The present age of Harish is 8 times the sum of the ages of his two sons. After 8 years, his age will be twice the sum of the ages of his sons. What is Harish’s present age?

The correct option is 32.

Let us break down the problem step-by-step to find Harish's present age.

Let the present age of Harish be represented by H.
Let the sum of the present ages of his two sons be represented by S.

According to the first condition, the present age of Harish is 8 times the sum of the ages of his two sons. This gives us our first equation:

$$H=8S$$

Now, let us consider the scenario after 8 years:
Harish’s age after 8 years will be H + 8.
Since there are two sons, each of their ages will increase by 8 years. Therefore, the sum of the ages of the two sons after 8 years will increase by 8 + 8 = 16 years. So, the new sum of the sons' ages will be S + 16.

According to the second condition, after 8 years, Harish's age will be twice the sum of the ages of his sons. This gives us our second equation:

$$H+8=2(S+16)$$

Now, we simplify the second equation:
H + 8 = 2S + 32
H - 2S = 32 - 8
H - 2S = 24

We can now substitute the value of H from the first equation (H = 8S) into this simplified equation:

$$8S-2S=24$$

Simplify to find S:
6S = 24
S = 4

Now that we have the sum of the sons' present ages (S = 4), we can calculate Harish's present age (H) using the first equation:

$$H=8\times 4=32$$

Thus, Harish’s present age is 32 years.