## ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 7 Percentage and Its applications Check Your Progress

Question 1.

Convert the following percentages into fractions in the simplest form:

(i) 12\(\frac { 1 }{ 2 }\) %

(ii) 66\(\frac { 2 }{ 3 }\) %

(iii) 8\(\frac { 1 }{ 3 }\) %

Solution:

Question 2.

Express each of the following fractions as a percentage:

(i) \(\frac { 5 }{ 8 }\)

(ii) \(\frac { 13 }{ 40 }\)

(iii) \(\frac { 7 }{ 6 }\)

Solution:

Question 3.

Express each of the following percentages as a decimal:

(i) 122%

(ii) 2.2%

(iii) 3\(\frac { 1 }{ 8 }\) %

Solution:

Question 4.

Express 0.0345 as a percentage.

Solution:

0.0345 as percentage = \(\frac { 0.0345 }{ 100 }\) = 3.45 %

Question 5.

Convert each part of the ratio 5 : 6 : 9 to a percentage.

Solution:

5 : 6 : 9

Sum of ratio = 5 + 6 + 9 = 20

Question 6.

(i) What percent of a day is half an hour?

(ii) What percent is \(\frac { 3 }{ 4 }\) metres of 4\(\frac { 1 }{ 2 }\) metres?

Solution:

(i) Half an hour = \(\frac { 1 }{ 2 }\) hour

Hours in a day = 24 hours

Question 7.

The population of a town decreased from 25000 to 24500. Find the percentage decrease.

Solution:

Decrease in population of a town = 25000 – 24500 = 500

Decrease % = \(\frac { 500\times 100 }{ 25000 }\) = 2%

Question 8.

Arun bought a car for ₹ 350000. The next year, the price went upto ₹ 370000. What was the precentage increase in the price?

Solution

C.P. of a car = ₹ 350000

Next year, price of car was = ₹ 320000

Increase = ₹ 370000 – ₹ 350000 = ₹ 20000

Increase % = \(\frac { 20600\times 100 }{ 350000 }\)

= \(\frac { 40 }{ 7 }\) % = 5\(\frac { 5 }{ 7 }\) %

Question 9.

The population of a village has decreased by 6%. If the original population was 3650, find the population after decrease.

Solution:

Decrease in population of a village = 6%

Original population = 3650

Question 10.

43% of the students in a school are girls. If the number of boys is 1482, find:

(i) the total strength of the school

(ii) number of girls in the school.

Solution:

In a school, percentage of girls = 43%

Percentage of boys = 100 – 43 = 57%

Number of boys = 1482

(i) 52% of total students = 1482

Total students = \(\frac { 1482\times 100 }{ 57 }\) = 2600 students

(ii) Number of girls = 2600 – 1482 = 1118 girls

Question 11.

Rohan bought a calculator for ₹ 760 and sold it for ₹ 874. Find his profit and profit percentage.

Solution:

C.P. of a calculator = ₹ 760 and S.P. = ₹ 874

Profit = S.P. – C.P. = ₹ 874 – ₹ 760 = ₹ 114

Question 12.

On selling an article for ₹ 1027, Meena suffered a loss of ₹ 273. Find her loss percentage.

Solution:

S.P. of an article = ₹ 1027

Loss = ₹ 273

C.P. = S.P. + Loss = ₹ 1027 + ₹ 273 = ₹ 1300

Question 13.

By selling a fan for ₹ 710, a trader suffers a loss of ₹ 40. Find the cost price of the fan. At what price this fan should be sold in order to gain 10%?

Solution:

S.P. of a fan = ₹ 710

Loss = ₹ 40

C.P. = S.P. + Loss = ₹ 710 + ₹ 40 = ₹ 750

If Gain = 10%

Question 14.

A shopkeeper sells an article at ₹ 300, thus earning a profit of 20%. Find the cost price of the article.

Solution:

S.P. of an article = ₹ 300

Profit = 20%

Question 15.

A shopkeeper sells an article at ₹ 320, thus suffering a loss of 20%. Find the cost price of the article.

Solution:

S.P. of an article = ₹ 320

Loss = 20%

Question 16.

If ₹ 6000 is borrowed at 6.5% per annum simple interest, find the interest and the amount to be paid at the end of 3 years.

Solution:

Principal (P) = ₹ 1600

Rate (R) = 6.5% p.a.

Time (T) = 3 years

and amount = P + S.I. = ₹ 6000 + ₹ 1170 = ₹ 7170

Question 17.

How long will it take for ₹ 1860 invested at the rate of 9.5% per annum simple interest to amount to ₹ 2449?

Solution:

Principal (P) = ₹ 1860

Amount (A) = ₹ 12449

S.I. = A – P = ₹ 2445 – ₹ 1860 = ₹ 589

Question 18.

At what rate will ₹ 7200 fetch a simple interest of ₹ 3024 in 4 years?

Solution:

Principal (P) = ₹ 7200

S.I. = ₹ 3024

Time = 4 years

Question 19.

What sum of money will yield a simple interest of ₹ 1155in 3 years 6 months at 11% p.a.?

Solution:

S.I. = ₹ 1155

Rate (R) = 11% p.a.

Time (T) = 3 years 6 months