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ICSE

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Ratio and Proportion Ex 7.1

Question 1.

An alloy consists of \(27 \frac { 1 }{ 2 } \) kg of copper and \(2 \frac { 3 }{ 4 } \) kg of tin. Find the ratio by weight of tin to the alloy

Solution:

Question 2.

Find the compounded ratio of:

(i) 2 : 3 and 4 : 9

(ii) 4 : 5, 5 : 7 and 9 : 11

(iii) (a – b) : (a + b), (a + b)^{2} : (a^{2} + b^{2}) and (a^{4} – b^{4}) : (a^{2} – b^{2})^{2}

Solution:

Question 3.

Find the duplicate ratio of

(i) 2 : 3

(ii) √5 : 7

(iii) 5a : 6b

Solution:

Question 4.

Find the triplicate ratio of

(i) 3 : 4

(ii) \(\\ \frac { 1 }{ 2 } \) : \(\\ \frac { 1 }{ 3 } \)

(iii) 1^{3} : 2^{3}

Solution:

Question 5.

Find the sub-duplicate ratio of

(i) 9 : 16

(ii) \(\\ \frac { 1 }{ 4 } \) : \(\\ \frac { 1 }{ 9 } \),

(iii) 9a^{2} : 49b^{2}

Solution:

Question 6.

Find the sub-triplicate ratio of

(i) 1 : 216

(ii) \(\\ \frac { 1 }{ 8 } \) : \(\\ \frac { 1 }{ 125 } \)

(iii) 27a^{3} : 64b^{3}

Solution:

Question 7.

Find the reciprocal ratio of

(i) 4 : 7

(ii) 3^{2} : 4^{2}

(iii) \(\frac { 1 }{ 9 } :2 \)

Solution:

Question 8.

Arrange the following ratios in ascending order of magnitude:

2 : 3, 17 : 21, 11 : 14 and 5 : 7

Solution:

Question 9.

(i) If A : B = 2 : 3, B : C = 4 : 5 and C : D = 6 : 7, find A : D

(ii) If x : y = 2 : 3, and y : z = 4 : 7, find x : y : z

Solution:

Question 10.

(i) If A : B = \(\frac { 1 }{ 4 } :\frac { 1 }{ 5 } \) and B : C = \(\frac { 1 }{ 7 } :\frac { 1 }{ 6 } \), find A : B : C.

(ii) If 3A = 4B = 6C, find A : B : C

Solution:

Question 11.

(i) If \(\frac { 3x+5y }{ 3x-5y } =\frac { 7 }{ 3 } \) , Find x : y

(ii) ) If a : b = 3 : 11, find (15a – 3b) : (9a + 5b). a

Solution:

Question 12.

(i) If (4x² + xy) : (3xy – y²) = 12 : 5, find (x + 2y) : (2x + y).

(ii) If y (3x – y) : x (4x + y) = 5 : 12. Find (x² + y²) : (x + y)².

Solution:

Question 13.

(i) If (x – 9) : (3x + 6) is the duplicate ratio of 4 : 9, find the value of x.

(ii) If (3x + 1) : (5x + 3) is the triplicate ratio of 3 : 4, find the value of x.

(iii) If (x + 2y) : (2x – y) is equal to the duplicate ratio of 3 : 2, find x : y.

Solution:

Question 14.

(i) Find two numbers in the ratio of 8 : 7 such that when each is decreased by \(12 \frac { 1 }{ 2 } \), they are in the ratio 11 : 9.

(ii) The income of a man is increased in the ratio of 10 : 11. If the increase in his income is Rs 600 per month, find his new income.

Solution:

Question 15.

(i) A woman reduces her weight in the ratio 7 : 5. What does her weight become if originally it was 91 kg?

(ii) A school collected Rs 2100 for charity. It was decided to divide the money between an orphanage and a blind school in the ratio of 3 : 4. How much money did each receive?

Solution:

Question 16.

(i) The sides of a triangle are in the ratio 7 : 5 : 3 and its perimeter is 30 cm. Find the lengths of sides.

(ii) If the angles of a triangle are in the ratio 2 : 3 : 4, find the angles.

Solution:

Question 17.

Three numbers are in the ratio \(\frac { 1 }{ 2 } :\frac { 1 }{ 3 } :\frac { 1 }{ 4 } \) If the sum of their squares is 244, find the numbers.

Solution:

Question 18.

(i) A certain sum was divided among A, B and C in the ratio 7 : 5 : 4. If B got Rs 500 more than C, find the total sum divided.

(ii) In a business, A invests Rs 50000 for 6 months, B Rs 60000 for 4 months and C, Rs 80000 for 5 months. If they together earn Rs 18800 find the share of each.

Solution:

Question 19.

(i) In a mixture of 45 liters, the ratio of milk to water is 13 : 2. How much water must be added to this mixture to make the ratio of milk to water as 3 : 1?

(ii) The ratio of the number of boys to the number of girls in a school of 560 pupils is 5 : 3. If 10 new boys are admitted, find how many new girls may be admitted so that the ratio of the number of boys to the number of girls may change to 3 : 2.

Solution:

Question 20.

(i) The monthly pocket money of Ravi and Sanjeev are in the ratio 5 : 7. Their expenditures are in the ratio 3 : 5. If each saves Rs 80 every month, find their monthly pocket money.

(ii) In class X of a school, the ratio of the number of boys to that of the girls is 4 : 3. If there were 20 more boys and 12 fewer girls, then the ratio would have been 2 : 1, How many students were there in the class?

Solution:

Question 21.

In an examination, the ratio of passes to failures was 4 : 1. If 30 less had appeared and 20 less passed, the ratio of passes to failures would have been 5 : 1. How many students appeared for the examination

Solution:

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