## RS Aggarwal Class 7 solutions of Chapter 8 Ratio and Proportion CCE Test Paper in pdf free download

**Question 1.****Compare 4 : 5 and 7 : 9.****Solution:**

**Question 2.****Divide ₹ 1100 among A, B and C in the ratio 2 : 3 : 5.****Solution:**

The sum of ratio terms is = 2 + 3 + 5 = 10

Then, we have :

A’s share = ₹ x 1100 = ₹ 220

B’s share = ₹

C’s share = ₹ x 1100 = ₹ 550

**Question 3.****Show that the numbers 25, 36, 5, 6 are not in proportion.****Solution:**

Product of the extremes = 25 x 6 = 150

Product of the means = 36 x 5 = 180

The product of the extremes is not equal to that of the means.

Hence, 25, 36, 5 and 6 are not in proportion.

**Question 4.****If x, 18, 108 are in continued proportion, find the value of x.****Solution:**

x : 18 :: 18 : 108

⇒ x x 108 = 18 x 18

(Product of extremes = Product of means)

⇒ 108x = 324

⇒ x = 3

Hence, the value of x is 3.

**Question 5.****Two numbers are in the ratio 5 : 7. If the sum of these numbers is 84, find the numbers.****Solution:**

Suppose that the numbers are 5x and 7x

Then, 5x + 7x = 84

12x = 84

x = 7

Hence, the numbers are (5 x 7) = 35 and (7 x 7) = 49.

**Question 6.****The ages of A and B are in the ratio 4 : 3. Eight years ago, their ages were in the ratio 10 : 7. Find their present ages.****Solution:**

Suppose that the present ages of A and B are 4x yrs and 3x yrs, respectively

Eight years ago, age of A = (4x – 8) yrs

Eight years ago, age of B = (3x – 8) yrs

Then,

(4x – 8) : (3x – 8) = 10 : 7

⇒ =

⇒ 28x – 56 = 30x – 80

⇒ 2x = 24

⇒ x = 12

**Question 7.****If a car covers 54 km in an hour, how much distance will it cover in 40 minutes ?****Solution:**

Distance covered in 60 min = 54 km

Distance covered in 1 min = km

Distance covered in 40 min = x 40 = 36 km

**Question 8.****Find the third proportional to 8 and 12.****Solution:**

Suppose that the third proportional to 8 and 12 is x

Then, 8 : 12 :: 12 : x

⇒ 8x = 144 (Product of extremes = Product of means)

x = 18

Hence, the third proportional is 18.

**Question 9.****If 40 men can finish a piece of work in 60 days, in how many days will 75 men finish the same work ?****Solution:**

40 men can finish the work in 60 days

1 man can finish the work in 60 x 40 days [Less men, more days]

75 men will finish the work in = = 32 days

Hence, 75 men will finish the same work in 32 days.

**Mark (✓****) against the correct answer in each of the following :****Question 10.****If 2A = 3B = 4C then A : B : C = ?****(a) 2 : 3 : 4****(b) 3 : 4 : 6****(c) 4 : 3 : 2****(d) 6 : 4 : 3****Solution:**

(d) 6 : 4 : 3

A = B

C = B

A : B : C = B : B : B

= 6 : 4 : 3

**Question 11.****If = = then A : B : C = ?****(a) 2 : 3 : 4****(b) 4 : 3 : 2****(c) 3 : 2 : 4****(d) none of these****Solution:**

(a) 2 : 3 : 4

**Question 12.****If (x : y) = 3 : 4, then (7x + 3y) : (7x – 3y) = ?****(a) 7 : 3****(b) 5 : 2****(c) 11 : 3****(d) 14 : 9****Solution:**

(c) 11 : 3

**Question 13.****What least number must be subtracted from each term of the ratio 15 : 19 to make the ratio 3 : 4?****(a) 3****(b) 5****(c) 6****(d) 9****Solution:**

(a) 3

Let us assume that the number to be subtracted is x

Then, (15 – x) : (19 – x) = 15 : 3

⇒ =

⇒ 60 – 4x = 57 – 3x

⇒ x = 3

**Question 14.****If ₹ 840 is divided between A and B in the ratio 4 : 3, then B’s share is****(a) ₹ 480****(b) ₹ 360****(c) ₹ 320****(d) ₹ 540****Solution:**

(b) ₹ 360

Sum of the ratio terms = 4 + 3 = 7

B’s share = ₹ 840 x = ₹ 360

**Question 15.****The ages of A and B are in the ratio 5 : 2. After 5 years, their ages will be in the ratio 15 : 7. The present age of A is****(a) 48 years****(b) 36 years****(c) 40 years****(d) 35 years****Solution:**

(c) 40 years

Suppose that the present ages of A and B are 5x yrs and 2x yrs, respectively

After 5 years, the ages of A and B will be (5x + 5) yrs and (2x + 5) yrs, respectively

Then, (5x+ 5) : (2x + 5) = 15 : 7

⇒ =

Cross multiplying; we get:

⇒ 35x + 35 = 30x + 75

⇒ 5x = 40

⇒ x = 8

Then, the present age of A is 5 x 8 = 40 yrs.

**Question 16.****The boys and girls in a school are in the ratio 9 : 5. If the number of girls is 320, then the total strength of the school is****(a) 840****(b) 896****(c) 920****(d) 576****Solution:**

(a) 896

Suppose that the number of boys in the school is x

Then, x : 320 = 9 : 5

⇒ 5x = 2880

⇒ x = 576

Hence, total strength of the school = 576 + 320 = 896

**Question 17.****Fill in the blanks.****(i) If A : B = 2 : 3 andB : C = 4 : 5, then C : A = …………****(ii) If 16% of A = 20% of B, then A : B = ………….****(iii) If A = B and B= C, then A : B : C = ………….****(iv) If A : B = 5 : 7 and B : C = 6 : 11, then A: B : C = ………….****Solution:**

**Question 18.****Write ‘T’ for true and ‘F’ for false for each of the following :****(i) Mean proportional between 0.4 and 0.9 is .6.****(ii) The third proportional to 9 and 12 is 10.5****(iii) If 8 : x :: 48 : 18, then x = 3.****(iv) If (3a + 5b): (3a – 5b) = 5 : 1, then a : b = 5 : 2.****Solution:**

(i) True

Suppose that the men proportional is x

Then, 0.4 : x :: x : 0.9

⇒ 0.9 x 0.4 = x x x (Product of extremes = Product of means)

⇒ x² = 0.36

⇒ x = 0.6

(ii) False

Suppose that the third proportional is x.

Then, 9: 12 :: 12 : x

⇒ 9x = 144 (Product of extremes = Product of means)

⇒ x = 16

(iii) True

8 : x :: 48 : 18

⇒ 144 = 48x (Product of extremes = Product of means)

⇒ x = 3

(iv) True

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