Each question below is followed by two statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. 11 Aman is how many years younger than Jadhav? I. Six years back Lokesh was as old as Aman is now. The ratio of age of Lokesh three ago and age of Jadhav 2 years ago was 7 ∶ 11. II. Jadhav is 3 years younger than Ranjit. The ratio of the age of Lokesh 2 years ago and the present age of Ranjit is 3 ∶ 5.
Each question below is followed by two statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. 11 Aman is how many years younger than Jadhav? I. Six years back Lokesh was as old as Aman is now. The ratio of age of Lokesh three ago and age of Jadhav 2 years ago was 7 ∶ 11. II. Jadhav is 3 years younger than Ranjit. The ratio of the age of Lokesh 2 years ago and the present age of Ranjit is 3 ∶ 5. Correct Answer If the data in both statements I and II together are needed to answer the question.
Using statement I
Six years back Lokesh was as old as Aman is now
⇒ Let the present age of Aman be x
Then, the present age of Lokesh = x + 6
The ratio of age of Lokesh three ago and age of Jadhav 2 years ago was 7 ∶ 11.
⇒ (x + 6 – 3)/(J – 2) = 7/11
J → Present age of Jadhav
⇒ 11x + 33 = 7J – 14
⇒ (11x + 47)/7 = J
∴ Statement I alone is not sufficient to answer the question
Using statement II
Jadhav is 3 years younger than Ranjit
⇒ Present age of Ranjit (R) = J + 3
The ratio of the age of Lokesh 2 years ago and the present age of Ranjit is 3 ∶ 5
(L – 2)/R = 3/5
⇒ (L – 2)/(J + 3) = 3/5
∴ Statement II alone is not sufficient to answer the question
Using Statement I and Statement II together
(11x + 47)/7 = J ----(i)
(L – 2)/(J + 3) = 3/5
⇒ (x + 4)/(J + 3) = 3/5
⇒ 5x + 20 = 3J + 9
⇒ (5x + 11)/3 = J ----(ii)
Equating (i) and (ii)
(5x + 11)/3 = (11x + 47)/7
⇒ 35x + 77 = 33x + 141
⇒ 2x = 64
⇒ x = 32
∴ Present age of Aman = 32 yrs
Present age of Jadhav = (5 × 32 + 11)/3 = 171/3 = 57
∴ Required difference = 57 – 32 = 25 yrs
∴ The data in both statements I and II together are needed to answer the question.