Two rectangular containers P and Q hold water. The base of container P measures 12 cm by 10 cm. The base of container Q measures 15 cm by 12 cm. Container Q contains 2700 cm³ more water than container P. The height of the water level in container Q is 10 cm more than that in container P.
- Find the height of the water level in container P.
- Ravi pours some water from container Q into container P until the water levels in both containers are at the same height. Find the amount of water in container P in the end.
Need a hint?
In (a), write the water in each container as base area times height, and use the 10 cm height difference to rewrite Q's height in terms of P's height. In (b), the total water stays the same and is shared over the two bases together.
Worked answer
- (a) Let the height of the water in P be h cm, so the height in Q is (h + 10) cm.
- (a) Base of P is 12 × 10 = 120 cm², so water in P = 120h cm³.
- (a) Base of Q is 15 × 12 = 180 cm², so water in Q = 180(h + 10) = 180h + 1800 cm³.
- (a) (180h + 1800) − 120h = 2700, so 60h + 1800 = 2700.
- (a) 60h = 900, so h = 15. The water in container P is 15 cm high.
- (b) Water in P = 120 × 15 = 1800 cm³; water in Q = 180 × 25 = 4500 cm³.
- (b) Total water = 1800 + 4500 = 6300 cm³.
- (b) Combined base = 120 + 180 = 300 cm², so the common height = 6300 ÷ 300 = 21 cm.
- (b) Water in P in the end = 120 × 21 = 2520 cm³.
The mistake this question tests
Calculation slip
Pupils often take the 10 cm height difference as the answer to (a), or divide 2700 by the base area of P alone. In (b) they often use only Q's 4500 cm³ or forget that the total water is shared across both bases.
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