Referring to his two sons Ram and Shyam, their father says - 12 years ago, Ram…
2025
Referring to his two sons Ram and Shyam, their father says - 12 years ago, Ram was 3 times as old as Shyam. 12 years later, the ratio of the ages of Shyam and Ram will be 2:3. What is the present age of Ram?
- A.
24 years
- B.
36 years
- C.
54 years
- D.
144 years
Attempted by 5 students.
Show answer & explanation
Correct answer: B
Concept: In a multi-stage age problem, first assign variables to the present ages of the people involved. Any age at another point in time is obtained by adding or subtracting the number of elapsed years from the present age. Each verbal relationship (a multiple or a ratio) at a given time point then becomes one linear equation in the present-age variables; solving the resulting system gives the present ages.
Let Shyam's present age be S years and Ram's present age be R years.
12 years ago, Ram was 3 times as old as Shyam, so R − 12 = 3(S − 12), which gives R = 3S − 24.
12 years later, the ratio of Shyam's age to Ram's age will be 2:3, so (S + 12) / (R + 12) = 2/3, which gives 3(S + 12) = 2(R + 12), i.e. 2R = 3S + 12, so R = (3S + 12) / 2.
Equating the two expressions for R: 3S − 24 = (3S + 12) / 2. Multiplying both sides by 2 gives 6S − 48 = 3S + 12, so 3S = 60 and S = 20.
Substituting S = 20 back into R = 3S − 24 gives R = 3(20) − 24 = 36.
Cross-check: 12 years ago, Ram's age was 36 − 12 = 24 and Shyam's age was 20 − 12 = 8, giving a ratio of 24:8 = 3:1, matching "3 times as old." 12 years later, Shyam's age will be 20 + 12 = 32 and Ram's age will be 36 + 12 = 48, giving a ratio of 32:48 = 2:3, exactly as required. Both conditions confirm Ram's present age is 36 years.
