RD Sharma solution class 8 chapter 13 Profit ,Discount and Value Added Tax(VAT) Exercise 13.2

Exercise 13.2

page-13.26

Question 1:

Find the S.P. if
(i) M.P. = Rs 1300 and Discount = 10%
(ii) M.P. = Rs 500 and Discount = 15%

Answer 1:

$$\begin{gathered} \left(\mathrm{i}\right) \mathrm{We} \mathrm{know} \mathrm{that} \mathrm{SP}=\mathrm{MP}-D\mathrm{iscount} \\ \mathrm{Discount}\%=\frac{\mathrm{Discount}}{\mathrm{MP}}\times 100 \\ \mathrm{Discount}=\frac{\mathrm{Discount} \%\times \mathrm{MP}}{100} \\ =\frac{10\times 1300}{100} \\ \mathrm{So}, \mathrm{SP}=\mathrm{Rs}.\left(1300-\left(\frac{10}{100}\times 1300\right)\right) \\ =1300-130 \\ =\mathrm{Rs}. 1170 \\ \left(\mathrm{ii}\right) \mathrm{We} \mathrm{know} \mathrm{that} \mathrm{SP}=\mathrm{MP}- D\mathrm{iscount} \\ \mathrm{Discount} \%=\frac{\mathrm{Discount}}{\mathrm{MP}}\times 100 \\ \mathrm{Discount}=\frac{\mathrm{Discount} \%\times \mathrm{MP}}{100} \\ =\frac{15\times 500}{100} \\ \mathrm{So}, \mathrm{SP}=\mathrm{Rs}.\left( 500-\left(\frac{15}{100}\times 500\right)\right) \\ =\mathrm{Rs}.(500-75) \\ =\mathrm{Rs}. 425 \end{gathered}$$

Question 2:

Find the M.P. if
(i) S.P. = Rs 1222 and Discount = 6%
(ii) S.P. = Rs 495 and Discount = 1%

Answer 2:

$$\begin{gathered} \left(\mathrm{i}\right) Given, \\ \mathrm{SP}=\mathrm{Rs} 1222 \\ \mathrm{Discoun}t=6\% \\ \mathrm{So}, \mathrm{MP}=\left(\frac{100\times \mathrm{SP}}{100-\mathrm{Discount}\%}\right) \\ =\frac{100\times 1222}{100-6} \\ =\mathrm{Rs}. 1300 \\ \left(\mathrm{ii}\right) Given, \\ \mathrm{SP}=\mathrm{Rs}. 495 \\ \mathrm{Discount}=1\% \\ \mathrm{So}, \mathrm{MP}=\left(\frac{100\times \mathrm{SP}}{100-\mathrm{Discount}\%}\right) \\ =\frac{100\times 495}{100-1} \\ =\mathrm{Rs}. 500 \end{gathered}$$

Question 3:

Find discount in percent when
(i) M.P. = Rs 900 and S.P. = Rs 873
(ii) M.P. = Rs 500 and S.P. = Rs 425

Answer 3:

$$\begin{gathered} \left(\mathrm{i}\right) \mathrm{We} \mathrm{know} \mathrm{that} \mathrm{SP}=\mathrm{MP}-D\mathrm{iscount} \\ \mathrm{So}, 873=900-D\mathrm{iscount} \\ Therefore, \mathrm{Discount}=\mathrm{Rs}. (900-873) \\ =\mathrm{Rs}. 27 \\ \mathrm{Discount}\%=\frac{\mathrm{Discount}}{\mathrm{MP}}\times 100\% \\ =\frac{27}{900}\times 100\% \\ =3\% \\ \left(\mathrm{ii}\right) \mathrm{We} \mathrm{know} \mathrm{that} \mathrm{SP}=\mathrm{MP}-D\mathrm{iscount} \\ \mathrm{So}, 425=500-D\mathrm{iscount} \\ Therefore, \mathrm{Discount}=\mathrm{Rs}.(500-425) \\ =\mathrm{Rs}. 75 \\ \mathrm{Discount}\%=\frac{\mathrm{Discount}}{\mathrm{MP}}\times 100\% \\ =\frac{75}{500}\times 100\% \\ =15\% \end{gathered}$$

Question 4:

A shop selling sewing machines offers 3% discount on all cash purchases. What cash amount does a customer pay for a sewing machine the price of which is marked as Rs 650.

Answer 4:

$$\begin{gathered} D\mathrm{iscount} = 3\% \\ \mathrm{Marked} \mathrm{price}=\mathrm{Rs}. 650 \\ \mathrm{Now}, 3\% \mathrm{of} \mathrm{the} \mathrm{MP} = \frac{3}{100}\times 650 \\ =\mathrm{Rs} 19.50 \\ So, \mathrm{SP}=\mathrm{MP}-\mathrm{Discount} \\ =650-19.50 \\ =\mathrm{Rs} 630.50 \end{gathered}$$

Question 5:

The marked price of a ceiling fan is Rs 720. During off season, it is sold for Rs 684. Determine the discount percent.

Answer 5:

$$\begin{gathered} \mathrm{Given}, \\ \mathrm{MP} \mathrm{of} \mathrm{the} \mathrm{ceiling} \mathrm{fan}=\mathrm{Rs}. 720 \\ \mathrm{SP} \mathrm{of} \mathrm{the} \mathrm{ceiling} \mathrm{fan}= \mathrm{Rs}. 684 \\ \mathrm{Since} \mathrm{SP}=\mathrm{MP}-\mathrm{Discount}, \\ \mathrm{Discount}=\mathrm{MP}-\mathrm{SP} \\ =\mathrm{Rs}. (720-684) \\ =\mathrm{Rs}. 36 \\ \mathrm{Discount}\%=\left(\frac{\mathrm{Discount}}{\mathrm{MP}}\right)\times 100\% \\ =\frac{36}{720}\times 100\% \\ =5\% \end{gathered}$$

Question 6:

On the eve of Gandhi Jayanti a saree is sold for Rs 720 after allowing 20% discount. What is its marked price?

Answer 6:

$$\begin{gathered} \mathrm{Given}, \\ \mathrm{SP} \mathrm{of} \mathrm{the} \mathrm{saree} =\mathrm{Rs}. 720 \\ \mathrm{Discount} on the saree=20\% \\ We know, \mathrm{Discount}\%=\frac{\mathrm{Discount}}{\mathrm{MP}}\times 100 \\ Or, \mathrm{Discount}=\frac{\mathrm{Discount}\%\times \mathrm{MP}}{100} \\ \mathrm{Let} the \mathrm{MP} of the saree \mathrm{be} \mathrm{Rs}. x \\ Therefore, \mathrm{Discount}=\frac{20}{100}x=\mathrm{Rs}. 0.02x \\ \mathrm{Since} \mathrm{S}.\mathrm{P}=\mathrm{MP}- D\mathrm{iscount}, \\ 720=x-0.20x \\ 720=0.80x \\ x=\frac{720}{0.80} \\ =\mathrm{Rs}. 900 \\ \mathrm{Thus}, the \mathrm{MP} of the saree \mathrm{is} \mathrm{Rs}. 900. \end{gathered}$$

Question 7:

After allowing a discount of $7\frac{1}{2}\%$ on the marked price, an article is sold for Rs 555. Find its markd price.

Answer 7:

$$\begin{gathered} \mathrm{Given}, \\ \mathrm{SP} of the article=\mathrm{Rs}. 555 \\ \mathrm{Discount}=7.5\% \\ \mathrm{Let} the \mathrm{MP} of the article \mathrm{b}e \mathrm{Rs}. x. \\ Therefore, \mathrm{Discount}=\frac{\mathrm{Discount}\times \mathrm{MP}}{100}=\mathrm{Rs}.\frac{7.5x}{100}=\mathrm{Rs}. 0.075x \\ \mathrm{Since} \mathrm{SP}=\mathrm{MP}- D\mathrm{iscount}, \\ 555=x-0.075x \\ 555=0.925x \\ x=\frac{555}{0.925} \\ =Rs. 600 \\ \mathrm{Thus}, the \mathrm{MP} of the article \mathrm{is} \mathrm{Rs}. 600. \end{gathered}$$

Question 8:

A shopkeeper allows his customers 10% off on the marked price of goods and still gets a profit of 25%. What is the actual cost to him of an article marked Rs 250?

Answer 8:

$$\begin{gathered} \mathrm{Let} the \mathrm{CP} of the article \mathrm{be} \mathrm{Rs}. x. \\ \mathrm{MP} \mathrm{of} \mathrm{the} \mathrm{article} = \mathrm{Rs}. 250 \\ \mathrm{Discount}=10\% \\ \mathrm{Discount}= 10\% \mathrm{of} 250 \\ =0.10\times 250 \\ =\mathrm{Rs}. 25 \\ \mathrm{SP}=\mathrm{MP}-D\mathrm{iscount} \\ =250-25 \\ =\mathrm{Rs}. 225 \\ \mathrm{Given}, \\ P\mathrm{rofit}=25\% \\ \mathrm{CP}=\left[\frac{100}{\left(100+\mathrm{Gain}\%\right)}\times \mathrm{SP}\right] \\ x=\left[\frac{100}{\left(100+25\right)}\times 225\right] \\ =\left[\frac{100}{125}\times 225\right] \\ =Rs. 180 \\ \mathrm{Thus}, the \mathrm{CP} of the article \mathrm{is} \mathrm{Rs}. 180. \end{gathered}$$

Question 9:

A shopkeeper allows 20% off on the marked price of goods and still gets a profit of 25%. What is the actual cost to him of an article marked Rs 500?

Answer 9:

$$\begin{gathered} \mathrm{Given}, \\ \mathrm{MP} \mathrm{of} \mathrm{an} \mathrm{article}=\mathrm{Rs}. 500 \\ \mathrm{Discount}=20\% \\ Therefore, \mathrm{Discount}=20\% \mathrm{of} 500 \\ =0.20\times 500 \\ =100 \\ \mathrm{So}, \mathrm{SP}=\mathrm{MP}-\mathrm{Discount} \\ =\mathrm{Rs}.(500-100) \\ =\mathrm{Rs}. 400 \\ \mathrm{CP}=\left[\frac{100}{\left(100+\mathrm{Gain}\%\right)}\times \mathrm{SP}\right] \\ =\left[\frac{100}{\left(100+25\right)}\times 400\right] \\ =\frac{40000}{125} \\ =Rs. 320 \\ \mathrm{Thus}, the \mathrm{actual} \mathrm{cost} of the article \mathrm{is} \mathrm{Rs}. 320. \end{gathered}$$

Question 10:

A tradesman marks his goods at such a price that after allowing a discount of 15%, he makes a profit of 20%. What is the marked price of an article whose cost price is Rs 170?

Answer 10:

$$\begin{gathered} Given, \\ CP of the article = Rs. 170 \\ Profit = 20\% \\ \mathrm{We} \mathrm{know} \mathrm{that}, \\ \mathrm{SP}=\left[\frac{\left(100+\mathrm{Gain}\%\right)}{100}\times \mathrm{CP}\right] \\ =\left[\frac{120}{100}\times 170\right] \\ =\frac{20400}{100} \\ =\mathrm{Rs}. 204 \\ \mathrm{Let} the \mathrm{MP} of the article \mathrm{be} \mathrm{Rs}. x. \\ \mathrm{Discount}=15\% \\ Therefore, \mathrm{Discount}=15\% \mathrm{of} x \\ =0.15x \\ \mathrm{So}, \mathrm{SP}=\mathrm{MP}-\mathrm{Discount} \\ \mathrm{MP}=\mathrm{SP}+\mathrm{Discount} \\ x=204+0.15x \\ x-0.15x=204 \\ 0.85x=204 \\ x=\mathrm{Rs}. 240 \\ \mathrm{Thus}, \mathrm{the} \mathrm{marked} p\mathrm{rice} of the article \mathrm{is} \mathrm{Rs}. 240. \end{gathered}$$

Question 11:

A shopkeeper marks his goods in such a way that after allowing a discount of 25% on the marked price, he still makes a profit of 50%. Find the ratio of the C.P. to the M.P.

Answer 11:

$$\begin{gathered} \mathrm{Let} \mathrm{C}.\mathrm{P} \mathrm{be} \mathrm{Rs} x \mathrm{and} \mathrm{M}.\mathrm{P} \mathrm{be} \mathrm{Rs} y. \\ \text{Gain\% }= 50 \\ \mathrm{We} \mathrm{know} \mathrm{that}, \\ \mathrm{S}.\mathrm{P} = \left[\frac{\left(100+\mathrm{Gain}\%\right)}{100} \times \mathrm{C}.\mathrm{P}\right] \\ = \left[\frac{150}{100} \times x\right] \\ = \frac{3}{2}x \\ \mathrm{Discount}\% = 25 \\ \mathrm{Discount} = 25\% \mathrm{of} y \\ = \mathrm{Rs} 0.25y \\ \mathrm{So}, \mathrm{S}.\mathrm{P} = \mathrm{M}.\mathrm{P} - \mathrm{Discount} \\ = y - 0.25y \\ = 0.75y \\ \mathrm{So}, \mathrm{S}.\mathrm{P} = 0.75y \\ \mathrm{Also}, \mathrm{S}.\mathrm{P} = \frac{3}{2}x \\ \text{Comparing both values for S.P., we get: } \\ \frac{3}{2}x = 0.75y \\ \frac{x}{y} = \frac{0.75 \times 2}{3} \\ =\frac{1.5}{3} \\ =\frac{1}{2} \\ \mathrm{Thus}, \mathrm{C}.\mathrm{P}:\mathrm{M}.\mathrm{P} = 1:2 \end{gathered}$$

Question 12:

A cycle dealer offers a discount of 10% and still makes a profit of 26%. What is the actual cost to him of a cycle whose marked price is Rs 840?

Answer 12:

$$\begin{gathered} Given, \\ \mathrm{MP} \mathrm{of} \mathrm{the} \mathrm{cycle}=\mathrm{Rs}. 840 \\ \mathrm{Discount}=10\% \\ \mathrm{So}, \mathrm{SP}=\mathrm{MP}\times \left(\frac{100-\mathrm{Discount}\%}{100}\right) \\ =840\times \left(\frac{100-10}{100}\right) \\ =\mathrm{Rs}. 756 \\ \mathrm{Now}, \mathrm{SP}=\mathrm{Rs}. 756 \mathrm{and} \mathrm{Gain}=26\% \\ \mathrm{So}, \mathrm{CP}=\frac{100}{100+\mathrm{Gain}\%}\times 756 \\ =\frac{100}{126}\times 756 \\ =\mathrm{Rs}. 600 \\ \mathrm{Hence}, \mathrm{the} \mathrm{actual} \mathrm{cost} of the cycle \mathrm{is} \mathrm{Rs}. 600. \end{gathered}$$

Question 13:

A shopkeeper allows 23% commision on his advertised price and still makes a profit of 10%. If he gains Rs 56 on one item, find his advertised price.

Answer 13:

$$\begin{gathered} \mathrm{Let} the \mathrm{CP} of the item \mathrm{be} \mathrm{Rs}. x. \\ \mathrm{Profit}=10\% \\ \mathrm{SP}=\mathrm{CP}\left(\frac{100+\mathrm{Profit}\%}{100}\right) \\ \mathrm{SP}=x\left(\frac{110}{100}\right) \\ \mathrm{SP}=\mathrm{Rs}.1.1x \\ Again, \mathrm{Profit}=\mathrm{SP}-\mathrm{CP} \\ Therefore, \mathrm{Profit}=\mathrm{Rs}. (1.1x-x) \\ =\mathrm{Rs}. 0.1x \\ \mathrm{We} \mathrm{get}, \\ 0.1x=56 \\ x=\mathrm{Rs}. 560 \\ \mathrm{Now}, the \mathrm{advertise}d \mathrm{price} =\frac{1.1x}{1-0.23} \\ =\mathrm{Rs}.\frac{560\times 1.1}{0.77} \\ =\mathrm{Rs}. 800 \\ Therefore, the advertised price of the item is Rs. 800. \end{gathered}$$

Question 14:

A shopkeeper marks his goods at 40% above the cost price but allows a discount of 5% for cash payment to his customers. What actual profit does he make, if he receives Rs 1064 after paying the discount?

Answer 14:

$$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{original} \mathrm{cost} \mathrm{price} of the item \mathrm{be} \mathrm{Rs}. x. \\ \mathrm{MP}=x+\frac{40x}{100}=1.4x \\ \mathrm{Discount}=MP-SP \\ \mathrm{MP}-\frac{\mathrm{Discount}\%\times \mathrm{MP}}{100}=\mathrm{SP} \\ 1.4x-\frac{5\times 1.4x}{100}=1064 \\ \frac{1.4x\times 100-5\times 1.4x}{100}=1064 \\ \mathrm{So}, x\left(1.4\right)\left(0.95\right)=1064 \\ x= \frac{1064}{\left(1.4\times 0.95\right)} \\ =\frac{1064}{1.33} \\ =\mathrm{Rs}. 800 \\ \mathrm{Profit}=\mathrm{Rs}. (1064-800) \\ =\mathrm{Rs}. 264 \\ \mathrm{Thus}, the \mathrm{actual} \mathrm{profit} by the shopkeeper \mathrm{is} \mathrm{Rs}. 264. \end{gathered}$$

Question 15:

By selling a pair of earings at a discount of 25% on the marked price, a jeweller makes a profit of 16%. If the profit is Rs 48, what is the cost price? What is the marked price and the price at which the pair was eventually bought?

Answer 15:

$$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{cost} \mathrm{price} of the pair of earrings \mathrm{be} \mathrm{Rs}. \mathrm{x}. \\ \mathrm{Profit}=16\% \\ Therefore, \mathrm{SP}=\left(\frac{\mathrm{Profit}\%+100}{100}\right)\times \mathrm{CP} \\ =\left(\frac{16+100}{100}\right)\mathrm{x} \\ =Rs. \frac{116\mathrm{x}}{100} \\ \mathrm{SP}-\mathrm{CP}=48 \\ \Rightarrow \frac{116\mathrm{x}}{100}-\mathrm{x}=48 \\ \Rightarrow 16\mathrm{x}=4800 \\ \Rightarrow \mathrm{x}=\mathrm{Rs}. 300 \\ \mathrm{SP}=\frac{116\mathrm{x}}{100}=\mathrm{Rs}. 348 \\ \mathrm{MP}=\frac{100\times \mathrm{SP}}{100-\mathrm{Discount}\%} \\ =\frac{34800}{75}=\mathrm{Rs}. 464 \\ \mathrm{Thus}, \mathrm{CP} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} \mathrm{o}\mathrm{f} \mathrm{e}\mathrm{a}\mathrm{r}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{s}=\mathrm{Rs}. \mathrm{x}=\mathrm{Rs}. 300 \\ \mathrm{SP} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} \mathrm{o}\mathrm{f} \mathrm{e}\mathrm{a}\mathrm{r}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{s}=\mathrm{Rs}. 348 \\ \mathrm{MP} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{p}\mathrm{a}\mathrm{i}\mathrm{r} \mathrm{o}\mathrm{f} \mathrm{e}\mathrm{a}\mathrm{r}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{s}=\mathrm{Rs}. 464 \end{gathered}$$

Question 16:

A publisher gives 32% discount on the printed price of a book to booksellers. What does a bookseller pay for a book whose printed price is Rs 275?

Answer 16:

$$\begin{gathered} \mathrm{Discount} allowed by the publisher=32\% \mathrm{on} the \mathrm{printed} \mathrm{price} \\ \mathrm{Printed} \mathrm{price}=\mathrm{Rs}. 275 \\ \mathrm{So}, 32\% \mathrm{of} 275=\frac{32}{100}\times 275 \\ =\mathrm{Rs}. 88 \\ \mathrm{So}, the \mathrm{bookseller} \mathrm{pay}s = \mathrm{Rs}. 275-\mathrm{Rs}. 88 \\ =\mathrm{Rs}. 187 for a book \end{gathered}$$

Question 17:

After allowing a discount of 20% on the marked price of a lamp, a trader loses 10%. By what percentage is the marked price above the cost price?

Answer 17:

$$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{CP} of the lamp be \mathrm{Rs}. 100. \\ \mathrm{Loss}=10\% \mathrm{of} \mathrm{CP}=\mathrm{Rs}. 10 \\ \mathrm{So}, \mathrm{SP}=\mathrm{CP}-L\mathrm{oss}=\mathrm{Rs}. 100-\mathrm{Rs}. 10=\mathrm{Rs}. 90 \\ \mathrm{The} \mathrm{trader} \mathrm{allows} \mathrm{a} \mathrm{discount} \mathrm{of} 20\%. \\ \mathrm{This} \mathrm{means} \mathrm{that} \mathrm{when} the \mathrm{MP} \mathrm{is} \mathrm{Rs}. 100, \mathrm{the} \mathrm{SP} \mathrm{will} \mathrm{be} \mathrm{Rs}. 80. \\ \mathrm{Now}, \\ \mathrm{If} \mathrm{Rs}. 80 \mathrm{is} \mathrm{the} \mathrm{SP}, \mathrm{th}e \mathrm{MP}=\mathrm{Rs}. 100 \\ \mathrm{If} \mathrm{Re}. 1 \mathrm{is} \mathrm{the} \mathrm{SP}, \mathrm{the} \mathrm{M}.\mathrm{P}=\mathrm{Rs}. \frac{100}{80} \\ \mathrm{If} Rs. 90 \mathrm{is} \mathrm{the} \mathrm{SP}, \mathrm{the} \mathrm{MP}=\mathrm{Rs}. \left(\frac{100}{80}\times 90\right)=\mathrm{Rs}. 112.50 \\ \mathrm{Hence}, \mathrm{the} \mathrm{trader} \mathrm{mark}s \mathrm{his} \mathrm{good}s at 12.5\% \mathrm{above} \mathrm{the} \mathrm{cost} \mathrm{price}. \end{gathered}$$

Question 18:

The list price of a table fan is Rs 480 and it is available to a retailer at 25% discount. For how much should a retailer sell it to gain 15%?

Answer 18:

$$\begin{gathered} \mathrm{Marked} \mathrm{price} of the table fan=\mathrm{Rs}. 480 \\ \mathrm{Discount} =25\% \\ \mathrm{Therefore}, \mathrm{cost} \mathrm{price} = 25\% \mathrm{of} Rs. 480 \\ \frac{25}{100}\times 480=\mathrm{Rs}. 360 \\ \mathrm{It} \mathrm{is} \mathrm{given} \mathrm{that} the profit on the table fan is 15\%. \\ \mathrm{Gain}\%=\frac{\mathrm{Gain}}{\mathrm{CP}}\times 100 \\ 15=\frac{\mathrm{Gain}}{360}\times 100 \\ \mathrm{Gain}=\mathrm{Rs}. 54 \\ \mathrm{Gain}=\mathrm{SP}-\mathrm{CP} \\ 54=\mathrm{SP}-360 \\ \mathrm{SP}=\mathrm{Rs}. 414 \\ Thus, the retailer will sell the table fan for Rs. 414. \end{gathered}$$

Page-13.27

Question 19:

Rohit buys an item at 25% discount on the marked price. He sells it for Rs 660, making a profit of 10%. What is the marked price of the item?

Answer 19:

$$\begin{gathered} Given, \\ SP of the item = Rs. 660 \\ Discount on the item = 25\% \\ Profit on the item = 10\% \\ \mathrm{We} \mathrm{know}, \\ \mathrm{MP}=\left(\frac{100\times \mathrm{SP}}{100-\mathrm{Discount}\%}\right) \\ =\left(\frac{100\times 660}{100-25}\right) \\ =\mathrm{Rs}. 880 \\ \mathrm{Thus}, \mathrm{the} \mathrm{marked} \mathrm{price} of the item \mathrm{is} \mathrm{Rs}. 880. \end{gathered}$$

Question 20:

A cycle merchant allows 20% discount on the marked price of the cycles and still makes a profit of 20%. If he gains Rs 360 over the sale of one cycle, find the marked price of the cycle.

Answer 20:

$$\begin{gathered} \mathrm{Given}, \\ Gain on one cycle=\mathrm{Rs}. 360 \\ \mathrm{Gain}=20\% \\ \mathrm{Gain}\%=\frac{\mathrm{Gain}}{\mathrm{CP}}\times 100 \\ 20=\frac{360}{\mathrm{CP}}\times 100 \\ \mathrm{CP}=\mathrm{Rs}. 1800 \\ \mathrm{SP}=\frac{100+\mathrm{Gain}\%}{100}\times \mathrm{CP} \\ \mathrm{SP}=\frac{120}{100}\times 1800=\mathrm{Rs}. 2160 \\ \mathrm{SP}=\mathrm{Rs}. 2160 \\ \mathrm{Discount}=20\% \\ \mathrm{MP}=\frac{100\times \mathrm{SP}}{100-\mathrm{Discount}\%} \\ \mathrm{MP}=\frac{100\times 2160}{80}=\mathrm{Rs}. 2700 \\ \mathrm{Hence}, the MP of one cycle is \mathrm{Rs}. 2700. \end{gathered}$$

Question 21:

Jyoti and Meena run a ready-made garment shop. They mark the garments at such a price that even after allowing a discount of 12.5%, they make a profit of 10%. Find the marked price of a suit which costs them Rs 1470.

Answer 21:

$$\begin{gathered} Given, \\ C\mathrm{P} \mathrm{of} \mathrm{the} \mathrm{suit}=\mathrm{Rs}. 1470 \\ \mathrm{Gain}=10\% \\ \mathrm{So}, \mathrm{SP}=\mathrm{Rs}. \left(\frac{100+\mathrm{Gain}}{100}\times \mathrm{CP}\right) \\ =\mathrm{Rs}. \left(\frac{100+10}{100}\times 1470\right) \\ =\mathrm{Rs}. 1617 \\ \mathrm{Now}, \\ \mathrm{SP}=\mathrm{Rs}. 1617 \\ D\mathrm{iscount}=12.5\% \\ \mathrm{So}, \mathrm{MP}=\mathrm{Rs}. \left(\frac{100\times \mathrm{SP}}{100-\mathrm{Discount}\%}\right) \\ =\mathrm{Rs}. \left(\frac{100\times 1617}{100-12.5}\right)=\mathrm{Rs}. 1848 \\ Therefore, the marked price of the suit is Rs. 1848. \end{gathered}$$

Question 22:

What price should Aslam mark on a pair of shoes which costs him Rs 1200 so as to gain 12% after allowing a discount of 16%?

Answer 22:

$$\begin{gathered} Given, \\ \mathrm{CP} \mathrm{of} \mathrm{the} \mathrm{pair} \mathrm{of} \mathrm{shoes}=\mathrm{Rs}. 1470 \\ \mathrm{Gain}=12\% \\ \mathrm{Discount}=16\% \\ \mathrm{So}, \mathrm{SP}=\mathrm{Rs}. \left(\frac{100+\mathrm{Gain}}{100}\times \mathrm{CP}\right) \\ =\mathrm{Rs}. \left(\frac{100+12}{100}\times 1200\right) \\ =\mathrm{Rs}. 1344 \\ \mathrm{Now}, \\ \mathrm{SP} \mathrm{of} \mathrm{the} \mathrm{pair} \mathrm{of} \mathrm{shoes}=\mathrm{Rs}. 1344 \\ D\mathrm{iscount}=16\% \\ \mathrm{So}, \mathrm{MP}=\mathrm{Rs}. \left(\frac{100\times \mathrm{SP}}{100-\mathrm{Discount}\%}\right) \\ =\mathrm{Rs}. \left(\frac{100\times 1344}{100-16}\right)=\mathrm{Rs}. 1600 \\ Aslam should sell the pair of shoes for Rs. 1600. \end{gathered}$$

Question 23:

Jasmine allows 4% discount on the marked price of her goods and still earns a profit of 20%. What is the cost price of a shirt for her marked at Rs 850?

Answer 23:

$$\begin{gathered} Given, \\ \mathrm{MP} \mathrm{of} \mathrm{the} \mathrm{shirt}=\mathrm{Rs}. 850 \\ \mathrm{Discount}=4\% \\ \mathrm{Discount} \mathrm{allowed}=\mathrm{Rs}. \left(\frac{4}{100}\times 850\right) \\ =\mathrm{Rs}. 34 \\ \mathrm{Thus}, \mathrm{SP} \mathrm{of} the \mathrm{shirt}=\mathrm{Rs}. \left(850-34\right)=\mathrm{Rs}. 816 \\ \mathrm{Now}, \\ P\mathrm{rofi}t earned by \mathrm{Jasmine}=20\% \\ \mathrm{Thus}, \mathrm{CP}=\frac{100\times \mathrm{SP}}{\left(100+\mathrm{Profit}\%\right)} \\ =\mathrm{Rs}. \left(\frac{100\times 816}{100+20}\right) \\ =\mathrm{Rs}. \left(\frac{100\times 816}{120}\right) \\ =\mathrm{Rs}. 680 \\ \mathrm{Thus}, \mathrm{the} \mathrm{cost} \mathrm{price} \mathrm{of} the \mathrm{shirt} \mathrm{is} \mathrm{Rs}. 680. \end{gathered}$$

Question 24:

A shopkeeper offers 10% off-season discount to the customers and still makes a profit of 26%. What is the cost price for the shopkeeper on a pair of shoes marked at Rs 1120?

Answer 24:

$$\begin{gathered} \mathrm{Given}, \\ \mathrm{MP} \mathrm{of} \mathrm{the} \mathrm{pair} \mathrm{of} \mathrm{shoes}=\mathrm{Rs}. 1120 \\ Discount = 10\% \\ \mathrm{So}, \mathrm{SP}=\mathrm{MP} \left(\frac{100-\mathrm{Discount}\%}{100}\right) \\ =1120\times \frac{90}{100} \\ =\mathrm{Rs}. 1008 \\ \mathrm{Now}, \\ Profit=26\% \\ \mathrm{SP}=\mathrm{Rs}. 1008 \\ \mathrm{Therefore}, \mathrm{CP}=\left(\frac{100\times \mathrm{SP}}{100+Profit\%}\right) \\ \mathrm{Cost} \mathrm{price} =\left(\frac{100\times 1008}{100+26}\right) \\ =\mathrm{Rs}. 800 \\ The \cos t price of the pair of shoes will be Rs. 800. \end{gathered}$$

Question 25:

A lady shopkeeper allows her customers 10% discount on the marked price of the goods and still gets a profit of 25%. What is the cost price of a fan for her marked at Rs 1250?

Answer 25:

$$\begin{gathered} \mathrm{Given}, \\ \mathrm{MP} \mathrm{of} \mathrm{the} \mathrm{fan}=\mathrm{Rs}. 1250 \\ \mathrm{Discount}=10\% \\ \mathrm{So}, \mathrm{Discount} = 10\% \mathrm{of} 1250 \\ =0.10\times 1250 \\ =\mathrm{Rs}. 125 \\ \mathrm{Since} \mathrm{SP}=\mathrm{MP}-\mathrm{Discount}, \\ S\mathrm{P}=\mathrm{Rs}. \left(1250-125\right) \\ =\mathrm{Rs}. 1125 \\ Now, \\ SP of the fan = Rs. 1125 \\ Profit = 25\% \\ \mathrm{CP}=\left[\frac{100}{\left(100+Profit\%\right)}\times \mathrm{SP}\right] \\ =\left[\frac{100}{125}\right]1125 \\ =\mathrm{Rs}. 900 \\ \mathrm{Thus}, the \cos t price of the fan is \mathrm{Rs}. 900. \end{gathered}$$