Multiple choice

The square of the difference between the age of Mohit's eldest brother Niranjan and the age of Mohit's sister Sunita (who is only 10 years old) is equal to the square of the number obtained by subtracting 8 years from Mohit's present age. The number obtained by subtracting Mohit's age from Niranjan's age equals the difference between the square of the sums of Niranjan's and Mohit's ages and 1762. How old is Mohit?

  1. 16 years

  2. 18 years

  3. 20 years

  4. 22 years

  5. 24 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let N, S, M be ages. S=10. (N-10)^2 = (M-8)^2. Since N > S, N-10 = M-8, so N = M+2. Also N-M = (N+M)^2 - 1762. Substituting N=M+2: (M+2)-M = (M+2+M)^2 - 1762. 2 = (2M+2)^2 - 1762. 1764 = (2M+2)^2. 42 = 2M+2. 40 = 2M, M = 20.

AI explanation

Let Mohit's age be m and Niranjan's age be n. The first statement gives the equation (n minus 10) squared equals (m minus 8) squared, meaning the absolute difference between n and 10 equals the absolute difference between m and 8. Testing the ages from the options shows that m equals 20 forces n to equal 22 or 18. The second statement says (n minus m) equals ((n plus m) squared minus 1762), which evaluates to zero for m equals 20 and n equals 22, since (42 squared minus 1762) equals zero. Therefore, Mohit is 20 years old.

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