Two cylindrical candles A and B are of the same height. The radius of A is twice that of B. If A takes 120 minutes to completely burn, how long does B take to burn half its initial height?

Correct option is A

Solution :
Relation Between Candle Volumes: The volume of a cylinder is proportional to the square of the radius.
Let the radius of B be   so the radius of A is 2r.
The volumes of A and are:
Volume of A = π$$(2r)^2$$h==4π$$r^2$$h Volume of B = π$$r^2$$h
Thus, A's volume is 4 times that of B.
Burning Rates: Since A burns completely in 120 minutes, its burning rate is:
Burning rate of A=$$\frac{Volume of A}{120}$$=$$\frac{πr^2h}{30}$$

Given that B's volume is $$\frac{1}{4}$$ of A's, its burning rate is:​​
Burning rate of B = $$\frac{πr^2h}{120}$$
Burn Time for Half of B's Height: When B burns to half its height, its volume burned is:​​
Burned volume = $$\frac{πr^2h}{2}$$
Using B's burning rate:
Time taken = $$\frac{Burned volume}{Burning rate}$$ = $$\frac{120}{2}$$ = 60 minutes​​