The ratio of present ages of Ajay and Atul is 4 9 The ratio of their ages 9 years ago was 1 3 Find t...........

The ratio of present ages of Ajay and Atul is 4 : 9. The ratio of their ages 9 years ago was 1 : 3. Find the ratio of their ages 6 years from now.

This questions was previously asked in

RRB Clerk Prelims (13 Aug, 2022 Shift 1)

2 : 1

1 : 3

3 : 1

1 : 2

2 : 7

Sure, let's solve this step by step and break down the options.

- Let Ajay's present age = 4x, Atul's present age = 9x.

- 9 years ago, Ajay's age = 4x - 9; Atul's age = 9x - 9.

- The ratio 9 years ago:

(4x - 9) / (9x - 9) = 1/3

Cross-multiply: 3(4x - 9) = 1(9x - 9)

12x - 27 = 9x - 9

12x - 9x = -9 + 27

3x = 18

x = 6

- Present ages: Ajay = 4x = 24, Atul = 9x = 54

- 6 years from now: Ajay = 24 + 6 = 30; Atul = 54 + 6 = 60

- Ratio after 6 years: 30 : 60 = 1 : 2

Here’s a quick take on the options:

- Option 1: 2 : 1 — Would be if Ajay was older, which isn’t the case.

- Option 2: 1 : 3 — Ajay would be much younger, which doesn’t fit.

- Option 3: 3 : 1 — Again, Ajay being much older, nope.

- Option 4: 1 : 2 — This means Atul is double Ajay’s age; fits our numbers.

- Option 5: 2 : 7 — Atul being way older, not matching the calculation.

So, the correct answer is Option 4: 1 : 2.

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