Two candles of the same length are made of different materials so that one burns out completely at a uniform rate in 3 hours and the other in 4 hours. At what time (P.M.), should the candles be lighted so that at 5 P.M., one stub is twice the length of the other ?

Let length of each candle be $$l$$ cm

Time taken to burn each candle is 3 hours and 4 hours respectively.

=> Candle burn in 1 minute = $$\frac{l}{180}$$ cm and $$\frac{l}{240}$$ cm

Let required time be $$t$$ minutes.

Thus, candle burnt in $$t$$ minutes = $$l-\frac{tl}{180}$$ cm and $$l-\frac{tl}{240}$$ cm

According to ques,

=> $$(l-\frac{tl}{180}):(l-\frac{tl}{240})=1:2$$

=> $$2l-\frac{tl}{90}=l-\frac{tl}{240}$$

=> $$l=\frac{tl}{30}(\frac{1}{3}-\frac{1}{8})$$

=> $$\frac{30}{t}=\frac{5}{24}$$

=> $$t=30\times\frac{24}{5}=144$$ minutes

$$\therefore$$ Candles should be lit 144 minutes prior to 5 pm, i.e. at 2:36 pm

=> Ans - (B)