A candle of 6 cm long burns at the rate of 5 cm in 5 h and another candle of 8cm long burns at the rate of 6 cm in 4 h. What is the time required by each candle to remain of equal lengths after burning for some hours, when they starts to burn simultaneously with uniform rate of burning?

Options

A. 1h
B. 1.5h
C. 2h
D. none of these

Answer

To solve the problem, we need to determine the time required for both candles to reach the same length after burning simultaneously.

### Step-by-Step Solution:

1. **Identify the initial lengths of the candles**:
- Candle A: 6 cm
- Candle B: 8 cm

2. **Determine the burning rates**:
- Candle A burns at a rate of 5 cm in 5 hours, which translates to:
\[ \text{Burning rate of Candle A} = \frac{5 \text{ cm}}{5 \text{ h}} = 1 \text{ cm/h} \]
- Candle B burns at a rate of 6 cm in 4 hours, which translates to:
\[ \text{Burning rate of Candle B} = \frac{6 \text{ cm}}{4 \text{ h}} = 1.5 \text{ cm/h} \]

3. **Set up the equations for the lengths of the candles after t hours**:
- Length of Candle A after t hours:
\[ L_A = 6 - 1t \]
- Length of Candle B after t hours:
\[ L_B = 8 - 1.5t \]

4. **Set the lengths equal to find t**:
\[ 6 - 1t = 8 - 1.5t \]

5. **Solve for t**:
- Rearranging the equation:
\[ 1.5t - 1t = 8 - 6 \]
\[ 0.5t = 2 \]
\[ t = \frac{2}{0.5} = 4 \text{ hours} \]

6. **Conclusion**:
The time required for both candles to remain of equal lengths after burning simultaneously is **4 hours**.