Tanks X and Y are each filled with some water. If water from Tank Y is poured into Tank X until the water in Tank X reaches the brim, there will be 8 litres of water left in Tank Y. If water from Tank X is poured into Tank Y until the water in Tank Y reaches the brim, there will be 26 litres of water left in Tank X. The ratio of the volume of Tank X to the volume of Tank Y is 5:3. How many more litres of water are needed to fill both tanks to their brim?

Working

Tank X: 5U
Tank Y: 3U

5U-3U = 2U -> 26-8=18
1U= 18/2 =9
5U =5 x 9 =45
45 + 8 = 53
8U = 8 x 9 =72
72 - 53 = 19 (Ans: 19 litre more needed)

Explanation following next

Explanation

Tank X: 5U <- since tank x to tank y is 5:3 let them be 5u & 3U litres respectively
Tank Y: 3U

5U-3U = 2U -> 26-8=18 -> see model below (worth thousand words )

[unit][unit][unit][unit][unit][..8..] all the water into tank X
[unit][unit][unit][.........26..........] all the water into tank Y

1U= 18/2 =9
5U =5 x 9 =45 <- vol of tank x we had taken as 5 units
45 + 8 = 53 <- all the water into tank x (see top part of model)
8U = 8 x 9 =72 <- tank x is 5U and tank y is 3U. combined volume is 8U 72 litres

72 - 53 = 19 <- combined X+Y volume less current combined water is the top-up requirement

sorry put in wrong spot

can somebody delete this?

Hi Reynold,

Thks for your helpful and clear explanations. Just curious, are you from the onSponge team as you seem to be actively involved in providing Maths solutions to needy users like us?

No, just a kaypoh parent