Multiple choice

Amit, Vikas and Pushap are three friends. The square of difference between the ages of Amit and Vikas is equal to the square of the number obtained by subtracting 8 from Pushap's present age. Difference in ages of Amit and Pushap equals the difference between the square of the sum of ages of Amit and Pushap and 160. Find Pushap's present age if Vikas is 5 years old such that Amit is older than Pushap.

  1. 2 years

  2. 6 years

  3. 4 years

  4. 10 years

  5. 8 years
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A Correct answer
Explanation

Let A, V, P be ages. (A-V)^2 = (P-8)^2. Given V=5, (A-5)^2 = (P-8)^2. Also A-P = (A+P)^2 - 160. Solving these equations with A > P yields P = 2.

AI explanation

Let Amit, Vikas, and Pushap's ages be A, V, and P. Since Vikas is 5, the first condition gives (A - 5)^2 = (P - 8)^2, which means A - 5 = 8 - P since Amit is older than Pushap, yielding A + P = 13. The second condition states A - P = (A + P)^2 - 160, so substituting the sum gives A - P = 169 - 160 = 9. Solving the system A + P = 13 and A - P = 9 gives Pushap's age as 2 years.

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