DAV Class 8 Maths Chapter 5 Practice Worksheet
Profit, Loss & Discount Practice Worksheet
1. Arun bought a pair of skates at a sale where the discount is 25%. If the amount he paid is ₹ 3,600, then find the marked price on the pair of skates.
Solution
\[ \begin{align*} \text{S.P} &= \text{₹}\,3600 \\ \text{Discount } \% &= 25\% \\[6pt] \color{green}\text{M.P} &= \color{green}\frac{\text{S.P}\times 100}{100-\text{Discount }\%} \\[6pt] &= \frac{3600\times 100}{100-25} \\[6pt] &= \frac{3600\times 100}{75} \\[6pt] &= \frac{\cancel{3600}^{48}\times 100}{\cancel{75}_1} \\[6pt] &= 48\times 100 \\[6pt] \text{M.P} &= \text{₹}\,4800 \end{align*} \]
Answer Marked price \(=\ \color{red}{\text{₹}\,4800}\)
2. A Mobile phone and a Microwave Oven were bought for ₹ 8,000 each. The shopkeeper made a loss of 4% on the Microwave Oven and a profit of 8% on the Mobile phone. Find the gain or loss percent on the whole transaction.
Solution
\[ \begin{align*} & \color{magenta} Microwave \\[6pt] \text{C.P} &= \text{₹}\,8000 \\ \text{L %} &= 4\% \\[6pt] \color{green} S.P &= \color{green} \frac{\text{C.P} \times (100 - \text{L}\%)}{100} \\[6pt] & = \frac{8000\times (100-4)}{100} \\[6pt] &= \frac{\cancel{8000}^{80} \times 96}{\cancel{100}_1} \\[6pt] & = 80 \times 96 \\ S.P &= \text{₹}\,7680 \\ \\ & \color{magenta} Mobile \\[6pt]\text{C.P} &= \text{₹}\,8000 \\ \text{P %} &= 8\% \\[6pt] \color{green} S.P &= \color{green} \frac{\text{C.P} \times (100 + \text{P}\%)}{100} \\[6pt] & = \frac{8000\times (100+8)}{100} \\[6pt] &= \frac{\cancel{8000}^{80} \times 108}{\cancel{100}_1} \\[6pt] & = 80 \times 108 \\ S.P &= \text{₹}\,8640 \\[8pt] \text{Total S.P} &= 7680+8640 \\[2pt] \implies & \text{₹}\,16320 \\[8pt] \text{Total C.P} &= 8000+8000 \\ \implies & \text{₹}\,16000 \\[6pt] \color{green} \text{Gain} &= \color{green} \text{S.P}-\text{C.P} \\[2pt] &= 16320-16000 \\[2pt] &= \text{₹}\,320 \\[8pt] \color{green} \text{Gain }\% &= \color{green} \frac{\text{Gain}}{\text{C.P}}\times 100 \\[6pt] &= \frac{\cancel{320}^{\ 2}}{\cancel{16000}_{\ \cancel{160}_1}}\times \cancel{100}^{\ 1} \\[6pt] &= 2 \\[2pt] &= 2\% \end{align*} \]
Answer Gain \( = \color{red}{2\% } \)
3. A shopkeeper buys 80 toys for ₹ 2,400 and sells them for a profit of 16%. Find the selling price of a toy.
Solution
\[ \begin{align*} \text{C.P of 80 toys} &= \text{₹}\,2400 \\[6pt] \text{C.P of 1 toy} &= \frac{2400}{80} \\[6pt] \implies & \text{₹}\,30 \\[8pt] \color{green} \text{S.P of 1 toy} & = \color{green} \frac{\text{C.P} \times (100 + \text{P}\%)}{100} \\[6pt] &= 30\times \frac{100+16}{100} \\[6pt] &= 30\times \frac{116}{100} \\[6pt] &= \frac{\cancel{30}^{3}\times 116}{\cancel{100}_{10}} \\[6pt] &= \frac{348}{10} \\[6pt] \text{S.P of 1 toy} &= \text{₹}\,34.80 \end{align*} \]
Answer Selling price of a toy \(=\ \color{red}{\text{₹}\,34.80}\)
4. A shopkeeper allows a discount of 10% to his customers and still gains 20%. Find the marked price of an item that costs him ₹ 1,190.
Solution
\[ \begin{align*} \text{C.P} &= \text{₹}\,1190 \\[2pt] \text{Gain }\% &= 20\% \\[6pt] \text{S.P} & = \color{green} \frac{\text{C.P} \times (100 + \text{P}\%)}{100} \\[6pt] &= \frac{1190\times (100+20)}{100} \\[6pt] &= \frac{1190\times 120}{100} \\[6pt] &= 119 \times 12 \\[6pt] \text{S.P} &= \text{₹}\,1428 \\ \text{Discount }\% &= 10\% \\[6pt] \color{green} \text{ M.P} &= \color{green} \frac{\text{S.P} \times 100}{100 - \text{Discount} \%} \\ \\&= \frac{1428\times 100}{100 - 90} \\[6pt] &= \frac{1428\times \cancel{100}^{10}}{\cancel{90}_9} \\[6pt] &= \frac{14280}{9} \\[6pt] &= \text{₹}\,1586.67 \\[6pt] \end{align*} \]
Answer Marked price \( = \color{red}{\text{₹}\,1586.67}\)
5. Ravi bought four cricket balls for ₹ 250 and sold them at ₹ 340 for five balls. Find his gain or loss percent.
Solution
\[ \begin{align*} \text{C.P of 4 balls} &= \text{₹}\,250 \\[6pt] \text{C.P of 1 ball} & = \frac{250}{4} \\[6pt] \implies & \text{₹}\,62.5 \\[6pt] \text{S.P of 5 balls} &= \text{₹}\, 340 \\[6pt] \text{S.P of 1 ball} &= \frac{340}{5} \\[6pt] \implies & \text{₹}\,68 \\[6pt] \color{green} \text{Gain} &= \color{green} \text{S.P}-\text{C.P} \\ \text{Gain} &= 68-62.5 \\ &= \text{₹}\,5.5 \\[8pt] \color{green} \text{Gain }\% &= \color{green} \frac{\text{Gain}}{\text{C.P}}\times 100 \\[6pt] &= \frac{5.5}{62.5}\times 100 \\[6pt] &= \frac{550 \times 10}{62.5 \times 10} \\[6pt] &= \frac{5500}{625} \\[6pt] &= 8.8\% \end{align*} \]
Answer Gain \( = \color{red}{8.8\%\ } \)
6. A dealer purchased a washing machine for ₹ 7,660. He allows a discount of 12% on its marked price and still gains 10%. Find the marked price of the machine.
Solution
\[ \begin{aligned} \text{C.P} &= \text{₹}\,7660 \\ \text{P }\% &= 10\% \\[6pt] \color{green}\text{S.P} &= \color{green}\frac{\text{C.P}\times(100+\text{P}\%)}{100} \\[6pt] &= \frac{7660\times (100 + 10)}{100} \\[6pt] &= \frac{\cancel{7660}^{766}\times \cancel{110}^{11}}{\cancel{100}_{\cancel{10}_1}} \\[6pt] &= 766 \times 11 \\[6pt] \text{S.P} &= \text{₹}\,8426 \\[8pt] \text{Discount }\% &= 12\% \\[6pt] \color{green}\text{M.P} &= \color{green}\frac{\text{S.P}\times 100}{100-\text{Discount }\%} \\[6pt] &= \frac{8426\times 100}{100 - 12} \\[6pt] &= \frac{\cancel{8426}^{383} \times \cancel{100}^{25}}{\cancel{88}_{\cancel{22}_1}} \\[6pt] &= 383 \times 25 \\[6pt] \text{M.P} &= \text{₹}\,9575 \end{aligned} \]
Answer Marked price \(=\ \color{red}{\text{₹}\,9575}\)
7. The cost price of an Almirah was ₹ 15,500 and ₹ 450 were spent on its repairs. If it is sold for a profit of 15%, then find the selling price of the Almirah.
Solution
\[ \begin{aligned} \text{C.P} &= \text{₹}\,15500 \\ \text{Repairs} &= \text{₹}\,450 \\[4pt] \text{Total C.P} &= 15500+450 \\ &= \text{₹}\,15950 \\[6pt] \text{Profit }\% &= 15\% \\[6pt] \color{green}\text{S.P} &= \color{green}\frac{\text{C.P}\times(100+\text{P}\%)}{100} \\[6pt] &= \frac{15950\times (100 + 15)}{100} \\[6pt] &= \frac{15950 \times 115}{100} \\[6pt] &= \frac{1834250}{100} \\[6pt] \text{S.P} &= \text{₹}\,18342.5 \end{aligned} \]
Answer Selling price \(=\ \color{red}{\text{₹}\,18342.5}\)
8. During a sale, a shop offered a discount of 10% on the marked prices of all the items. What would a customer have to pay for a pair of jeans marked at ₹ 1450 and two shirts marked at ₹ 850 each?
Solution
\[ \begin{aligned} \text{M.P (jeans)} &= \text{₹}\,1450 \\ \text{M.P (2 shirts)} &= 2\times 850\\ \implies & \text{₹}\,1700 \\[4pt] \text{Total M.P} &= 1450+1700 \\ \implies & \text{₹}\,3150 \\[6pt] \text{Discount }\% &= 10\% \\[6pt] \color{green}\text{Customer pays } (S.P) &= \color{green}\frac{\text{M.P}\times(100-\text{Discount }\%)}{100} \\[6pt] &= \frac{3150\times (100 - 10)}{100} \\[6pt] &= \frac{\cancel{3150}^{315}\times \cancel{90}^9}{\cancel{100}_{\cancel{10}_1}} \\[6pt] &= 315\times 9 \\[2pt] &= \text{₹}\,2835 \end{aligned} \]
Answer Customer pays \(=\ \color{red}{\text{₹}\,2835}\)
9. A milkman sold two of his buffaloes for ₹ 20,000 each. On one, he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss.
Solution
\[ \begin{aligned} & \color{magenta}\text{Buffalo 1 }\\[6pt] SP &= \text{₹} \ 20000 \\ P \% & = 5 \% \\[6pt] \color{green}\text{C.P} &= \color{green}\frac{\text{S.P}\times 100}{100+\text{P}\%} \\[6pt] & = \frac{20000\times 100}{100 + 5} \\[6pt] & = \frac{20000\times \cancel{100}^{20}}{\cancel{105}_{21}} \\[6pt] &= \frac{400000}{21} \\[6pt] &= \text{₹}\,19047.62 \\ \\ &\color{magenta}\text{Buffalo 2}\\ \\ SP &= \text{₹} \ 20000 \\ L \% & = 10 \% \\[6pt] \color{green}\text{C.P} &= \color{green}\frac{\text{S.P}\times 100}{100-\text{L}\%} \\[6pt] & = \frac{20000\times 100}{100 - 10} \\[6pt] & = \frac{20000\times \cancel{100}^{10}}{\cancel{90}_9} \\[6pt] & = \frac{200000}{9} \\[6pt] & = \text{₹}\,22222.22 \\[8pt] \text{Total C.P} & = 19047.62+22222.22 \\ \implies & \text{₹}\,41269.84 \\[6pt] \text{Total S.P} &= 20000+20000 \\ \implies & \text{₹}\,40000 \\[6pt] \color{green}\text{Loss} &= \color{green}\text{C.P}-\text{S.P} \\ &= 41269.84-40000 \\ &= \text{₹}\,1269.84 \end{aligned} \]
Answer Loss \(= \color{red} { \text{₹}\,1269.84 }\)
10. By selling 150 hens, Raghav lost the selling price of 10 hens. Find his loss percent.
Solution
\[ \begin{aligned} \text{Let S.P of 1 hen} &= \text{₹}\,1 \\ \text{S.P of 150 hens} &= \text{₹}\,150 \\[4pt] \text{Loss} &= \text{S.P of 10 hens} \\ \implies & \text{₹}\,10 \\[4pt] \text{C.P of 150 hens} &= \text{S.P}+\text{Loss} \\ &= 150+10 \\ &=\text{₹}\,160 \\[6pt] \color{green}\text{Loss }\% &= \color{green}\frac{\text{Loss}}{\text{C.P}}\times 100 \\[6pt] & = \frac{10}{160}\times 100 \\[6pt] &= \frac{\cancel{100}^{25}}{\cancel{16}_4} \\[6pt] &= \frac{25}{4} \\[6pt] &= 6.25\% \end{aligned} \]
Answer Loss \(=\ \color{red}{6.25\%}\)
11. How much percent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gains 20%?
Solution
\[ \begin{aligned} \text{Let C.P} &= \text{₹}\,100 \\[6pt] P\% &= 20\% \\[6pt] \color{green} \text{S.P} &= \color{green}\frac{\text{C.P}\times(100+P\%)}{100} \\[6pt] & = \frac{100\times(100+20)}{100} \\[6pt] & = \frac{\cancel{100}^1 \times 120}{\cancel{100}_1} \\[6pt] \text{S.P} &= \text{₹}\,120 \\[10pt] D\% &= 25\% \\[6pt] \color{green}\text{M.P} &= \color{green}\frac{\text{S.P}\times 100}{100-\text{Discount }\%} \\[6pt] & = \frac{120\times 100}{100 - 25} \\[6pt] & = \frac{\cancel{120}^{40} \times \cancel{100}^{4}}{\cancel{75}_{\cancel3_1}} \\[6pt] \text{M.P} & = \text{₹}\,160 \\[10pt] \color{green}\text{Required }\% &= \color{green}\frac{\text{M.P}-\text{C.P}}{\text{C.P}}\times 100 \\[6pt] &= \frac{160-100}{100}\times 100 \\[6pt] &= \frac{60}{\cancel{100}_1}\times \cancel{100}^1 \\[6pt] &= 60\% \end{aligned} \]
Answer He should mark the goods \( \color{red}{60\%} \) above C.P.
12. Rohit marked his goods at a price that gave a profit of 25%. After allowing a certain discount, that profit reduces to 12.5%. Find his rate of discount.
Solution
\[ \begin{aligned} \text{Let C.P} &= \text{₹}\,100 \\ P\ \% &= 25\% \\[6pt] \text{M.P} &= \frac{100 \times (100 + 25)}{100} \\[6pt] &= \frac{\cancel{100}^1 \times 125}{\cancel{100}_1} \\[6pt] \text{M.P} &= \text{₹}\,125 \\[6pt] \text{After Discount profit } &= 12.5\% \\[6pt] \text{S.P} &= \frac{100 \times (100 + 12.5)}{100} \\[6pt] &= \frac{\cancel{100}^1 \times 112.5}{\cancel{100}_1} \\[6pt] \text{S.P} &= \text{₹}\,112.5 \\[6pt] \text{Discount} &= \text{M.P}-\text{S.P} \\ &= 125-112.5 \\ \text{Discount} &= 12.5 \\[6pt] \color{green}\text{Discount }\% &= \color{green}\frac{Discount}{MP} \times 100 \\[6pt] &= \frac{12.5}{125}\times 100 = 10\% \\[6pt] \text{Discount }\% & = 10 \% \end{aligned} \]
Answer Rate of discount \(=\ \color{red}{10\%}\)
13. A shopkeeper purchased 200 bulbs for ₹ 10 each. 5 bulbs were fused and had to be thrown away. The remaining bulbs were sold at ₹ 12 each. Find the gain or loss percent.
Solution
\[ \begin{aligned} \text{Total C.P} &= 200\times 10 \\ \implies & \text{₹}\,2000 \\[4pt] \text{Good bulbs} &= 200-5 \\ \implies & 195 \\[4pt] \text{Total S.P} &= 195\times 12 \\ \implies & \text{₹}\,2340 \\[6pt] \color{green}\text{Gain} &= \color{green}\text{S.P}-\text{C.P}\\ &=2340-2000\\ &=\text{₹}\,340 \\[6pt] \color{green}\text{Gain }\% &= \color{green}\frac{\text{Gain}}{\text{C.P}} \times 100 \\[6pt] &= \frac{\cancel{340}^{17}}{\cancel{2000}_{\cancel{20}_1}}\times \cancel{100}^{1} \\[6pt] & = 17\% \end{aligned} \]
Answer Gain \(=\ \color{red}{17\%}\)
14. Kamal buys a plot of land for ₹ 96,000. He sells \( \dfrac{2}{5} \) of it at a loss of 6%. At what gain percent should he sell the remaining part of the plot to gain 10% on the whole transaction?
Solution
\[ \begin{aligned} \text{Total C.P of the plot} &= \text{₹}\,96000 \\[4pt] \text{C.P of } \frac{2}{5}th \text{ of the plot} &= \frac{2}{5}\times 96000\\[6pt] &=\text{₹}\,38400 \\[4pt] \text{Loss } & = 6\% \\ \\ \text{S.P of } \frac{2}{5}th \text{ of the plot} & = \color{green}\frac{\text{C.P}\times(100 - \text{L}\%)}{100} \\[6pt] &= 38400\times \frac{100 - 6}{100} \\[6pt] &= \cancel{38400}^{384} \times \frac{94}{\cancel{100}_1} \\[6pt] &= 384 \times 94 \\[6pt] &=\text{₹}\,36096 \\[6pt]\text{C.P of remaining } \frac{3}{5}th \text{ plot} &= 96000-38400\\ &=\text{₹}\,57600 \\[6pt] \text{Required }P \ \% &= 10 \% \\ \\ \text{Total S.P on full plot} &= \color{green}\frac{\text{C.P}\times(100 + \text{P}\%)}{100} \\[6pt] &= 96000 \times \frac{100 + 10}{100}\\[6pt] &= \cancel{96000}^{960} \times \frac{110}{\cancel{100}_1}\\[6pt] &= 960 \times 110 \\[6pt] \text{Total S.P} &=\text{₹}\,105600 \\[6pt] \text{S.P of } \frac{3}{5}th \text{ of the plot} &= 105600-36096 \\ & =\text{₹}\,69504 \\[6pt] \color{green}\text{Gain on } \frac{3}{5}th \text{ of the plot} &= 69504-57600\\ &=\text{₹}\,11904 \\[6pt] \color{green}\text{Required Gain }\% &= \color{green}\frac{\text{Gain}}{\text{C.P}} \times 100\\[6pt] & = \frac{11904}{\cancel{57600}_{576}}\times \cancel{100}^{1} \\[6pt] &= \frac{11904}{576} \\[6pt] & = 20\frac{2}{3}\% \end{aligned} \]
Answer Required gain on the remaining part \(=\ \color{red}{20\dfrac{2}{3}\%}\)
15. The marked price of a T.V. is ₹ 32,500. After allowing a 20% Diwali discount to the customer, a shopkeeper still makes a profit of 30%. Find the cost price of the T.V.
Solution
\[ \begin{aligned} \text{M.P} &= \text{₹}\,32500 \\ \text{Discount} &=20\% \\[4pt] \color{green}\text{S.P} &= \color{green}\frac{\text{M.P}\times(100- D \%)}{100}\\[6pt] &= \frac{32500 \times(100-20)}{100}\\[6pt] &= \frac{\cancel{32500}^{352} \times 80}{\cancel{100}_1} \\[6pt] &= 352 \times 80 \\[6pt] S.P &= \text{₹}\,26000 \\[6pt] \text{Profit } &= 30\% \\[4pt] \color{green}\text{C.P} &= \color{green}\frac{\text{S.P}\times 100}{100+\text{P}\%}\\[6pt] &= \frac{26000\times 100}{100 + 30} \\[6pt] &= \frac{\cancel{26000}^{200}\times 100}{\cancel{130}_1} \\[6pt] &= 260\times 100 \\ \text{C.P} &= \text{₹}\,20000 \end{aligned} \]
Answer Cost price of the T.V. \(=\ \color{red}{\text{₹}\,20000}\)
16. The price of the refrigerator was slashed from ₹ 35,000 to ₹ 29,400 in the winter season. Find the rate of discount.
Solution
\[ \begin{aligned} \text{M.P} &= \text{₹}\,35000 \\ \text{S.P} &= \text{₹}\,29400 \\[4pt] \color{green}\text{Discount} &= \color{green}\text{M.P}-\text{S.P} \\ & = 35000-29400 \\ &=\text{₹}\,5600 \\[6pt] \color{green} \text{Discount } \% &= \color{green} \frac{\text{Discount}}{\text{M.P}} \times 100 \\ \\ &= \frac{\cancel{5600}^{80}}{\cancel{35000}_{\cancel{350}_5}}\times \cancel{100}^{1} \\[6pt] &= \frac{80}{5}\\[6pt] D \% &=16\% \end{aligned} \]
Answer Rate of discount \(=\ \color{red}{16\%}\)
17. A dealer buys a bicycle for ₹ 1,250 and marks it at 40% above its cost price. If he allows 8% discount find the selling price of the bicycle and the profit percentage of the bicycle.
Solution
\[ \begin{align*} \text{C.P} &= \text{₹} 1250 \\ \color{green} \text{M.P} &= \color{green} \text{C.P} + 40 \% \text{ of C.P} \\ \\ &= 1250 + \left(\frac{\cancel{40}^{10}}{\cancel{100}_{\cancel4_1}} \times \cancel{1250}^{50} \right) \\ \\ &= 1250 + (10 \times 50) \\ &= 1250 + 500 \\ \text{M.P} &= \text{₹} 1750 \\ \\ \text{Discount } \% &= 8\% \\ \\ \color{green} \text{S.P} &= \color{green} \frac{\text{M.P} \times (100 - \text{D} \%)}{100} \\ \\ &= \frac{\cancel{1750}^{35} \times \cancel{92}^{46}}{\cancel{100}_{\cancel{2}_1}} \\ \\ &= 35 \times 46 \\ \text{S.P} &= \text{₹} 1610 \\ \\ \color{green} \text{Profit} &= \color{green} \text{S.P} - \text{C.P} \\ &= 1610 - 1250 \\ &= \text{₹} 360 \\ \\ \color{green} \text{Profit } \% &= \color{green} \frac{\text{Profit}}{\text{C.P}} \times 100 \\ \\ &= \frac{\cancel{360}^{72}}{\cancel{1250}_{\cancel{25}_5}} \times \cancel{100}^2 \\ \\ &= \frac{144}{5} \\ \\ &= 28\frac{4}{5} \% \end{align*} \]
Answer The selling price of the bicycle \( = \color{red} \text{₹} 1610 \) and Profit percentage \( = \color{red} 28\dfrac{4}{5} \% \)
18. Find the rate of discount given on a ceiling fan whose selling price is ₹ 1,175 after allowing a discount of ₹ 75 on its marked price.
Solution
\[ \begin{align*} \text{S.P} &= \text{₹} 1175 \\ \text{Discount} &= \text{₹} 75 \\ \\ \color{green} \text{M.P} &= \color{green} \text{S.P} + \text{Discount} \\ &= 1175 + 75 \\ \text{M.P} &= \text{₹} 1250 \\ \\ \color{green} \text{Discount } \% &= \color{green} \frac{\text{Discount}}{\text{M.P}} \times 100 \\ \\ &= \frac{75}{1250} \times 100 \\ \\ &= \frac{\cancel{7500}^6}{\cancel{1250}_1} \\ \\ \text{Discount } \% &= 6\% \\ \end{align*} \]
Answer The rate of discount \( = \color{red} 6\% \)