The figure shows a tank made up of 3 sections. Cuboid P with a square base of side 4 cm and height 49 cm. Cube Q with a side of 15 cm. Cuboid R that is 67 cm by 14 cm by 40 cm. Water from a tap above flows down at a rate of 2.5 litres per minute while water is drained out from the bottom at a rate of 2 litre per minute. How long did it take to fill up the tank to a height of 67 cm from the base? Give the answer in minutes correct to nearest whole number.
Volume of Q
= 15 x 15 x 15
= 3375 cm³ 

Volume of R
= 67 x 14 x 40
= 37520 cm³ 

2 ℓ = 2000 cm³ 
2.5 ℓ = 2500 cm³ 

Net increase in volume per minute
= 2500 - 2000
= 500 cm³/min

Height of P to be filled with water
= 67 - (40 + 15)
= 12 cm

Volume of water in P
= 4 x 4 x 12
= 192 cm³ 

Volume of water in R, Q and part of P
= 37520 + 3375 + 192
= 41087 cm³ 

Time taken to reach height
= 41087 ÷ 500
≈ 82 min (Correct to nearest whole number)

Answer(s): 82 min