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Question:

In 2004, Rohini was thrice as old as her brother Arvind. In 2014, Rohini was only six years older than her brother. In which year was Rohini born?

Explanation:

Let Rohini’s age in the year 2014 is R and Arvind’s age is A.

∴ R – A = 6      … (i)

∴ Rohini’s age in 2004 = R – 10 and Arvind’s age in 2004 = A – 10

∴ (R – 10) = 3(A – 10)

∴ 3A – R = 20 … (ii)

Solving (i) and (ii), we get

R = 19
 
∴ Rohini was born in year (2014 – 19 =) 1995.

Hence, option (c).

Alternatively,

Rohini’s age in 2004 for the given options:
1. 1984 : 20
2. 1986 : 22
3. 1995 : 9
4. 2000 : 4
As Rohini’s age was thrice as old as her brother, the correct answer should be option 3.

Hence, option (c).