Question

A candle of height 10 cm burns at the rate of 2 cm/hr initially. After it has burnt 20%, the rate increases to 3 cm/hr. Then, after it has burnt 50%, the rate of burning changes again such that it takes 2 hours for the remaining candle to burn up completely, then what is the overall average rate at which candle gets burnt?

• A. 2.6 cm/hr
• B. 2.7 cm/hr
• C. 2.4 cm/hr
• D. 2.5 cm/hr

Answer 1

The Correct Option is D

Average Burning Rate of Candle Calculation 

- The total height of the candle is 10 cm.

- Initially, the candle burns at the rate of 2 cm/hr. Thus, it burns 20% of its height:

\[ 0.2 \times 10 = 2 \text{ cm} \]

- The time taken to burn the first 2 cm is:

\[ \frac{2}{2} = 1 \text{ hour} \]

- After burning the first 2 cm, 80% of the candle remains:

\[ 0.8 \times 10 = 8 \text{ cm} \]

- The rate now increases to 3 cm/hr. The candle burns 50% of its remaining height:

\[ 0.5 \times 8 = 4 \text{ cm} \]

- The time taken to burn this 4 cm is:

\[ \frac{4}{3} \approx 1.33 \text{ hours} \]

- After burning 4 cm, the remaining height is:

\[ 8 - 4 = 4 \text{ cm} \]

- The candle now burns at a slower rate, taking 2 hours to burn the remaining 4 cm.

- Now, we calculate the overall average rate of burning:

• Total distance burnt: 10 cm
• Total time taken: 1 + 1.33 + 2 = 4.33 hours

- The average burning rate is:

\[ \text{Average rate} = \frac{10}{4.33} \approx 2.5 \text{ cm/hr} \]

Thus, the correct answer is (d) 2.5 cm/hr.