Question

Ramaswami was studying for his examinations and the lights went off. It was around 1:00 a.m. He lighted two uniform candles of equal length but one thicker than the other. The thick candle is supposed to last six hours and the thin one two hours less. When he finally went to sleep, the thick candle was twice as long as the thin one. For how long did Ramaswami study in candle light?

• A. 2 hours
• B. 3 hours
• C. 2 hours 45 minutes
• D. 4 hours

Answer 1

The Correct Option is B

Let the length of each candle be \( L \). The thick candle burns for 6 hours, meaning its burn rate is \( \frac{L}{6} \) per hour. The thin candle burns for 4 hours, so its burn rate is \( \frac{L}{4} \) per hour. Time when both candles were lit is \( t \) hours. Therefore, the remaining length of the thick candle after \( t \) hours is \( L-\frac{Lt}{6}=\frac{L(6-t)}{6} \) and for the thin candle, it is \( L-\frac{Lt}{4}=\frac{L(4-t)}{4} \). 

Given: the remaining length of the thick candle is twice that of the thin candle: \[\frac{L(6-t)}{6}=2\cdot\frac{L(4-t)}{4}\]

Simplify: \[\frac{6-t}{6}=2\cdot\frac{4-t}{4}\]

\[\frac{6-t}{6}=\frac{2(4-t)}{4}\]

\[\frac{6-t}{6}=\frac{8-2t}{4}\]

Cross-multiply: \[(6-t)\cdot4=(8-2t)\cdot6\]

\[24-4t=48-12t\]

Reorganize: \[12t-4t=48-24\]

\[8t=24\]

\[t=\frac{24}{8}=3\]

Thus, Ramaswami studied for 3 hours in candlelight.