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KVPY2016MathematicsApplication of Derivatives

There are two candles of same length and same size. Both of them burn at uniform rate. The first one burns in 5 hours and the second one burns in 3 hours. Both the candles are lit together. After how many minutes the length of the first candle is 3 times that of the other?

Options

  1. A90
  2. B120
  3. C135
  4. D150

Correct answer

D. 150

Step-by-step solution

Let V ₁ & ~V ₂ are rates of burning for both candles respectively & ~L is the length of each candle V ₁= L 5 ~V ₂= L 3 Let after time 't', their lengths are ₁ & ₂ array l ₁= L - L 5 t ₂= L - L 3 t & ₁=3 ₂ (Given) L - L 5 t = ( L - L 3 t ) 3 5- t 5 =3- t 5- t =15-5 t 4 t =10 t =2.5 hrs =150 ~min array

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