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The ratio of 2 numbers is 7 : 4, When 28 is added to the smaller number new ratio becomes 7 : 8. What is the minimum number to be added to the current smaller number so that ratio becomes 3 : 2?

The ratio of 2 numbers is 7 : 4, When 28 is added to the smaller number new ratio becomes 7 : 8. What is the minimum number to be added to the current smaller number so that ratio becomes 3 : 2? Correct Answer 35

Let first number be 7x and second number be 4x

When 28 is added in the smaller number then ratio becomes 7 : 8

So, 7x/(4x + 28) = 7/8

⇒ 56x = 28x + 28 × 7

⇒ 28x = 28 × 7

⇒ x = 7

So, first number is 7 × 7 = 49 and second number is 4 × 7 = 28

Now, new first number = 49 and new second number = 28 + 28 = 56

Again, from question let a be added to current smallest number then ratio becomes 3 : 2

So, (49 + a) /56 = 3/2

⇒ 98 + 2a = 168

⇒ 2a = 168 – 98 = 70

⇒ a = 35

∴ Minimum number = 35

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