DAV Class 7 Maths Chapter 5 Worksheet 1
Application of Percentage Worksheet 1
1. A property dealer charges 2% commission from a buyer or a seller of property. If Mr Ram Lal paid ₹ 20,000 as a commission for purchasing a flat, what was the value of the flat?
Solution
Let the value of the flat be \( = x \)\[ \begin{align*} \text{Commission} & = 2 \text{%} \\ \text{Paid Commission} & = \text{₹}20000 \\ 2 \text{% of } x & = 20000 \\ \\ \frac{2}{100} \times x & = 20000 \\ \\ x & = {\cancel{20000}}^{10000} \times \frac{100}{{\cancel2}^1} \\ \\ x & = 10000 \times 100 \\ x & = 1000000 \end{align*} \]
Answer Value of the flat \( = \color{red} \text{₹} 10,00,000 \)
2. A 3-star hotel in Delhi charges 10% sales tax on the price of the food taken. Mr Saxena and his family had food for ₹ 685. Find the total money he had to pay.
Solution
\[ \begin{align*} \text{Food bill} & = \text{ ₹}685 \\ \text{Sales Tax} & = 10\% \\ \text{Sales tax amount} & = 10 \text{ % of } \times 685 \\ \\ & = \frac{10}{100} \times 685 \\\\ & = \text{ ₹} 68.5 \\ \\ \text{Total amount to pay} & = 685 + 68.5 \\ & = \text{ ₹} 753.5 \end{align*} \]
Answer Total amount to be paid \( = \color{red} \text{₹} 753.50 \)
3. A painter paints 240 sq. feet of a wall. If this is 48% of the total wall surface, what is the area of the wall in sq. feet?
Solution
Let the total area of the wall be \( = x \text{ sq. ft.} \)\[ \begin{align*} \text{Painted area} & = 48\% \\ \text{Painted area} & = 240 \text{ sq. ft.} \\ 48 \text{ % of } x & = 240 \\ \\ \frac{48}{100} \times x & = 240 \\ \\ x & = {\cancel{240}}^5 \times \frac{100}{{\cancel{48}}^1} \\ & = 5 \times 100 \\ & = 500 \text{ sq. ft.} \end{align*} \]
Answer Total area of the wall \( = \color{red} 500 \text{ sq. ft.} \)
4. The salary of a person was increased by 15%. If his salary now is ₹ 9,936, what was his initial salary?
Solution
\[ \begin{align*} \text{Let initial salary be } & = x \text{ ₹} \\ \text{Increase in salary} & = 15\% \\ \text{Present salary} & = \text{ ₹} 9,936 \\ \\ x + (15 \text{ % of } x) & = 9936 \\ \\ x + \left(\frac{{\cancel{15}}^3}{{\cancel{100}}^{20}} \times x \right) & = 9936 \\ \\ x + \left(\frac{3}{20} \times x \right) & = 9936 \\ \\ x + \frac{3x}{20}& = 9936 \\ \\ \frac{20x + 3x}{20}& = 9936 \\ \\ \frac{23x}{20}& = 9936 \\ \\ x & = {\cancel{9936}}^{432} \times \frac{20}{{\cancel{23}}^1} \\ \\ x & =432 \times 20 \\ x & = 8640 \end{align*} \]
Answer Initial salary \( = \color{red} \text{₹} 8640 \)
5. In a co-educational school, 45% of the total students are girls. If there are 440 boys in the school, find the number of girls in the school.
Solution
Let the total number of students be \( = x \)\[ \begin{align*} \text{Girls } & = 45\% \\ \text{Boys} & = 100\% -45\% \\ & = 55\% \\ \text{Number of Boys } & = 440 \\ \\ 55 \text{ % of } x & = 440 \\ \\ \frac{55}{100} \times x & = 440 \\ \\ x & = {\cancel{440}}^{8} \times \frac{100}{{\cancel{55}}^{1}} \\ & = 8 \times 100 \\ & = 800 \\ \text{Number of girls} & = 800 - 440 \\ &= 360 \end{align*} \]
Answer Number of girls \( = \color{red} 360 \)
6. A potato seller sells 70% of the total potatoes and still has 150 kg potatoes left with him. Find the weight of potatoes he had originally.
Solution
Let the total weight of potatoes be \( = x \)\[ \begin{align*} \text{Sold potatoes } & = 70\% \\ \text{Unsold potatoes } & = 30\% \\ \text{Unsold potatoes } & = 150 \text{ kg} \\ 30 \text{ % of } x & = 150 \\ \\ \frac{30}{100} \times x & = 150 \\ x & = {\cancel{150}}^{5} \times \frac{100}{{\cancel{30}}^{1}} \\ & = 500 \text{ kg} \end{align*} \]
Answer Total weight of potatoes \( = \color{red} 500 \text{ kg} \)
7. In Rohan's birthday party, 90% of his friends came and three friends did not come. Find the total number of friends Rohan has.
Solution
Let the total number of friends be \( = x \)\[ \begin{align*} \text{Friends who came} & = 90\% \\ \text{Friends who didn't come} & = 10\% \\ \text{Friends who didn't come} & = 3 \\ \\ 10 \text{ % of } x & = 3 \\ \frac{10}{100} \times x & = 3 \\ x & = 3 \times \frac{100}{10} \\ & = 30 \end{align*} \]
Answer Total number of friends \( = \color{red} 30 \)
8. In a quiz competition, Ravi gave answers to 70% of the questions. He failed to give answers to six questions. Find the total number of questions asked in the quiz competition.
Solution
\[ \begin{align*} \text{Let the total number of questions be } & = x \\ \text{Ravi gave answers} & = 70\% \\ \text{Ravi failed to give answers} & = 30\% \\ \text{No. of questions not answered} & = 6 \\ 30 \text{ % of } x & = 6 \\ \frac{30}{100} \times x & = 6 \\ x & = {\cancel{6}}^{1} \times \frac{{\cancel{100}}^{\color{green}20}}{{{\cancel{30}}^{\cancel5}}^{\color{green}1}} \\ & = 20 \end{align*} \]
Answer Total number of questions \( = \color{red} 20 \)
9. Out of a class of 45 students, five were absent, 30% of the remaining had failed to do homework. Find the number of students who did the homework.
Solution
\[ \begin{align*} \text{Total students } & = 45 \\ \text{Absent students } & = 5 \\ \text{Remaining students } & = 40 \\ \text{Failed to do homework } & = 30\% \\ \text{Students who did the homework } & = 70\% \\ & = 70 \text{ % of } 40 \\ &= \frac{70}{100} \times 40 \\ &= 28 \text{ students} \end{align*} \]
Answer Number of students who did the homework \( = \color{red} 28 \)