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The difference between the present ages of Ayushi and Nidhi is 26 years. Five years ago from now, the sum of their ages was 30 years. If Ayushi is older than Nidhi, find Nidhi's present age (in years).
6
10
12
7
7
Let the ages be A and N. We know A - N = 26 and (A-5) + (N-5) = 30. Simplify to A + N = 40. Then N = (Sum - Difference) / 2.
Let the ages be A and N. We know A - N = 26 and (A-5) + (N-5) = 30. Simplify to A + N = 40. Then N = (Sum - Difference) / 2.
Define the variables
Let Ayushi's present age be A and Nidhi's present age be N. We are given A - N = 26 (Equation 1).
Account for time shift
Five years ago, their ages were (A-5) and (N-5). The sum of their ages was 30: (A-5) + (N-5) = 30. This simplifies to A + N - 10 = 30, so A + N = 40 (Equation 2).
Solve the system of equations
Subtract Equation 1 (A - N = 26) from Equation 2 (A + N = 40). This gives (A + N) - (A - N) = 40 - 26, which simplifies to 2N = 14. Therefore, N = 7.
A: If N=6, then A=32, sum 5 years ago would be 27+1=28 (incorrect); B: If N=10, then A=36, sum 5 years ago would be 31+5=36 (incorrect); C: If N=12, then A=38, sum 5 years ago would be 33+7=40 (incorrect).
D is correct because solving the system A - N = 26 and A + N = 40 yields N = 7, which satisfies all conditions given in the problem.
In age problems involving sums of ages at a past/future time, always remember to add or subtract the time shift for BOTH individuals; here, subtracting 5 twice is crucial (minus 10 total).
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