Practice Test: Ratio & Proportion- 1 - UPSC MCQ

(2A + 6)/(5A + 6) = 4/7
14A + 42 = 20A + 24, A = 3
Larger number = 5A = 15

Let shares of A, B, C and D are 5x, 2x, 4x and 3x respectively

4x - 3x = 1000, x =1000

B’s share = 2x = 2000

40% → 50% ← 70%
70 – 50 = 20
50 – 40 = 10
Ratio = 20:10 = 2:1

After 3 years, Ajay’s share is 5000 – 1000 = 4000
Ratio or profit 5000 × 3 + 4000 × 9 : 3000 × 9 = 51 : 27 = 17 : 9
Ajay’s share = 17/26 × 52,000 = 34,000

A : B = 2 : 3, B : C = 4 : 3, C : D = 5 : 4

Then A : B : C : D = (2 × 4 × 5) : (3 × 4 × 5) : (3 × 3 × 5) : (3 × 3 × 4) = 40 : 60 : 45 : 36

Given:

Two numbers are 30% and 20% less than a third number respectively.

Formula Used:

If a number is x% less than another number, then it is equal to (100 - x)% of that number.

Ratio = First number / Second number

Calculation:

Let the third number be 100.

First number = 100 - 30% of 100

First number = 100 - 30

First number = 70

Second number = 100 - 20% of 100

Second number = 100 - 20

Second number = 80

Ratio of the first two numbers = First number / Second number

⇒ Ratio = 70 / 80

⇒ Ratio = 7 / 8

The ratio of the first two numbers is 7 : 8.

Given:

The ratio of two numbers = 2:3

Their product = 726

Formula Used:

Let the numbers be 2x and 3x.

Product of numbers = (2x) × (3x)

Calculation:

Product of numbers = 726

⇒ (2x) × (3x) = 726

⇒ 6x² = 726

⇒ x² = 726 / 6

⇒ x² = 121

⇒ x = √121

⇒ x = 11

Smallest number = 2x = 2 × 11 = 22

The smallest number between the two numbers is 22.

Given:

t : u = 7 : 4

Formula Used:

(7t + 4u) : (7t - 4u)

Calculation:

Let t = 7k and u = 4k, where k is a constant.

So, 7t = 7 × 7k = 49k

4u = 4 × 4k = 16k

⇒ (7t + 4u) = 49k + 16k = 65k

⇒ (7t - 4u) = 49k - 16k = 33k

Therefore, (7t + 4u) : (7t - 4u) = 65k : 33k = 65 : 33

The value of (7t + 4u) : (7t - 4u) is 65 : 33.