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
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.6 Q1.1
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.6 Q1.2

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
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.6 Q4.1

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:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.6 Q6.1

Question 7.
Find the area of a square lawn whose one side is 5\(\frac { 7 }{ 9 }\) m long.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.6 Q7.1

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:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.6 Q8.1
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.6 Q8.2

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:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.6 Q9.1

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:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.6 Q10.1
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.6 Q10.2

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 = \(\frac { 1 }{ 5 }\)
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.6 Q12.1

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 – (\(\frac { 2 }{ 5 }\) + \(\frac { 1 }{ 4 }\))
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.6 Q13.1

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
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.6 Q14.1

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
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.6 Q15.1

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 – \(\frac { 1 }{ 10 }\) = \(\frac { 9 }{ 10 }\)
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.6 Q16.1

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,
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.6 Q17.1

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,
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.6 Q18.1

ML Aggarwal Class 8 Solutions for ICSE Maths

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