Rohan's age 6 years from now will be 5/3 of his age 6 years ago. What is his present age?
SHORT ANSWER
24 years. If his age is x, then x + 6 = (5/3)(x - 6). So 3x + 18 = 5x - 30, giving x = 24. Check: 30 is 5/3 of 18.
Explain it simply
A single person's age at two different times is linked by one equation. Write both times in terms of the present age x: six years later is x + 6, six years earlier is x - 6. The gap between them is always 12 years, which gives a quick ratio method too.
Example
Question: Age in 6 years = 5/3 x age 6 years ago. Present age?
Equation:
- x + 6 = (5/3)(x - 6).
- 3x + 18 = 5x - 30.
- 2x = 48, x = 24.
Ratio method:
- Future : past = 5 : 3, and the two ages differ by 12 years.
- The difference is 2 parts = 12 years, so 1 part = 6.
- Past age = 3 x 6 = 18, so present = 24.
Check: in 6 years he is 30; 6 years ago he was 18. 30 / 18 = 5/3.
js
const x = 24;
console.log((x + 6) / (x - 6) === 5 / 3); // Output: trueWhat to say in the interview
"The ages six years ahead and six years back are 12 years apart and in the ratio 5 to 3, so one part is 6. The past age is 18 and the present age is 24, which I check by substitution."
Common mistakes
- Using a gap of 6 years instead of 12 between the two times.
- Putting the 5/3 on the wrong side of the equation.