DAV Class 7 Maths Chapter 5 Practice Worksheet
Application of Percentage Practice Worksheet
1. Express (i) \( \color{black} 75\% \) (ii) \( \color{black} 128.8\% \) (iii) \( \color{black} 3\dfrac{3}{4}\% \ \) as decimals.
Solution
\[ \begin{aligned} \color{magenta} \textbf{(i)} & \quad \color{magenta} 75\% \\[8pt] &= \frac{75}{100} \\[8pt] &= 0.75 \\[8pt] \color{magenta} \textbf{(ii)} & \quad \color{magenta} \ 128.8\% \\[8pt] &= \frac{128.8}{100} \\[8pt] &= 1.288 \\[8pt] \color{magenta} \ \textbf{(iii)} & \quad \color{magenta} \ 3\dfrac{3}{4}\% \\[8pt] &= \dfrac{15}{4}\% \\[8pt] &= \frac{15}{4\times100} \\[8pt] &= \frac{3.75}{100} \\[8pt] &= 0.0375 \end{aligned} \]
Answer (i) \( \color{red} 0.75 \ \) (ii) \( \color{red} 1.288 \ \) (iii) \( \color{red} 0.0375 \ \)
2. Express the following as percents : (i) \( \color{black} 0.275 \) (ii) \( \color{black} 4:5 \) (iii) \( \color{black} 0.24 \) (iv) \( \color{black} 7:20 \) (v) \( \color{black} 4.05 \).
Solution
\[ \begin{aligned} \color{magenta}\textbf{(i)} & \quad \color{magenta} 0.275 \\ &= 0.275 \times 100\% \\ &= 27.5\% \\[10pt] \color{magenta}\textbf{(ii)} & \quad \color{magenta} 4:5 \\[8pt] &= \frac{4}{5} \\[8pt] &= \frac{4}{5} \times 100\% \\[8pt] &= 80\% \\[10pt] \color{magenta}\textbf{(iii)} & \quad \color{magenta} 0.24 \\ &= 0.24 \times 100\% \\ &= 24\% \\[10pt] \color{magenta}\textbf{(iv)} & \quad \color{magenta} 7:20 \\[8pt] &= \frac{7}{20} \\[8pt] &= \frac{7}{20} \times 100\% \\[8pt] &= 35\% \\[10pt] \color{magenta}\textbf{(v)} & \quad \color{magenta} 4.05 \\ &= 4.05 \times 100\% \\ &= 405\% \end{aligned} \]
Answer (i) \( \color{red}{27.5\%} \ \) (ii) \( \color{red}{80\%} \ \) (iii) \( \color{red}{24\%} \ \) (iv) \( \color{red}{35\%} \ \) (v) \( \color{red}{405\%} \ \)
3. A basket contains 350 eggs. If \(1\%\) of the eggs are rotten, find the number of eggs good enough to be sold.
Solution
\[ \begin{aligned} \text{Total eggs} &= 350 \\[4pt] \text{Rotten eggs} &= 1\% \text{ of } 350 \\[8pt] &= \frac{1}{100}\times350 \\[8pt] &= 3.5 \text{ eggs} \\[4pt] \text{Good eggs} &= 350 - 3.5 \\ &= 346.5 \text{ eggs} \\ & \implies 346 \text{ eggs} \end{aligned} \]
Answer Eggs good enough to be sold \( = \color{red}{346 \ eggs}\)
4. A man spends \(92\%\) of his monthly income. If he saves ₹ 220 per month, what is his monthly income?
Solution
\[ \begin{aligned} \text{Let his monthly income be } x \end{aligned} \] \[ \begin{aligned} \text{Savings} &= \text{₹ } 220 \\ \% \text{ spent} &= 92\% \\ \% \text{ saved} &= 100\% - 92\% \\ &= 8\% \\[4pt] 8\% \text{ of } x &= 220 \\[8pt] \frac{8}{100} \times x &= 220 \\[8pt] x &= \frac{{\cancel{220}}^{55}\times \cancel{100}^{50}}{{\cancel{8}}_{\cancel2_1}} \\[8pt] x &= 55 \times 50 \\[8pt] x &= 2750 \end{aligned} \]
Answer Monthly income \( = \color{red}\text{₹ }2750\)
5. \(45\%\) of the students in a school are boys. If the total number of students in the school is 880, find the number of girls in the school.
Solution
\[ \begin{aligned} \text{Total students} &= 880 \\[4pt] \% \text{ Boys} &= 45\% \\ \% \text{ Girls} &= 100 \% - 45\% \implies 55\% \\[8pt] \text{Number of girls} &= 55\% \text{ of } 880 \\[8pt] &= \frac{\cancel{55}^{11}}{\cancel{100}_{\cancel{20}_1}}\times \cancel{880}^{ \ 44} \\[8pt] &= 11 \times 44 \\[8pt] \text{Number of girls} &= 484 \end{aligned} \]
Answer Number of girls \( = \color{red}{484}\)
6. In an examination, \(92\%\) of the candidates passed and 46 candidates failed. How many candidates appeared in the examination?
Solution
\[ \begin{aligned} \text{Let the total number of candidates be } x \end{aligned} \] \[ \begin{aligned} \% \text{ Passed} &= 92\% \\[2pt] \% \text{ Failed} &= 100\% - 92\% \\ &= 8\% \\[4pt] 8\% \text{ of } x &= 46 \\ \frac{8}{100} \times x &= 46 \\[4pt] x &= \cancel{46}^{23} \times \frac{\cancel{100}^{25}}{\cancel8_{\cancel4_1}} \\ &= 23 \times 25 \\ &= 575 \end{aligned} \]
Answer Number of candidates who appeared \( = \color{red}{575}\)
7. If \(m\%\) of 75 is 12, then find the value of \(m\).
Solution
\[ \begin{aligned} m\% \text{ of } 75 &= 12 \\[8pt] \frac{m}{100}\times75 &= 12 \\[8pt] m &= \frac{{\cancel{12}}^{4}\times \cancel{100}^{\ 4}}{\cancel{75}_{\cancel{25}_1}} \\[8pt] &= 4 \times 4 \\ &= 16 \end{aligned} \]
Answer \(m = \color{red}{16}\)
8. Find the gain or loss percent, when :
(a) C.P = ₹ 3500, Overhead expenses = ₹ 150 and loss = ₹ 146
Solution
\[ \begin{aligned} \text{C.P} &= \text{₹ }3500 \\ \text{Overhead expenses} &= \text{₹ }150 \\ \text{Actual C.P} &= 3500 + 150 \\ & \implies \text{₹ }3650 \\[4pt] \text{Loss} &= \text{₹ }146 \\[4pt] \color{green}\text{Loss }\% &= \color{green}\frac{\text{Loss}}{\text{C.P}}\times 100 \\[8pt] &= \frac{\cancel{146}^{\ 2}}{\cancel{3650}_{\cancel{50}_1}}\times \cancel{100}^{2} \\[8pt] &= 2 \times 2 \\[8pt] &= 4\% \end{aligned} \]
Answer Loss \( = \color{red}{4\%}\)
(b) C.P = ₹ 2300, Overhead expenses = ₹ 300 and gain = ₹ 260
Solution
\[ \begin{aligned} \text{C.P} &= \text{₹ }2300 \\ \text{Overhead expenses} &= \text{₹ }300 \\ \text{Actual C.P} &= 2300 + 300\\&= \text{₹ }2600 \\[4pt] \text{Gain} &= \text{₹ }260 \\[4pt] \color{green}\text{Gain } \% &= \color{green}\frac{\text{Gain}}{\text{C.P}}\times100 \\[8pt] &= \frac{260}{2600}\times100 \\[8pt] &= 10\% \end{aligned} \]
Answer Gain \( = \color{red}{10\%}\)
9. Jyotsna bought 400 eggs at Rs. 8.40 a dozen. At what price per hundred must she sell them so as to earn a profit of \(15\%\)?
Solution
\[ \begin{aligned} \text{C.P of 12 eggs} &= \text{₹ }8.40 \\[8pt] \text{C.P of 1 egg} &= \frac{8.40}{12} \\[8pt] \text{C.P of 400 eggs} &= \frac{8.40}{12} \times 400 \\[8pt] &= \frac{\cancel{84}^7}{\cancel{12}_1} \times 40 \\[8pt] &= \text{₹ }280 \\[8pt] \text{Profit } \% &= 15\% \\[8pt] \text{Profit} &= 15\% \text{ of } 280 \\[8pt] &= \frac{15}{100}\times280 \\[8pt] Profit &= \text{₹ }42 \\[8pt] \text{S.P of 400 eggs} &= 280 + 42 \\[8pt] & \implies \text{₹ }322 \\[8pt] \text{S.P of 100 eggs} &= \frac{322}{4} \\[8pt] &= \text{₹ }80.50 \end{aligned} \]
Answer Selling price per 100 eggs \( = \color{red}\text{₹ }80.50\)