      $$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{original} \mathrm{price} \mathrm{be} \mathrm{Rs} x. \\ \mathrm{VAT}=10\% \mathrm{of} \mathrm{Rs} x \\ =\mathrm{Rs} \left(\mathrm{x}\times \frac{10}{100}\right) \\ =\mathrm{Rs} \frac{\mathrm{x}}{10} \\ \therefore \mathrm{Price} \mathrm{including} \mathrm{VAT}=\mathrm{Rs} \left(\mathrm{x}+\frac{\mathrm{x}}{10}\right) \end{gathered}$$
                                      $=\mathrm{Rs}.\frac{11x}{10}$
      $\therefore \frac{11x}{10}=1870$
      $$\begin{gathered} \Rightarrow x=\left(1870\times \frac{10}{11}\right) \\ \Rightarrow x=1700 \end{gathered}$$
     $\therefore \mathrm{The} \mathrm{original} \mathrm{price} \mathrm{of} \mathrm{the} \mathrm{watch} \mathrm{is} \mathrm{Rs} 1,700.$

Q7 | Test Paper 10 | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss

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Question 7:

Mark (✓) against the correct answer:
On selling 100 pens, a man gains the selling price of 20 pens. The gain per cent is
(a) 20%
(b) 25%
(c) $16\frac{2}{3}\%$
(d) 15%

Answer 7:

(b) 25%
​  
    $$\begin{gathered} \mathrm{Let} \mathrm{Rs} x \mathrm{be} \mathrm{the} \mathrm{SP} \mathrm{of} 100 \mathrm{pen}s. \\ \mathrm{SP} \mathrm{of} 1 \mathrm{pen}=\mathrm{Rs} \frac{\mathrm{x}}{100} \\ \mathrm{Profit} \mathrm{on} 100 \mathrm{pen}s =\mathrm{selling} \mathrm{price} \mathrm{of} 20 \mathrm{pens} \\ =\frac{20}{100}\times x \\ =\frac{\mathrm{x}}{5} \\ \mathrm{Now}, \mathrm{CP}=\mathrm{SP}-\mathrm{Profit} \\ =x-\frac{\mathrm{x}}{5} \\ =\frac{4\mathrm{x}}{5} \\ \therefore \mathrm{Profit} \mathrm{percent} \mathrm{on} 100 \mathrm{pens}=\frac{\mathrm{profit}}{\mathrm{CP}}\times 100 \\ =\frac{\frac{\mathrm{x}}{5}}{\frac{4\mathrm{x}}{5}}\times 100 \\ =25\% \end{gathered}$$
                 

Q8 | Test Paper 10 | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss

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Question 8:

Mark (✓) against the correct answer:
A man sells a bat for Rs 100 gaining Rs 20. His gain per cent is
(a) 20%
(b) 22%
(c) 18%
(d) 25%

Answer 8:

(d) 25%

$$\begin{gathered} \mathrm{SP}=\mathrm{Rs} 100 \\ \mathrm{Gain}=\mathrm{Rs} 20 \\ \mathrm{CP}=\mathrm{Rs} \left(100-20\right) \\ =\mathrm{Rs} 80 \\ \mathrm{Gain} \mathrm{percentage}=\left(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100\right)\% \\ =\left(\frac{20}{80}\times 100\right)\% \\ =25\% \end{gathered}$$

Q9 | Test Paper 10 | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss

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Question 9:

Mark (✓) against the correct answer:
The selling price of an article is $\frac{6}{5}$ of the cost price. The gain per cent is
(a) 15%
(b) 20%
(c) 25%
(d) 30%

Answer 9:

(b) 20%

​ $$\begin{gathered} \mathrm{Let} x \mathrm{be} \mathrm{the} \mathrm{CP} \mathrm{of} \mathrm{the} \mathrm{article}. \\ \mathrm{Then}, \mathrm{SP} \mathrm{of} \mathrm{the} \mathrm{article}=\frac{6}{5}x \\ \mathrm{Now}, \mathrm{gain}=\left(\mathrm{SP}-\mathrm{CP}\right) \\ =\left(\frac{6}{5}\mathrm{x}-\mathrm{x}\right) \\ =\frac{\mathrm{x}}{5} \\ \therefore \mathrm{Gain} \mathrm{percentage}=\left(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100\right)\% \\ =\left(\frac{{\displaystyle \frac{\mathrm{x}}{5}}}{\mathrm{x}}\times 100\right)\% \\ =\left(\left(\frac{\mathrm{x}}{5}\times \frac{1}{\mathrm{x}}\right)\times 100\right)\% \\ =20\% \end{gathered}$$

Q10 | Test Paper 10 | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss

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Question 10:

Mark (✓) against the correct answer:
On selling a chair for Rs 680, a man loses 15%. To gain 15%, it must be sold for
(a) Rs 800
(b) Rs 860
(c) Rs 920
(d) Rs 884

Answer 10:

(c) Rs.920    

 $$\begin{gathered} \mathrm{SP}=\mathrm{Rs} 680 \\ \mathrm{Loss} \mathrm{percentage}=15\% \\ \mathrm{Now}, \mathrm{CP}=\left\{\frac{100}{\left(100-\mathrm{loss}\%\right)}\times \mathrm{SP}\right\} \end{gathered}$$
          $$\begin{gathered} =\mathrm{Rs}.\left\{\frac{100}{\left(100-15\right)}\times 680\right\} \\ =\mathrm{Rs}.\left(\frac{100}{85}\times 680\right) \\ =\mathrm{Rs}.800 \end{gathered}$$
$\therefore \mathrm{Desired} \mathrm{SP}=\left\{\frac{\left(100+\mathrm{gain}\%\right)}{100}\times \mathrm{CP}\right\}$
                  $$\begin{gathered} =\mathrm{Rs} \left\{\frac{\left(100+15\right)}{100}\times 800\right\} \\ =\mathrm{Rs} \left(\frac{115}{100}\times 800\right) \\ =\mathrm{Rs} 920 \end{gathered}$$

Q11 | Test Paper 10 | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss

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Question 11:

Mark (✓) against the correct answer:
A dealer lists his goods at 20% above cost price and allows a discount of 10%. His gain per cent is
(a) 10%
(b) 9%
(c) 8%
(d) 12%

Answer 11:

​(c) 8%  

$$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{CP} \mathrm{be} \mathrm{Rs} 100. \\ \mathrm{Then}, \mathrm{marked} \mathrm{price}=\mathrm{Rs} 120 \\ \mathrm{Discount}=10\% \mathrm{of} \mathrm{MP} \end{gathered}$$

             $$\begin{gathered} =\left(10\% of \mathrm{Rs}.120\right) \\ =\mathrm{Rs}.\left(120\times \frac{10}{100}\right) \\ =\mathrm{Rs}.12 \end{gathered}$$

$$\begin{gathered} \mathrm{Now}, \mathrm{SP}=\left(\mathrm{MP}\right)-\left(\mathrm{discount}\right) \\ =\mathrm{Rs} \left(120-12\right) \\ =\mathrm{Rs} 108 \\ \therefore \mathrm{Gain} \mathrm{percentage}=\left(108-100\right)\% \\ =8\% \end{gathered}$$

Q12 | Test Paper 10 | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss

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Question 12:

Mark (✓) against the correct answer:
The price of a watch including 8% VAT is Rs 810. What is its basic price?
(a) Rs 675
(b) Rs 729
(c) Rs 750
(d) Rs 745

Answer 12:

​(c) Rs.750  

 $$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{original} \mathrm{price} \mathrm{be} \mathrm{Rs} x. \\ \mathrm{VAT}=8\% \mathrm{of} \mathrm{Rs} x \\ =\mathrm{Rs} \left(x\times \frac{8}{100}\right) \\ =\mathrm{Rs} \frac{8x}{100} \\ \therefore \mathrm{Price} \mathrm{including} \mathrm{VAT}=\mathrm{Rs} \left(x+\frac{8x}{100}\right) \end{gathered}$$
                                             $=Rs.\frac{108x}{100}$
$\mathrm{Now}, \frac{108x}{10}=810$
          $$\begin{gathered} \Rightarrow x=\left(810\times \frac{100}{108}\right) \\ \Rightarrow x=750 \end{gathered}$$
     

Q13 | Test Paper 10 | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss

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Question 13:

Fill in the blanks.
(i) The discount is reckoned on the ......... price.
(ii) Gain or loss is always reckoned on the .........
(iii) SP = (Marked price) − (.........)
(iv) VAT is charged on the ......... of the article.

Answer 13:

​(i) The discount is reckoned on the marked price.
(ii) Gain or loss is always reckoned on the cost price.
(iii) SP = (Marked price) − (Discount).
(iv) VAT is charged on the selling price of the article.

Q14 | Test Paper 10 | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss

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Question 14:

Write 'T' for true and 'F' for false for each of the following:
(i) SP = $\frac{(100+\mathrm{loss}\%)}{100}\times \mathrm{CP}.$
(ii) CP = $\frac{100}{(100+\mathrm{gain}\%)}\times \mathrm{SP}.$
(iii) Gain is reckoned on the selling price.
(iv) The discount is allowed on the marked price.

Answer 14:

​(i) False (F)

$\mathrm{SP}=\left\{\frac{\left(100-\mathrm{loss}\%\right)}{100}\times \mathrm{CP}\right\}$


(ii) True (T)

(iii) False (F)
Gain is reckoned on the cost price.

(iv) True (T)