Question

Two candles have different lengths and thickness. The shorter lasts $11$ hours and the longer $7$ hours when both are lit simultaneously. If after $3$ hours of being lit together at the same time, both have the same length, then the ratio of their original lengths is

• A. $5:8$
• B. $11:14$
• C. $10:13$
• D. $7:11$

Answer 1

The correct option is B $11:14$

Let the original lengths of the candles be L1 and L2

L1 lasts for 11 hrs

L2 lasts for 7 hrs

L1 burns out at the rate $\frac{L1}{11}$ cm/hr

L1 burns out at the rate $\frac{L2}{7}$ cm/hr

after 3 hrs portion left of L1 = portion left of L2

L1 - ($\frac{L1}{11}\times 3$) = L2 -($\frac{L2}{7}\times 3$)

$\frac{8L1}{11}$ = $\frac{4L2}{7}$

$\therefore$ $\frac{L1}{L2}$ = $\frac{11}{14}$

option B