Tank P and Tank Q are rectangular tanks. Tank P has a base of 30 cm by 20 cm. Tank Q has a base of 25 cm by 16 cm and a height of 20 cm. The total volume of water in both tanks at first was 15 600 cm³. The height of the water level in Tank P was 6 cm more than that of Tank Q.
- Find the height of the water level in Tank Q.
- Mrs Lim poured water from Tank P into Tank Q until Tank Q was full to its brim. Find the percentage decrease in the volume of water in Tank P. Give your answer correct to 1 decimal place.
Need a hint?
Find the water volume in each tank first, then work out how much water was added to Tank Q. The percentage decrease is taken over Tank P's original volume.
Worked answer
- (a) Let the water height in Tank Q be h cm, so Tank P's is (h + 6) cm.
- (a) Volume in P + volume in Q: 600(h + 6) + 400h = 15 600.
- (a) 1000h + 3600 = 15 600, so 1000h = 12 000 and h = 12.
- (a) Height of water in Tank Q is 12 cm.
- (b) Water in P at first: 600 × 18 = 10 800 cm³, and water in Q: 400 × 12 = 4800 cm³.
- (b) Tank Q is full at 20 cm, so it needs 400 × (20 − 12) = 3200 cm³ more.
- (b) Water left in P: 10 800 − 3200 = 7600 cm³.
- (b) Percentage decrease = 3200 ÷ 10 800 × 100% = 29.6% (1 d.p.).
The mistake this question tests
Percentage of a new total
Pupils often divide by the volume added to Tank Q, or by Tank Q's original volume, instead of Tank P's original volume.
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