Question

If 4 identical taps can fill a 100-litre tank in 6 hours, then how many hours will be required to fill a 150-litre tank by 8 such taps?

• A. 3 hours
• B. 4.5 hours
• C. 6 hours
• D. 7.5 hours

Answer 1

The Correct Option is B

Step 1: Determine the Rate of One Tap

4 taps fill 100 litres in 6 hours, so the rate of one tap is: 

\[ \text{Rate of 1 tap} = \frac{100}{4 \times 6} = \frac{100}{24} = \frac{25}{6} \text{ litres per hour}. \]

Step 2: Determine the Rate of 8 Taps

Since 8 taps will fill at double the rate of 4 taps, the rate of 8 taps is:

\[ \text{Rate of 8 taps} = 8 \times \frac{25}{6} = \frac{200}{6} \text{ litres per hour}. \]

Step 3: Calculate the Time Required to Fill 150 Litres

\[ \text{Time} = \frac{150}{\frac{200}{6}} = \frac{150 \times 6}{200} = 4.5 \text{ hours}. \]

Conclusion

The time required to fill the tank is 4.5 hours.