DAV Class 7 Maths Chapter 5 Worksheet 3

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DAV Class 7 Maths Chapter 5 Worksheet 3

Application of Percentage Worksheet 3


1. I purchased a watch for ₹ 330 and sold it at a loss of 20%. Find S.P. of the watch.

Solution

\[ \begin{align*} \text{C.P of watch} & = \text{₹} 330 \\ \text{Loss %} & = 20 \% \\ \color{green} \text{S.P} & = \color{green} C.P \times \frac{(100 - L\%)}{100} \\ \\ & = 330 \times \frac{(100 - 20)}{100} \\ \\ & = 330 \times \frac{80}{100} \\ \\ & = 33 \times 8 \\ & = \text{₹} 264 \end{align*} \]

Answer S.P. of the watch \( = \color{red}\text{₹} 264 \)

2. By selling a T.V. for ₹ 8,000, a shopkeeper loses 20% of his cost. If he sells it for ₹ 11,000, what profit or loss would be there for him?

Solution

\[ \begin{align*} \text{S.P. of TV} & = \text{₹} 8000 \\ \text{Loss %} & = 20 \% \\ \color{green} \text{C.P.} & = \color{green} S.P \times \frac{100}{100 - L\%} \\ \\ & = 8000 \times \frac{100}{100 - 20} \\ \\ & = {\cancel{8000}}^{100} \times \frac{100}{{\cancel{80}}^{1}} \\ \\ & = 100 \times 100 \\ \text{C.P.}& = \text{₹} 10000 \\ \\ \text{New S.P.} & = \text{₹} 11000 \\ \text{Profit} & = \text{New S.P.} - \text{C.P.} \\ & = 11000 - 10000 \\ & = 1000 \\ \\ \color{green} \text{Profit %} & = \color{green} \frac{\text{Profit }}{C.P} \times 100 \\ \\ & = \frac{1000}{10000} \times 100 \\\\ & = 10\% \end{align*} \]

Answer Profit percentage \( = \color{red} 10\% \)

3. A shopkeeper purchased a T.V. set for ₹ 9,000 and sold it at a loss of 5%. Find the selling price of the T.V. set.

Solution

\[ \begin{align*} \text{C.P. of T.V. set} & = \text{₹} 9000 \\ \text{Loss %} & = 5\% \\ \color{green} \text{S.P} & = \color{green} C.P \times \frac{(100 - L\%)}{100} \\ \\ & = 9000 \times \frac{(100 - 5)}{100} \\ \\ & = {\cancel{9000}}^{90} \times \frac{95}{{\cancel{100}}^{1}} \\ \\ & = 90 \times 95 \\ & = \text{₹} 8,550 \end{align*} \]

Answer S.P. of the T.V. set \( = \color{red}\text{₹} 8,550 \)

4. Seeta sells a dining set to Neeta for ₹ 6,000 and gains 20%. For how much should she sell it to increase her profit by another 5%?

Solution

\[ \begin{align*} \text{S.P} & = \text{₹} 6000 \\ \text{Profit %} & = 20\% \\ \\ \color{green} \text{C.P.} & = \color{green} S.P \times \frac{100}{100 + P\%} \\ \\ & = 6000 \times \frac{100}{100 + 20} \\ \\ & = {\cancel{6000}}^{50} \times \frac{100}{{\cancel{120}}^{1}} \\ \\ & = 50 \times 100 \\ \text{C.P.} & = \text{₹} 5000 \\ \\ \text{New Profit %} & = 20\% + 5\% \\ &= 25\% \\ \color{green} \text{New S.P.} & = \color{green} C.P \times \frac{(100 + P\%)}{100} \\ \\ & = {\cancel{5000}}^{50} \times \frac{125}{{\cancel{100}}^{1}} \\ \\ & = 50 \times 125 \\ & = \text{₹} 6250 \end{align*} \]

Answer New selling price \( = \color{red}\text{₹} 6250 \)

5. Ranjan bought a second-hand scooter for ₹ 6,000. He spent ₹ 300 on its repairs and sold it to Vineet at a profit of 10%. Vineet sold the scooter to Mukesh at a loss of 10%. At what price did Mukesh buy the scooter?

Solution

\[ \begin{align*} \color{orange} \text{Ranjan} \\ \text{C.P. of scooter} & = \text{₹} 6000 \\ \text{Repair expenses} & = \text{₹} 300 \\ \\ \text{Actual C.P.} & = 6000 + 300 \\ & = 6300 \\ \text{Profit} & = 10\% \\ \color{green} \text{S.P} & = \color{green} C.P \times \frac{(100 + P\%)}{100} \\ \\ & = {\cancel{6300}}^{63} \times \frac{(100 + 10)}{{\cancel{100}}^{1}} \\ \\ & = 63 \times 110 \\ \text{S.P} & = \text{₹} 6930 \\ \\ \color{orange} \text{Vineet} \\ \text{C.P} & = \text{₹} 6930 \\ \text{Loss %} & = 10\% \\ \color{green} \text{S.P} & = \color{green} C.P \times \frac{(100 -L\%)}{100} \\ \\ & = 6930 \times \frac{(100 - 10)}{100} \\ \\ & = 6930 \times \frac{90}{100} \\ \\ & = 693 \times 9 \\ & = \text{₹} 6237 \end{align*} \]

Answer Price at which Mukesh bought \( = \color{red}\text{₹} 6,237 \)

6. A man buys two pens at ₹ 20 each. He sells one at a gain of 5% and the other at a loss of 5%. Find his gain or loss percent.

Solution

\[ \begin{align*} &\color{orange} \text{First Pen} \\ \text{C.P.} & = \text{₹} 20 \\ \text{Profit %} & = 5\% \\ \color{green} \text{S.P} & = \color{green} C.P \times \frac{(100 + P \%)}{100} \\ \\ & = 20 \times \frac{(100+5)}{100} \\ \\ & = {\cancel{20}}^{1} \times \frac{{\cancel{105}}^{\color{red}21}}{{{\cancel{100}}^{\cancel5}}^{\color{red}1}} \\ \text{S.P of first pen} & = \text{₹} 21 \\ \\ &\color{orange} \text{Second Pen} \\ \text{C.P.} & = \text{₹} 20 \\ \text{Loss %} & = 5\% \\ \color{green} \text{S.P} & = \color{green} C.P \times \frac{(100 - L\%)}{100} \\ \\ & = 20 \times \frac{(100 - 5)}{100} \\ \\ & = {\cancel{20}}^{1} \times \frac{{\cancel{95}}^{\color{red}19}}{{{\cancel{100}}^{\cancel5}}^{\color{red}1}} \\ & = \text{₹} 19 \\ \\\text{Total C.P. of two pens} & = 20 \times 2 \, \,\,\implies \text{₹} 40 \\ \text{Total S.P. of two pens} & = 21 + 19 \implies \text{₹} 40 \end{align*} \]

Answer There is no gain or loss.

7. Mr. Tandon purchased a computer for ₹ 32,000 and a microwave oven for ₹ 6,500. On the computer, he lost 5% and on the microwave, he gained 15%. Find his total gain or loss percent.

Solution

\[ \begin{align*} \text{C.P. of computer} & = \text{₹} 32,000 \\ \text{Loss on computer} & = 5\% \\ \color{green} \text{S.P. of computer} & = \color{green} C.P \times \frac{(100 - L\%)}{100} \\ \\ & = {\cancel{3200}}^{320} \times \frac{95}{{\cancel{100}}^{1}} \\ & = 320 \times 95 \\ \text{S.P. of computer} & = \text{₹} 30400 \\ \\ \text{C.P. of microwave} & = \text{₹} 6500 \\ \text{Profit on microwave} & = 15\% \\ \color{green} \text{S.P. of microwave} & = \color{green} C.P \times \frac{(100 + P\%)}{100} \\ \\ & = {\cancel{6500}}^{65} \times \frac{115}{{\cancel{100}}^{1}} \\ & = 65 \times 115 \\ \text{C.P. of microwave} & = \text{₹} 7475 \\ \\ \text{Total C.P.} & = 32,000 + 6,500 \\ & = \text{₹} 38,500 \\ \\ \text{Total S.P.} & = 30,400 + 7,475 \\ & = \text{₹} 37,875 \\ \\ \text{Total Loss} & = \text{Total C.P.} - \text{Total S.P.} \\ & = 38500 - 37875 \\ & = \text{₹} 625 \\ \\ \color{green} \text{Loss %} & = \color{green} \frac{Loss}{C.P} \times 100 \\ \\ & = \frac{625}{38500} \times 100 \\ \\ & = \frac{{\cancel{625}}^{125}}{{\cancel{385}}^{77}}\\ \\ & = \frac{125}{77}\\ \\ & = \text{₹} 1.62\% \end{align*} \]

Answer Loss percentage \( = \color{red} 1.62\% \)

8. Mr. A sells a bicycle to Mr. B at a profit of 20% and Mr. B sells it to Mr. C at a profit of 25%. If Mr. C pays ₹ 1,500, what did Mr. A pay for it?

Solution

\[ \begin{align*} &\color{orange} Mr.B \\ \text{S.P} & = \text{₹} 1500 \\ \text{Profit} & = 25\% \\ \\ \color{green} \text{C.P.} & = \color{green} S.P. \times \frac{100}{(100 + P\%)} \\ \\ & = 1500 \times \frac{100}{(100 + 25)} \\ \\ & = {\cancel{1500}}^{12} \times \frac{100}{{\cancel{125}}^{1}} \\ \\ & = 12 \times 100 \\ & = \text{₹} 1200 \\ \\&\color{orange} Mr.A \\ \text{S.P} & = \text{₹} 1200 \\ \text{Profit} & = 20\% \\ \\ \color{green} \text{C.P.} & = \color{green} S.P. \times \frac{100}{(100 + P\%)} \\ \\ & = 1200 \times \frac{100}{(100 + 20)} \\ \\ & = {\cancel{1200}}^{10} \times \frac{100}{{\cancel{120}}^{1}} \\ & = 10 \times 100 \\ & = \text{₹} 1000 \end{align*} \]

Answer Mr. A paid \( = \color{red}\text{₹} 1000 \)