CUET UG 2024 — General Test Quantitative Reasoning

Let Harish's present age be $H$H and the sum of the ages of his two sons be $S$S.

From the first condition, we have:

$$H = 8S$$H=8S

After 8 years, Harish's age will be $H + 8$H+8, and the sum of his sons' ages will be $S + 16$S+16.

From the second condition, we have:

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

Substituting $H$H from the first equation into the second:

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

Expanding and simplifying:

$$8S + 8 = 2S + 32$$8S+8=2S+32

$$6S = 24$$6S=24

$$S = 4$$S=4

Now substituting back to find $H$H:

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

Thus, the present age of Harish is $32$32 years.