## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.6

Question 1.

In a bag, there are 20 kg of fruits. If 7\(\frac { 1 }{ 6 }\) kg of these fruits be oranges and 8\(\frac { 2 }{ 3 }\) kg of thee are apples and rest are grapes. Find the mass of the grapes in the bag.

Solution:

Total fruits in a bag = 20 kg

Question 2.

The population of a city is 6,63,432. If \(\frac { 1 }{ 2 }\) of the population are adult males and \(\frac { 1 }{ 3 }\) of the population are adult females, then find the number of children in the city.

Solution:

Population of a city = 6,63,432

Number of adult males = \(\frac { 1 }{ 2 }\) of 6,63,432 = 3,31,716

Number of adult females = \(\frac { 1 }{ 3 }\) of 6,63,432 = 2,21,144

Remaining population = 6,63,432 – (3,31,716 + 2,21,144)

= 6,63,432 – 5,52,860

= 1,10,572

Number of children = 1,10,572

Question 3.

In an election of housing society, there are 30 voters. Each of them gives the vote. Three persons X, Y and Z are standing for the post of Secretary. If Mr X got \(\frac { 2 }{ 5 }\) of the total votes and Mr Z got \(\frac { 1 }{ 3 }\) of the total votes, then find the number of votes which Mr Y got.

Solution:

Number of voters = 30

and number of person for election = X, Y, Z

X get \(\frac { 2 }{ 5 }\) of total votes = \(\frac { 2 }{ 5 }\) of 30 = 12

Z get \(\frac { 1 }{ 3 }\) of total votes = \(\frac { 1 }{ 3 }\) of 30 = 10

Remaining votes = 30 – (12 + 10) = 30 – 22 = 8

Y gets votes = 8

Question 4.

A person earns ₹ 100 in a day. If he spent ₹ 14\(\frac { 2 }{ 7 }\) on food and ₹ 30\(\frac { 2 }{ 3 }\) on petrol. How much did he save on that day?

Solution:

A man’s earnings per day = ₹ 100

Question 5.

In an examination, 400 students appeared. If \(\frac { 2 }{ 3 }\) of the boys and all 130 girls passed in examination, then find how many boys failed in examination?

Solution:

Number of students appears = 400

Number of boys = \(\frac { 2 }{ 3 }\) of total boys passed the examination

and all girls 130 passed

Number of total boys = 400 – 130 = 270

Number of students passed = \(\frac { 2 }{ 3 }\) of 270 = 180

and number of boys failed = 270 – 180 = 90

Question 6.

A car is moving at the speed of 40\(\frac { 2 }{ 3 }\) km/h. Find how much distance will it cover in \(\frac { 9 }{ 10 }\) hrs?

Solution:

Question 7.

Find the area of a square lawn whose one side is 5\(\frac { 7 }{ 9 }\) m long.

Solution:

Question 8.

Perimeter of a rectangle is 15\(\frac { 3 }{ 7 }\) m. If the length is 4\(\frac { 2 }{ 7 }\) m, find its breadth.

Solution:

Question 9.

Rahul had a rope of 325\(\frac { 4 }{ 5 }\) m long. He cut off a 150\(\frac { 3 }{ 5 }\) m long piece, then he divided the rest of the rope into 3 parts of equal length. Find the length of each part.

Solution:

Question 10.

If 3\(\frac { 1 }{ 2 }\) litre of petrol costs ₹ 270\(\frac { 3 }{ 8 }\), then find the cost of 4 litre of petrol.

Solution:

Question 11.

Ramesh earns ₹ 40,000 per month. He spends \(\frac { 3 }{ 8 }\) of the income on food, \(\frac { 1 }{ 5 }\) of the remaining on LIC premium and then \(\frac { 1 }{ 2 }\) of the remaining on other expenses. Find how much money is left with him?

Solution:

Monthly earnings of Ramesh = ₹ 40000

Expenditure on food = \(\frac { 3 }{ 8 }\) of ₹ 40000 = ₹ 15000

Remaining income = 40000 – 15000 = ₹ 25000

Expenditure on LIC premium = \(\frac { 1 }{ 5 }\) of ₹ 25000 = ₹ 5000

Remaining amount = ₹ 25000 – ₹ 5000 = ₹ 20000

Expenditure on other expenses = \(\frac { 1 }{ 2 }\) of ₹ 20000 = ₹ 10000

Remaining amount left = ₹ 20000 – ₹ 10000 = ₹ 10000

Question 12.

A, B, C, D and E went to a restaurant for dinner. A paid \(\frac { 1 }{ 2 }\) of the bill, B paid \(\frac { 1 }{ 5 }\) of the bill and rest of the bill was shared equally by C, D and E. What fraction of the bill was paid by each?

Solution:

Let total bill of the restaurant = 1

A pays the bill = \(\frac { 1 }{ 2 }\)

B pays the bill = \(\frac { 1 }{ 5 }\)

Question 13.

\(\frac { 2 }{ 5 }\) of total number of students of a school come by car while \(\frac { 1 }{ 4 }\) of students come by bus to school. All the other students walk to school of which \(\frac { 1 }{ 3 }\) walk on their own and the rest are escorted by their parents. If 224 students come to school walking on their own, how many students study in the school? Solution:

Let total number of students = 1

Students who come by car = \(\frac { 2 }{ 5 }\)

Who come by bus = \(\frac { 1 }{ 4 }\)

Who come walking = \(\frac { 1 }{ 3 }\) of remaining

Rest student = 1 – (\(\frac { 2 }{ 5 }\) + \(\frac { 1 }{ 4 }\))

Question 14.

A mother and her two sons got a room constructed for ₹ 60,000. The elder son contributes \(\frac { 3 }{ 8 }\) of his mother’s contribution while the younger son contributes \(\frac { 1 }{ 2 }\) of his mother’s share. How much do the three contribute individually?

Solution:

Cost of a room = ₹ 60000

Contribution of elder son = \(\frac { 3 }{ 8 }\) of her mother’s contribution

and contribution of younger son = \(\frac { 1 }{ 2 }\) of his mother’s share

Let mother contribution = 1

Then elder son’s contribution = \(\frac { 3 }{ 8 }\)

and younger’s = \(\frac { 1 }{ 2 }\)

Now ratios in their share = 1 : \(\frac { 3 }{ 8 }\) : \(\frac { 1 }{ 2 }\)

= 8 : 3 : 4

Sum of ratios = 8 + 3 + 4 = 15

Question 15.

In a class of 56 students, the number of boys is \(\frac { 2 }{ 5 }\) th of the number of girls. Find the number of boys and girls.

Solution:

Number of students in a class = 56

Let number of girls = 1

Question 16.

A man donated \(\frac { 1 }{ 10 }\) of his money to a school, \(\frac { 1 }{ 6 }\) th of the remaining to a church and the remaining money he distributed equally among his three children. If each child gets ₹ 50000, how much money did the man originally have?

Solution:

Let total money of a man = 1

Amount donated to a school = \(\frac { 1 }{ 10 }\)

Remaining money = 1 – \(\frac { 1 }{ 10 }\) = \(\frac { 9 }{ 10 }\)

Question 17.

If \(\frac { 1 }{ 4 }\) of a number is added to \(\frac { 1 }{ 3 }\) of that number, the result is 15 greater than half of that number. Find the number.

Solution:

Let a number be = x

Then according to the condition,

Question 18.

A student was asked to multiply a given number by \(\frac { 4 }{ 5 }\). By mistake, he divided the given number by \(\frac { 4 }{ 5 }\). His answer was 36 more than the correct answer. What was the given number?

Solution:

Let given number = x

According to the condition,