When asked about the time, Amit replied: "If you add one quarter of the time…

A statement relating "time elapsed since midnight" and "time remaining till the next midnight" to the current time is a linear-equation problem: if the current time is x hours after midnight (0 ≤ x < 24), the elapsed time equals x and the remaining time to the next midnight equals (24 − x). Any fractional combination of these two spans that is said to equal the current time becomes one linear equation in x.

1. Let the current time be x hours past midnight. Elapsed time since midnight = x; remaining time to the next midnight = 24 − x.

2. Amit's statement translates to: one quarter of the elapsed time plus half the remaining time equals the current time — (1/4)x + (1/2)(24 − x) = x.

3. Expand the bracket: (1/4)x + 12 − (1/2)x = x.

4. Combine the x-terms on the left: 12 − (1/4)x = x.

5. Move the x-term to the right and combine: 12 = x + (1/4)x = (5/4)x.

6. Solve for x: x = 12 × 4/5 = 48/5.

Check: with x = 48/5, elapsed time = 48/5 and remaining time = 24 − 48/5 = 72/5. One quarter of the elapsed time is 12/5 and half the remaining time is 36/5; their sum, 12/5 + 36/5 = 48/5, equals x, confirming the value.

So the current time is 48/5 hours past midnight (9.6 hours, i.e. 9:36).