Question

Two candles are of different lengths and thickness. The short and long ones can burn respectively for 3.5 hours and 5 hours. After burning for 2 hours, the lengths of candles are equal. What fraction of the long candle's height was the short candle initially?

• A. 2/7
• B. 5/7
• C. 3/5
• D. 4/5

Hint:

Assume the initial length of one candle to be 1 unit to simplify burn-rate comparison problems.

Answer 1

The Correct Option is B

Let the initial length of the long candle be 1 unit. Burn rate of the long candle = \( \frac{1}{5} \) per hour → In 2 hours: it burns \( 2 \times \frac{1}{5} = \frac{2}{5} \), remaining = \(1 - \frac{2}{5} = \frac{3}{5}\)
Let the initial height of the short candle be \( x \) units.
Burn rate of short candle = \( \frac{x}{3.5} = \frac{2x}{7} \) per hour → In 2 hours: it burns \( 2 \times \frac{2x}{7} = \frac{4x}{7} \), remaining = \(x - \frac{4x}{7} = \frac{3x}{7}\)
Now, after 2 hours both have equal height:
\[ \frac{3x}{7} = \frac{3}{5} \Rightarrow x = \frac{3}{5} \times \frac{7}{3} = \frac{7}{5} \]
Thus, short candle was initially \( \frac{7}{5} \) of long candle.
So, long candle was \( \frac{5}{7} \) of short candle.
Therefore, the correct fraction is 5/7.