The difference between the ages of two cousins is 10 years. 15 years ago, if the elder one was twice as old as the younger one, then their present ages are

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40, 50

20, 40

25, 35

30, 40

answer is A.

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Detailed Solution

It is given that the difference between the ages of two cousins is 10 years and 15 years ago, the elder cousin was twice the younger one.
So, assume the present age of the younger cousin to be x years.
Then as per the first condition, the age of the elder cousin will be (x+10).
Next, 15 years back, the ages of the younger and elder cousins would be (x-15) and
(x+10-15) = (x-5) respectively in years.
So, according to the second condition, we can form a linear equation as follows,

2 (x − 15) = x − 5 2 x − 30 = x − 5

2 x − 30 − x = x − 5 − x x − 30 = − 5

x − 30 + 30 = − 5 + 30 x = 25

From here, we have the present age of the younger cousin as 25 years.
Now, as per the assumption, the present age of the elder cousin can be found as follows,

x + 10 = 25 + 10 = 35

So, the present age of the elder cousin is 35 years.
The present age of elder and younger cousins are 35 years and 25 years respectively.
Hence, the correct option is (1).

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