DAV Class 7 Maths Chapter 5 Worksheet 2
Application of Percentage Worksheet 2
1. A shopkeeper purchased a pair of shoes for ₹ 800 and spent ₹ 20 on its box. He sold it at a profit of ₹ 80. Find
(i) Actual C.P. of shoes
Solution
\[ \begin{align*} \text{C.P of shoes} & = \text{₹} 800 \\ \text{Overhead expenses} & = \text{₹} 20 \\ \text{Actual C.P} & = 800 + 20 \\ & = 820 \\ \end{align*} \]
Answer Actual C.P. \( = \color{red} \text{₹} 820 \)
(ii) S.P. of shoes
Solution
\[ \begin{align*} \text{Actual C.P} & = \text{₹} 820 \\ \text{Profit} & = \text{₹} 80 \\ \text{S.P} & = \text{Actual C.P} + \text{Profit} \\ & = 820 + 80 \\ & = 900 \\ \end{align*} \]
Answer S.P. \( = \color{red} \text{₹} 900 \)
(iii) Profit or Loss %
Solution
\[ \begin{align*} \text{Profit} & = \text{₹} 80 \\ \text{C.P} & = \text{₹} 820 \\ \\ \color{green} \text{Profit %} & = \color{green} \frac{Profit}{C.P} \times 100 \\ \\ & = \frac{{\cancel{80}}^{4}}{{\cancel{820}}^{41}} \times 100 \\ \\ & = \frac{400}{41} \% \\ \end{align*} \]
AnswerProfit \( = \color{red} \frac{400}{41} \% \)
2. 400 mangoes were purchased at ₹ 125 per hundred and sold at a loss of ₹ 100. Find the S.P. of one dozen mangoes.
Solution
\[ \begin{align*} \text{C.P of 100 mangoes} & = \text{₹} 125 \\ \\ \text{C.P of 1 mangoes} & = \frac{125}{100} \\ \\ \text{C.P of 400 mangoes} & = \frac{125}{{\cancel{100}}^{1}} \times {\cancel{400}}^{4} \\ \\ \text{C.P} & = \text{₹} 500 \\ \text{Loss} & = \text{₹} 100 \\ \color{green} \text{S.P} & = \color{green} C.P - Loss \\ & = 500 - 100 \\ & = 400 \\ \\ \text{S.P of 400 mangoes} & = \text{₹}400 \\ \\ \text{S.P of 1 mangoes} & =\frac{400}{400} \implies \text{₹}1 \\ \\ \text{S.P of 12 mangoes} & = 1 \times 12 \implies \text{₹}12 \\ \\ \end{align*} \]
Answer S.P. of one dozen mangoes \( = \color{red}\text{₹} 12 \)
3. A man purchased a cell phone for ₹ 2,000. By paying ₹ 200 more, he replaces its body (case). If he sells the cell phone for ₹ 2,500, find his profit or loss per cent.
Solution
\[ \begin{align*} \text{C.P of cell phone} & = \text{₹} 2000 \\ \text{Overhead expenses} & = \text{₹} 200 \\ \\ \text{Actual C.P} & = 2000 + 200 \\ & = \text{₹} 2200 \\ \\ \text{S.P of cell phone} & = \text{₹} 2500 \\ \\ \color{green} \text{Profit} & = \color{green} \text{S.P} - \text{C.P} \\ & = 2500 - 2200 \\ & = 300 \\ \\ \color{green} \text{Profit %} & = \color{green} \frac{\text{Profit}}{\text{C.P}} \times 100 \\ \\ & = \frac{{\cancel{300}}^{\color{violet}150}}{{{\cancel{2200}}^{\cancel{22}}}^{\color{violet}11}} \times {\cancel{100}}^{1} \\ \\ & = \frac{150}{11}\% \\ \\ & = 13\frac{7}{11}\% \, \text{ or } \, 13.64\% \\ \end{align*} \]
Answer Profit % \( = \color{red} 13\frac{7}{11}\% \, \text{ or } \, 13.64\% \)
4. A man buys 5 dozen eggs at ₹ 36 per dozen. Out of which 5% got broken. He sold the remaining eggs for ₹ 48 per dozen. What was his total gain?
Solution
\[ \begin{align*} \text{C.P of 1 dozen eggs} & = \text{₹} 36 \\ \text{C.P of 5 dozen eggs} & = 36 \times 5 \\ & = \text{₹} 180 \\ \\ \text{Total eggs} & = 5 \, dozen \\ & = 5 \times 12 \\ & = 60 \, eggs \\ \\ \text{Broken eggs} & = 5\% \text{ of 60} \\ \\ & = \frac{{\cancel{5}}^{\color{red}1}}{{{\cancel{100}}^{\cancel{\color{red}20}}}^{\color{violet}1}} \times {\cancel{60}}^{\color{violet}3} \\ \\ & = 3 \, eggs \\ \\ \text{Remaining eggs} & = 60 - 3 \\ & = 57 \, eggs \\ \\ \text{S.P of 1 dozen (12 eggs)} & = \text{₹} 48 \\ \\ \text{S.P of 1 eggs} & = \frac{{\cancel{48}}^{4}}{{\cancel{12}}^{1}} \implies \text{₹} 4\\ \\ \text{S.P of 57 eggs} & = 4 \times 57 \\ & = \text{₹} 228 \\ \\ \text{Total gain} & = \text{S.P} - \text{C.P} \\ & = 228 - 180 \\ & = \text{₹} 48 \\ \end{align*} \]
Answer Total gain \( = \color{red}\text{₹} 48 \)
5. Rahul buys an almirah for ₹ 2,000 and spends ₹ 400 as its transportation charges. If he sells the almirah for ₹ 3,000, determine his profit per cent.
Solution
\[ \begin{align*} \text{C.P of almirah} & = \text{₹} 2000 \\ \text{Transportation charges} & = \text{₹} 400 \\ \\ \text{Actual C.P} & = 2000 + 400 \\ & = \text{₹} 2400 \\ \\ \text{S.P of almirah} & = \text{₹} 3000 \\ \\ \color{green} \text{Profit} & = \color{green} \text{S.P} - \text{C.P} \\ & = 3000 - 2400 \\ & = 600 \\ \\ \color{green} \text{Profit %} & = \color{green} \frac{\text{Profit}}{\text{C.P}} \times 100 \\ \\ & = \frac{{\cancel{600}}^{\color{red}1}}{{{\cancel{2400}}^{\cancel{\color{red}4}}}^{\color{green}1}} \times {\cancel{100}}^{\color{green}25} \\ \\ & = 25\% \\ \end{align*} \]
Answer Profit percentage \( = \color{red} 25\% \)