# DAV Class 7 Maths Chapter 5 Worksheet 1 Solutions

The DAV Class 7 Maths Solutions and DAV Class 7 Maths Chapter 5 Worksheet 1 Solutions of Application of Percentage offer comprehensive answers to textbook questions.

## DAV Class 7 Maths Ch 5 WS 1 Solutions

Question 1.
A property dealer charges 2% commission from a buyer or a seller of property. If Mr. Ram Lai paid ₹ 20,000 as a commission for purchasing aflat, what was the value of the flat?
Answer:
Let the value of the flat be ₹ x
Commission = $$\frac{2}{100}$$x
$$\frac{2}{100}$$x = 20000
x = 20000 × $$\frac{100}{2}$$
⇒ x = 10000 × 100 = 1000000
Hence the value of flat = ₹ 1000000

Question 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.
Answer:
Price of food = ₹ 685
Sales Tax = $$\frac{10}{100}$$ × 685
= ₹ 68.50
∴ Money paid by Mr. Saxena = ₹ (685 + 68.50)
= ₹ 753.50

Question 3.
A painter paints 240 feet of a wall. If this is 48% of the total wall surface, what is the area of the wall in sq. feet?
Answer:
Let the total surface area of the wall be x sq. feet
∴ 48% of x = 240
⇒ $$\frac{48}{100}$$ × x
= 240
⇒ x = $$\frac{240 \times 100}{48}$$
= 500 sq.feet
Hence the surface area of the wall = 500 sq. feet.

Question 4.
The salary of a person was increased by 15%. If his salary now is ₹ 9936, what was his initial salary?
Answer:
Let the initial salary be ₹ x
Increase in salary = $$\frac{15}{100}$$ × x
= ₹ $$\frac{3}{20}$$ x
Now increased salary = x + $$\frac{3}{20}$$x
= ₹ $$\frac{23}{20}$$ x
∴ $$\frac{23}{20}$$ x = 9936
⇒ x = 9936 × $$\frac{20}{23}$$
= ₹ 8640
Hence the initial salary was ₹ 8640

Question 5.
In a co-education school, 45% of the total students are girls, If there are 440 boys in the school, find the number of girls in the school.
Answer:
Let total number of students be x
Number of girls = $$\frac{45}{100}$$ × x
= $$\frac{9}{20}$$x
Number of boys = x – $$\frac{9x}{20}$$
= $$\frac{11 x}{20}$$
$$\frac{11 x}{20}$$ = 440
⇒ x = $$\frac{440 \times 20}{11}$$
⇒ x = 800
Number of girls = $$\frac{9}{20}$$ × 800 = 360
Hence, the number of girls = 360

Question 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.
Answer:
Let the weight of potatoes originally be x kg
Weight of potatoes sold = $$\frac{70}{100}$$kg
= $$\frac{7}{10}$$x kg
Left quantities of potatoes = x – $$\frac{7}{10}$$x
= $$\frac{3 x}{10}$$kg
$$\frac{3 x}{10}$$ = 150
⇒ x = $$\frac{150 \times 10}{3}$$ = 500 kg
Hence the original weight of potatoes = 500 kg

Question 7.
In Rohan’s birthday party, 90% of his friends came and 3 friends did not come. Find the total number of friends Rohan has.
Answer:
Let the total number of friends be x
Number of friends who attended the party = $$\frac{90}{100}$$x = $$\frac{9}{10}$$x
and 3 friends did not attend
$$\frac{9}{10}$$x + 3 = x
x – $$\frac{9x}{10}$$ = 3
$$\frac{x}{10}$$ = 3
x = 30
Hence the total number of friends = 30

Question 8.
In a quiz competition, Ravi gave answer of 70% of the questions. He failed to give answers of 6 questions. Find the total number of questions asked in the quiz competition.
Answer:
Let the total number of questions be x
∴ Number of answers given = x × $$\frac{70}{100}=\frac{7 x}{10}$$
Number of answers not given = x – $$\frac{7 x}{10}=\frac{3 x}{10}$$
$$\frac{3 x}{10}$$ = 6
⇒ x = $$\frac{6 \times 10}{3}$$
x = 20
Hence total number of questions = 20

Question 9.
Out of a class of 45 students, 5 were absent, 30% of the remaining has failed to do homework. Find the number of students who did the homework.
Answer:
Number of students in the class = 45
Number of absent students = 5
Number of present students = 45 – 5 = 40
Number of students who did not do homework = $$\frac{30}{100}$$ × 40 = 12
Number of students who did the homework = 40 – 12 = 28
Hence the number of students who did the homework = 28.

### DAV Class 8 Maths Chapter 5 Worksheet 1 Notes

• Percent means per hundred. It is represented by %.
e.g. 19% = $$\frac{19}{100}$$
• 4% = $$\frac{4}{100}$$
• 0.6% = $$\frac{0.6}{100}$$ etc.
• Percent can be converted into fraction, ratio and decimal.
• If S.P. > C.P., then there is a profit.
• If C.P. > S.P., then there is a loss.
• Profit = S.P. – C.P.
• Loss = C.P. – SP.
• Profit percent or loss percent are always calculated on C.P.
• Profit % = $$\frac{\text { Profit }}{\text { C.P. }}$$ × 100
• Loss% = $$\frac{\text { Loss }}{\text { C.P. }}$$ × 100
• S.P. = C.P. [1 + $$\frac{\mathrm{P} \%}{100}$$]
• S.P. = C.P. [1 – $$\frac{\mathrm{L} \%}{100}$$]

Simple Interest (S.I.) = $$\frac{\text { Principal } \times \text { Rate } \times \text { Time }}{100}$$
Amount = Principal + S.I.

Example 1:
Express the following percents in lowest terms.

(i) 7$$\frac{1}{2}$$ %
Answer:
7$$\frac{1}{2}$$ %
= $$\frac{15}{2}$$ %
= $$\frac{15}{2} \times \frac{1}{100}$$
= $$\frac{3}{40}$$

(ii) 4%
Answer:
4% = $$\frac{4}{100}$$
= $$\frac{2}{50}$$

(iii) 0.25%
Answer:
0.25% = $$\frac{0.25}{100}$$
= $$\frac{25}{100 \times 100}$$
= $$\frac{1}{400}$$

(iv) 12.5%
Answer:
12.5% = $$\frac{12.5}{100}$$
= $$\frac{125}{100 \times 10}$$
= $$\frac{1}{8}$$

Example 2:
In a class of 40 students, 25% like football, 40% like cricket and rest of the students like tennis to play. Find the number of students who like tennis to play.
Answer:
Number of students who like football = 40 × $$\frac{25}{100}$$ = 10
Number of students who like cricket = 40 × $$\frac{40}{100}$$ = 16
Number of students who like tennis = 40 – (10 + 16)
= 40 – 26 = 14.

Example 3:
Ramesh purchases sorne goods for ₹ 25000 and spends ₹ 250 as overhead. He sold them at a profit of 12%. Find the selling price of the goods.
Answer:
C.P. = ₹ 25000
Overhead = ₹ 250
Total C.P. = ₹ 25000 + ₹ 250 = ₹ 25250
Profit = $$\frac{12}{100}$$ × 25250
= ₹ 3030

Example 4:
Find the simple interest on ₹ 1500 for 3 years at 5% per annum. Also, find the amount.
Solution:
Here P = ₹ 1500,
T = 3 years,
R = 5% p.a.
S.I. = $$\frac{P \times R \times T}{100}$$
S.I. = $$\frac{1500 \times 5 \times 3}{100}$$
= ₹ 225
A = P + S.I.
= ₹ 1500 + ₹ 225 = ₹ 1725.