Rohan's present age is two-fifth of the age of his elder sister Radha. After 7…
2024
Rohan's present age is two-fifth of the age of his elder sister Radha. After 7 years, he will be two-third of the age of Radha. How old is the Radha at present (in years)?
- A.
11
- B.
7.52
- C.
9
- D.
8.75
Attempted by 24 students.
Show answer & explanation
Correct answer: D
Let Rohan's age be R and Radha's age be S.
From the problem: R = 2/5 · S.
After 7 years: R + 7 = 2/3 · (S + 7).
Substitute R = 2S/5 into the second equation: (2S/5) + 7 = (2/3)(S + 7).
Clear denominators by multiplying both sides by 15: 6S + 105 = 10S + 70.
Rearrange: 105 - 70 = 10S - 6S ⇒ 35 = 4S ⇒ S = 35/4 = 8.75 years.
Check: R = 2/5 · 8.75 = 3.5. After 7 years R = 10.5 and S = 15.75, and 10.5/15.75 = 2/3, so the solution is correct.