An empty rectangular tank measuring 35 cm by 20 cm by 50 cm is being filled with water from Tap A at a rate of 700 ml per minute. Tap B drains out water from the tank at 0.5 l per minute. Tap A is turned on 6 minutes before tap B.

1. Calculate the volume of water filled by Tap A in 6 minutes

$\text{Volume} = 700 \times 6 = 4200\text{ ml}$

1. Calculate the total volume of the tank

$\text{Total volume} = 35 \times 20 \times 50 = 35000 \text{ cm}^3 = 35 \text{ l}$

2. Calculate the target volume (60% of the tank)

$\text{Target volume} = 60\% \times 35 = 0.6 \times 35 = 21 \text{ l}$

3. Calculate the volume of water already in the tank after the first 6 minutes

$\text{Volume after 6 mins} = 700 \text{ ml/min} \times 6 \text{ min} = 4200 \text{ ml} = 4.2 \text{ l}$

4. Calculate the remaining volume needed to reach 60%

$\text{Remaining volume needed} = 21 - 4.2 = 16.8 \text{ l}$

5. Calculate the net rate of filling when both taps are on

$\text{Rate of Tap A} = 700 \text{ ml/min} = 0.7 \text{ l/min}$
$\text{Net rate} = 0.7 - 0.5 = 0.2 \text{ l/min}$

6. Calculate the time taken to fill the remaining volume

$\text{Time for remaining volume} = \frac{16.8}{0.2} = 84 \text{ minutes}$