The age of ‘E’ is twice the age of ‘S’. To find out the difference in their ages, which of the following information is/are sufficient ?
I. After five years, the ratio of their ages would be 9 : 5
II. Before ten years, the ratio of their ages was 3 : 1
Only I
Only II
Either I or II
Both I and II
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CAPF – 2015
Given: E = 2S. We need to find the difference E – S.
Statement I: After five years, the ratio of their ages is 9:5. So, (E+5)/(S+5) = 9/5. Substituting E=2S, we get (2S+5)/(S+5) = 9/5. This is a linear equation in S, which can be solved to find a unique value for S. Since S can be determined, E can also be determined, and thus the difference E-S can be found. So, Statement I alone is sufficient.
Statement II: Before ten years, the ratio of their ages was 3:1. So, (E-10)/(S-10) = 3/1. Substituting E=2S, we get (2S-10)/(S-10) = 3/1. This is a linear equation in S, which can be solved to find a unique value for S. Since S can be determined, E can also be determined, and thus the difference E-S can be found. So, Statement II alone is sufficient.
Since either statement alone provides enough information to find the difference in their ages, the answer is C.
From Statement II: (2S-10) = 3(S-10) => 2S – 10 = 3S – 30 => S = 20. E = 2*20 = 40. Difference = 20.
Both statements lead to the same ages and difference, confirming that each is independently sufficient.