10 years ago, the age of Sunita was thrice the age of her daughter Tanya. 10 years hence, the age of Sunita will be twice the age of Tanya. What is the ratio of their present ages?
- (a)2 : 7
- (b)7 : 2
- (c)7 : 3
- (d)3 : 7
Answer
Why
Correct — C. Call Sunita's present age S and Tanya's T, then write both conditions in those two letters.
10 years ago: S − 10 = 3(T − 10) → S = 3T − 20
10 years hence: S + 10 = 2(T + 10) → S = 2T + 10
Equate the two: 3T − 20 = 2T + 10 → T = 30
So S = 2(30) + 10 = 70
S : T = 70 : 30 = 7 : 3 → option (c)
Why the others are wrong
- (a)2 : 7 — 2 : 7 makes Sunita younger than her own daughter, which no reading of the stem allows — she was three times Tanya's age a decade ago.
- (b)7 : 2 — 7 : 2 pairs Sunita's correct present age of 70 with Tanya's age ten years ago (20). The question asks for present ages, and Tanya is 30 now.
- (d)3 : 7 — 3 : 7 is the right pair written backwards. The stem names Sunita first, so 70 goes on the left of the colon.
Concept
An age problem with one past and one future condition is a pair of linear equations in disguise. Fix the present ages as the unknowns and translate each time-stamp into them: ten years ago every age drops by 10, ten years hence every age rises by 10.
Both conditions then describe the same two unknowns, so eliminating S gives Tanya directly.
The point worth carrying away is that a ratio of ages is not a constant. It was 3 : 1, it is 7 : 3, and it will be 2 : 1 — while the gap of 40 years never moves.
The stem gives the multiplier in words (thrice, twice), so the only place to go wrong is in shifting both ages by the same 10 years each time.
Key facts
- Ten years ago Sunita was 60 and Tanya 20, and 60 = 3 × 20 as the first condition demands.
- Ten years hence Sunita is 80 and Tanya 40, and 80 = 2 × 40.
- The age difference stays at 40 years throughout, while the ratio falls from 3 : 1 to 7 : 3 to 2 : 1.
Study next
Common traps
- Adding 10 to Sunita but not to Tanya in the years-hence equation
- Answering with Tanya : Sunita when the stem names Sunita first
- Carrying the 3 : 1 ratio of ten years ago into the present
Two time-stamped conditions, then a question about the present, is the standard shape — so read the last line before you set up.
At 09 Sep 2024, 12:30, Quant Q.6 the two conditions are again one past and one future (Prachi and her daughter), but the question asks for the sum of the present ages.
At 24 Sep 2024, 12:30, Quant Q.2 they are one present and one past (Ghanshyam thrice Akash now, four times him ten years ago), and the question asks for the difference.
Related PYQs
No directly related past PYQ was found.