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The difference between the ages of Sakshi and Priya is 37 years. Five years ago from now, the sum of their ages was 95 years. If Sakshi is older than Priya, find Priya's present age (in years).
43
24
34
28
34
Let Priya's age be P. Sakshi's age is P+37. Five years ago, (P-5) + (P+37-5) = 95. Simplify to 2P + 27 = 95, so 2P = 68, P = 34.
Let Priya's age be P. Sakshi's age is P+37. Five years ago, (P-5) + (P+37-5) = 95. Simplify to 2P + 27 = 95, so 2P = 68, P = 34.
Define variables
Let Priya's present age be P. Since the difference between Sakshi and Priya's ages is 37 years and Sakshi is older, Sakshi's present age = P + 37.
Formulate equation for five years ago
Five years ago, Sakshi's age was (P + 37 - 5) = P + 32 and Priya's age was (P - 5). Their sum was 95: (P + 32) + (P - 5) = 95.
Solve for P
Combining terms gives 2P + 27 = 95. Subtracting 27 from both sides gives 2P = 68. Dividing by 2, we get P = 34.
A: 43 results in a sum of 113 five years ago; B: 24 results in a sum of 75 five years ago; D: 28 results in a sum of 83 five years ago.
C is correct because setting up the linear equation for their ages five years ago (P-5) + (P+37-5) = 95 correctly identifies Priya's current age as 34.
In age problems involving multiple people, always convert the 'years ago/hence' conditions to current age variables first to avoid calculation errors.
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