Question

In five years Rajat will be twice as old as Ojas, thirteen years ago Rajat was three times as old as Ojas, how many years
ago Rajat was four times as old as Ojas
​

Answer 1

I think 20

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Answer 2

Given :- In five years Rajat will be twice as old as Ojas . thirteen years ago Rajat was three times as old as Ojas . How many years ago Rajat was four times as old as Ojas ?

Solution :-

Let us assume that, Ojas age after 5 years will be x years.

then,

→ Rajat age after 5 years = 2 * ojas age = 2x years.

So,

→ Present age of ojas = (x - 5) years.

→ Present age of Rajat = (2x - 5) years.

Now,

→ 13 years ago Ojas age was = (x - 5) - 13 = (x - 18) years.

→ 13 years ago Rajat age was = (2x - 5) - 13 = (2x - 18) years.

A/q,

→ Rajat age = 3 * Ojas age .

→ 2x - 18 = 3(x - 18)

→ 2x - 18 = 3x - 54

→ 3x - 2x = 54 - 18

→ x = 36 years.

therefore,

→ Present age of ojas = (x - 5) = 36 - 5 = 31 years.

→ Present age of Rajat = (2x - 5) = 72 - 5 = 67 years.

Now, Let us assume that, y years ago Rajat was four times as old as Ojas .

then,

→ 67 - y = 4(31 - y)

→ 67 - y = 124 - 4y

→ -y + 4y = 124 - 67

→ 3y = 57

→ y = 19 (Ans.)

Hence, 19 years ago Rajat was four times as old as Ojas .

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