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The difference between the present ages of Juhi and Surbhi is 24 years. Five years ago from now, the sum of their ages was 66 years. If Juhi is older than Surbhi, find Surbhi's present age (in years).
20
26
33
18
26
Let Juhi be J and Surbhi be S. J - S = 24. 5 years ago, (J-5) + (S-5) = 66, which means J + S = 76. Solve J+S=76 and J-S=24 by adding them: 2J = 100, so J=50, S=26.
Let Juhi be J and Surbhi be S. J - S = 24. 5 years ago, (J-5) + (S-5) = 66, which means J + S = 76. Solve J+S=76 and J-S=24 by adding them: 2J = 100, so J=50, S=26.
Define the Variables
Let Juhi's present age be J and Surbhi's present age be S. We are given J - S = 24 (Equation 1).
Formulate the Age Sum Equation
Five years ago, their ages were (J-5) and (S-5). The sum is given as 66: (J-5) + (S-5) = 66, which simplifies to J + S - 10 = 66, so J + S = 76 (Equation 2).
Solve the Equations
Add Equation 1 and Equation 2: (J-S) + (J+S) = 24 + 76. This gives 2J = 100, so J = 50. Substitute J=50 into Equation 1: 50 - S = 24, which results in S = 26.
A: 20 gives a difference of 30 (not 24), C: 33 gives a sum of 76 leading to J=43 and difference of 10, D: 18 gives a difference of 40.
B is correct because solving the system of linear equations J-S=24 and J+S=76 yields Surbhi's present age of 26 years.
In age problems involving multiple people, always convert the 'past/future' sum condition to the 'present' by adding/subtracting the number of years for EACH person involved.
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