The ratio between the present ages of Amit and Amita is 7 : 5, respectively. The ratio between Amit’s age 5 years ago and Amita’s age 5 years hence is 1 ; 1. What is the ratio between Amit’s age 5 years hence and Amita’s age 5 years ago? 

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  1. 2 : 1
  2. 1 : 2
  3. 2 : 3
  4. 3 : 2

Answer (Detailed Solution Below)

Option 1 : 2 : 1
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Detailed Solution

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Given:

The ratio between the present ages of Amit and Amita is 7:5.

Calculation:

Let the present ages of Amit and Amita be 7x and 5x respectively.

Amit's age 5 years ago = 7x - 5

Amita's age 5 years hence = 5x + 5

Given, the ratio between Amit's age 5 years ago and Amita's age 5 years hence is 1:1

⇒ 7x - 5 = 5x + 5

⇒ 7x - 5x = 5 + 5

⇒ x = 5

Amit's age 5 years hence = 7x + 5 = 7(5) + 5 = 35 + 5 = 40

Amita's age 5 years ago = 5x - 5 = 5(5) - 5 = 25 - 5 = 20

The ratio between Amit's age 5 years hence and Amita's age 5 years ago = 40:20 = 2:1

∴ The correct answer is option 1.

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