DAV Class 8 Maths Chapter 5 Worksheet 1
Profit, Loss & Discount Worksheet 1
1. By selling a bedsheet for ₹ 640, a shopkeeper earns a profit of 28%. How much did it cost the shopkeeper?
Solution
\[ \begin{align*} \text{Bedsheet } (S.P) &= \text{₹} 640 \\ \text{Profit } \% &= 28\% \\[6pt] C.P &= \frac{\text{S.P} \times 100}{100 + \text{P}\%} \\[6pt] &= \frac{640 \times 100}{100 + 28} \\[6pt] &= \frac{\cancel{640}^{ \ 5} \times 100}{\cancel{128}_1} \\[6pt] &= 5 \times 100 \\[6pt] C.P &= \text{₹} 500 \end{align*} \]
Answer The cost price of the bedsheet is \( \color{red} \text{₹} 500 \)
2. Rajan purchased 250 packets of blades at the rate of ₹ 8 per packet. He sold 70% of the packets at the rate of ₹ 11 per packet and the remaining packets at the rate of ₹ 9 per packet. Find his gain per cent.
Solution
\[ \begin{align*} \text{Total packets purchased} &= 250 \\ \text{Cost price per packet} &= \text{₹} 8 \\ \text{Total C.P} &= 250 \times 8 \\ C.P &= \text{₹} 2000 \\ \\ 70\% \text{ of } 250\text{ packets } & = \frac{70}{100} \times 250 \\[6pt] & = 7 \times 25 \\[6pt] & = 175 \text{ packets} \\ \\ \text{Remaining packets } & = 250 -175\\ & = 75 \text{ packets} \\ \\ \text{S.P of } 175\text{ packets } & = 175 \times 11 \\ & = \text{₹}1925 \\ \\ \text{S.P of } 75\text{ packets } & = 75 \times 9 \\ & = \text{₹} 675 \\ \\ \text{Total S.P} &= 1925 + 675 \\ \text{S.P} &= \text{₹} 2600 \\ \\ \text{Gain} &= \text{S.P} - \text{C.P} \\ &= 2600 - 2000 \\ &= \text{₹} 600 \\ \\ \text{Gain } \% &= \frac{\text{Gain}}{\text{C.P}} \times 100 \\ \\ &= \frac{\cancel{600}^{30}}{\cancel{2000}_{\cancel{20}_1}} \times \cancel{100}^1 \\ \\ \text{Gain } \% &= 30\% \\ \end{align*} \]
Answer Rajan's gain percentage \( = \color{red} 30\% \)
3. Ankit sold two jeans for ₹ 990 each. On one he gains 10% and on the other he lost 10%. Find his gain or loss per cent in the whole transaction.
Solution
\[ \begin{align*} \color{green} 1st & \color{green} \ \text{Jean} \\[6pt] S.P & = \text{₹} 990 \\ Profit & = 10\% \\ \\ C.P &= \frac{\text{S.P} \times 100}{100 + \text{P}\%} \\ \\ &= \frac{990 \times 100}{100 + 10} \\ \\ &= \frac{\cancel{990}^{ \ 9} \times 100}{\cancel{110}_1} \\[6pt] \text{C.P of first jeans} &= \text{₹} 900 \\ \\ \color{green} 2nd & \color{green} \ \text{Jean} \\[6pt] S.P & = \text{₹} 990 \\ Loss & = 10\% \\ \\ C.P &= \frac{\text{S.P} \times 100}{100 - \text{L}\%} \\ \\ &= \frac{990 \times 100}{100 - 10} \\ \\ &= \frac{\cancel{990}^{ \ 11} \times 100}{\cancel{90}_1} \\[6pt] \text{C.P of second jeans} &= \text{₹} 1100 \\ \\\text{Total C.P} &= 900 + 1100 \\ C.P &= \text{₹} 2000 \\ \\ \text{Total S.P} &= 990 + 990 \\ S.P &= \text{₹} 1980 \\ \\ \text{Loss} &= \text{C.P} - \text{S.P} \\ & = 2000 - 1980 \\ &= \text{₹} 20 \\ \\ \text{Loss }\% &= \frac{\text{Loss}}{\text{C.P}} \times 100 \\ \\ &= \frac{\cancel{20}^1}{\cancel{2000}_{\cancel{20}_1}} \times \cancel{100}^1 \\ \\ &= 1\% \end{align*} \]
Answer Loss \( = \color{red} 1\% \)
4. Nidhi purchased two sarees for ₹ 2,150 each. She sold one saree at a loss of 8% and the other at a gain. If she had a gain of ₹ 1,230 on the whole transaction, find the selling price of the second saree.
Solution
\[ \begin{align*} & \color{green} \text{First Saree (Loss)} \\ C.P & = \text{₹} 2150 \\ Loss & = 8\% \\ \\ S.P &= \frac{\text{C.P} \times (100 - \text{L}\%)}{100} \\ \\ &= \frac{2150 \times (100 - 8)}{100} \\ \\ &= \frac{\cancel{2150}^{ \ 43} \times \cancel{92}^{46}}{\cancel{100}_{\cancel2_1}} \\[6pt] &= 43 \times 46 \\ S.P &= 1978 \\ \\ S.P \text{ of } 1^{st} \text{ saree}&= \text{₹} 1978 \\ \text{Let S.P of } 2^{nd} \text{ saree} &= x \\ \text{Total S.P} &= 1978 + x \\ \\ \text{Gain} &= \text{₹} 1230 \\ \\ C.P &= 2150 + 2150 \\ \text{Total C.P} &= \text{₹} 4300 \\ \\ \text{Total S.P} - \text{Total C.P} &= Gain \\ (1978 + x) - 4300 & = 1230\\ 1978 + x - 4300 & = 1230\\ x - 2322 & = 1230 \\ x &= 1230 + 2322 \\ x &= \text{₹} 3552 \end{align*} \]
Answer The selling price of the second saree \( = \color{red} \text{₹} 3552 \)
5. By selling 35 greeting cards, a shopkeeper loses an amount equal to the selling price of five greeting cards. Find his loss per cent.
Solution
\[ \begin{align*} \text{Let S.P of 1 greeting card} & = \text{₹} 1 \\ \text{S.P of 35 greeting cards} &= \text{₹} 1 \times 35 \\ S.P &= \text{₹} 35 \\ \\ Loss &= \text{S.P of 5 cards} \\ & = \text{₹} 1 \times 5 \\ Loss & = \text{₹} 5 \\ \\ \text{C.P of 35 greeting cards} & = Loss + S.P \\ & = \text{₹} 35 + \text{₹} 5\\ C.P & = \text{₹} 40 \\ \\ \text{Loss } \% &= \frac{Loss}{C.P} \times 100 \\ \\ &= \frac{\cancel5^1}{\cancel{40}_8} \times 100 \\ \\ &= \frac{100}{8} \\ \\ \text{Loss } \% &= 12.5 \\ \end{align*} \]
Answer The shopkeeper's loss percentage \( = \color{red} 12.5\% \)
6. A man bought bananas at the rate of 10 for ₹ 45 and sold at the rate of one dozen bananas for ₹ 51. Find his gain or loss per cent.
Solution
\[ \begin{align*} \text{C.P for 10 bananas} & = \text{₹} 45 \\[6pt] \text{C.P of 1 banana} & = \frac{45}{10} \implies \text{₹} 4.5 \\[6pt] \text{C.P of 12 bananas} & = 12 \times 4.5 \implies \text{₹} 54 \\[6pt]\text{S.P for 12 bananas} & = \text{₹} 51 \\ \\ \text{Loss} & = \text{C.P} - \text{S.P} \\ & = 54 - 51 \\ Loss &= \text{₹} 3 \\ \\ \text{Loss } \% & = \frac{Loss}{C.P} \times 100 \\ \\ & = \frac{3}{54} \times 100 \\ \\ & = \frac{\cancel3^1}{\cancel{54}_{18}} \times 100 \\ \\ & = \frac{100}{18} \\ \\ & = 5\frac{5}{9}\% \end{align*} \]
Answer Loss \( \% = \color{red} 5\dfrac{5}{9}\% \)