DAV Class 8 Maths Chapter 5 Worksheet 2
Profit, Loss & Discount Worksheet 2
1. The marked price of a pant is ₹ 1,250 and the shopkeeper allows a discount of 8% on it. Find the discount and the selling price of the pant.
Solution
\[ \begin{align*} M.P &= \text{₹} 1250 \\ \text{Discount} &= 8\% \\ \\\color{green} S.P &= \color{green} \frac{M.P \times (100 - Discount \, \%)}{100} \\ \\ &= \frac{1250 \times (100 - 8)}{100} \\ \\ &= \frac{\cancel{1250}^{25} \times \cancel{92}^{46}}{\cancel{100}_{\cancel2_1}} \\ \\ &= 25 \times 46 \\ \\ S.P &= \text{₹} 1150 \\ \\Discount &= \text{M.P} - \text{S.P} \\[6pt] &= 1250 - 1150 \\[6pt] \text{Discount} &= \text{₹} 100 \end{align*} \]
Answer Discount \( = \color{red} \text{₹} 100 \) and the selling price of the pant \( = \color{red} \text{₹} 1150 \)
2. The marked price of a water cooler is ₹ 5,400. The shopkeeper offers an off-season discount of 20% on it. Find its selling price.
Solution
\[ \begin{align*} \text{M.P} &= \text{₹} 5400 \\ \text{Discount} &= 20\% \\ \\ \color{green} S.P &= \color{green} \frac{M.P \times (100 - Discount \, \%)}{100} \\ \\ &= \frac{5400 \times (100 - 20)}{100} \\ \\ &= \frac{\cancel{5400}^{54} \times 80}{\cancel{100}_1} \\ \\ &= 54 \times 80 \\ \\ \text{S.P} &= \text{₹} 4320 \end{align*} \]
Answer The selling price of the water cooler \( = \color{red} \text{₹} 4320 \)
3. An almirah of marked price ₹ 4,000 is sold for ₹ 3,700 after allowing a certain discount. Find the rate of discount.
Solution
\[ \begin{align*} \text{M.P} &= \text{₹} 4000 \\ \text{ S.P} &= \text{₹} 3700 \\ \\ \color{green} \text{Discount} &= \color{green} \text{M.P} - \text{S.P} \\ &= 4000 - 3700 \\ &= \text{₹} 300 \\ \\ \color{green} \text{Discount } \% &= \color{green} \frac{\text{Discount}}{\text{M.P}} \times 100 \\ \\ &= \frac{\cancel{300}^{ \ 15}}{\cancel{4000}_{\cancel{40}_{2}}} \times \cancel{100}^1 \\ \\ &= \frac{15}{2} \\ \\ \text{Discount } \% &= 7.5\% \end{align*} \]
Answer The rate of discount \( = \color{red} 7.5\% \)
4. Find the rate of discount being 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 \( = \color{red} 6\% \)
5. Find the marked price of a washing machine which is sold at ₹ 8,400 after allowing a discount of 16%.
Solution
\[ \begin{align*} \text{S.P} &= \text{₹} 8400 \\ \text{Discount } \% &= 16\% \\ \\ \color{green} \text{M.P} &= \color{green} \frac{\text{S.P} \times 100}{100 - \text{Discount} \%} \\ \\ &= \frac{8400 \times 100}{100 - 16} \\ \\ &= \frac{\cancel{8400}^{100} \times 100}{\cancel{84}_1} \\ \\ &= 100 \times 100 \\ \text{M.P} &= \text{₹} 10000 \end{align*} \]
Answer The marked price of the washing machine \( = \color{red} \text{₹} 10000 \)
6. A dinner set was bought for ₹ 2,464 after getting a discount of 12% on its marked price. Find the marked price of the dinner set.
Solution
\[ \begin{align*} \text{S.P} &= \text{₹} 2464 \\ \text{Discount } \% &= 12\% \\ \\ \color{green} \text{ M.P} &= \color{green} \frac{\text{S.P} \times 100}{100 - \text{Discount} \%} \\ \\ &= \frac{2464 \times 100}{100 - 12} \\ \\ &= \frac{\cancel{2464}^{28} \times 100}{\cancel{88}_1} \\ \\ &= 28 \times 100 \\ \text{M.P} &= \text{₹} 2800 \end{align*} \]
Answer The marked price of the dinner set \( = \color{red} \text{₹} 2800 \)
7. The marked price of a computer is ₹ 22,000. After allowing a 10% discount, a dealer still makes a profit of 20%. Find the cost price of the computer.
Solution
\[ \begin{align*} \text{M.P} &= \text{₹} 22000 \\ \text{Discount } \% &= 10\% \\ \\ \color{green} \text{S.P} &= \color{green} \frac{\text{M.P} \times (100 - \text{Discount} \%)}{100} \\ \\ &= \frac{\cancel{22000}^{220} \times 90}{\cancel{100}_1} \\ \\ &= 220 \times 90 \\ S.P&= \text{₹} 19800 \\ \\ \text{Profit } \% &= 20\% \\ \\ \color{green} \text{C.P} &= \color{green} \frac{\text{S.P} \times 100}{100 + \text{Profit } \%} \\ \\ &= \frac{\cancel{19800}^{165} \times 100}{\cancel{120}_1} \\ \\ &= 165 \times 100 \\ \text{C.P} &= \text{₹} 16500 \end{align*} \]
Answer The cost price of the computer \( = \color{red} \text{₹} 16500 \)
8. The marked price of a double bed is ₹ 9,575. A shopkeeper allows a discount of 12% and still gains 10%. Find the cost price of the double bed.
Solution
\[ \begin{align*} \text{M.P} &= \text{₹} 9575 \\ \text{Discount } \% &= 12\% \\ \\ \text{S.P} &= \frac{\text{M.P} \times (100 - \text{Discount }\%)}{100} \\ \\ &= \frac{\cancel{9575}^{383} \times \cancel{88}^{22}}{\cancel{100}_{\cancel{25}_1}} \\ \\ &= 383 \times 22 \\[6pt] S.P &= \text{₹} 8426 \\ \\ \text{Gain } \% &= 10\% \\ \\ \text{C.P} &= \frac{\text{S.P} \times 100}{100 + \text{Gain } \%} \\ \\ &= \frac{\cancel{8426}^{766} \times \cancel{100}^{10}}{\cancel{110}_{\cancel{11}}} \\ \\ &= 766 \times 10\\ \text{C.P} &= \text{₹} 7660 \end{align*} \]
Answer The cost price of the double bed \( = \color{red} \text{₹} 7666 \)
9.
A dealer buys a bicycle for ₹ 1,250 and marks it at 40% above its cost price. If he allows 8% discount, find:
(i) Selling price of the bicycle
(ii) Profit percentage
Solution
(i) Selling price of the bicycle \[ \begin{align*} \text{C.P} &= \text{₹} 1250 \\ \text{M.P} &= \text{C.P} + 40 \% \text{ of C.P} \\ \\ &= 1250 + \left(\frac{\cancel{40}^{10}}{\cancel{100}_{\cancel4_1}} \times \cancel{1250}^{50} \right) \\ \\ &= 1250 + (10 \times 50) \\ &= 1250 + 500 \\ \text{M.P} &= \text{₹} 1750 \\ \\ \text{Discount } \% &= 8\% \\ \\ \text{S.P} &= \frac{\text{M.P} \times (100 - \text{Discount } \%)}{100} \\ \\ &= \frac{\cancel{1750}^{35} \times \cancel{92}^{46}}{\cancel{100}_{\cancel{2}_1}} \\ \\ &= 35 \times 46 \\ \text{S.P} &= \text{₹} 1610 \end{align*} \]
(ii) Profit percentage
\[ \begin{align*} \text{Profit} &= \text{S.P} - \text{C.P} \\ &= 1610 - 1250 \\ &= \text{₹} 360 \\ \\ \text{Profit } \% &= \frac{\text{Profit}}{\text{C.P}} \times 100 \\ \\ &= \frac{\cancel{360}^{72}}{\cancel{1250}_{\cancel{25}_5}} \times \cancel{100}^2 \\ \\ &= \frac{144}{5} \\ \\ &= 28\frac{4}{5} \% \end{align*} \]Answer The selling price of the bicycle \( = \color{red} \text{₹} 1610 \) and Profit percentage \( = \color{red} 28\dfrac{4}{5} \% \)
10. Priti allows 8% discount on the marked price of the suits and still makes a profit of 15%. If her gain over the sale of a suit is ₹ 156, find the marked price of a suit.
Solution
\[ \begin{align*} \text{Profit} &= \text{₹} 156 \\ \text{Profit } \%&= 15\% \\ \\ \text{C.P} &= \frac{\text{Profit} \times 100}{\text{Profit }\%} \\ \\ &= \frac{{\cancel{156}}^{\color{blue}52} \times {\cancel{100}}^{\color{brown}20}}{{\cancel{15}_\cancel{\color{brown}3}}_{\color{blue}1}} \\ \\ &= 52 \times 20 \\ \text{C.P} &= \text{₹} 1040 \\ \\ \text{S.P} &= \text{C.P} + \text{Profit} \\ &= 1040 + 156 \\ \text{S.P} &= \text{₹} 1196 \\ \text{Discount }\% &= 8\% \\ \\ \color{green} \text{ M.P} &= \color{green} \frac{\text{S.P} \times 100}{100 - \text{Discount} \%} \\ \\ &= \frac{1196 \times 100}{100-8} \\ \\ &= \frac{{\cancel{1196}}^{13} \times 100}{{\cancel{92}}_1} \\[6pt] &= 13 \times 100 \\ M.P&= \text{₹} 1300 \end{align*} \]
Answer The marked price of the suit \( = \color{red} \text{₹} 1300 \)