Solution: `960 (ml)`
Step by step:
Let the amount of water in cup `A, B, C` at first `= a, b, c (a, b, c >0; a>b)`
Given that,
`+)` Tuan transferred `25%` of the water from cup `C` to cup `A.`
`∴` The amount of water in cup `A, B, C` after that was:
`a+25%c ; b ; 75%c`
`+)` Then, Tuan continued to transfer `25%` of the remaining water from cup `C` to cup `B.`
`∴` The amount of water in cup `A, B, C` after that was:
`a+25%c ;`
`b+(25%×75%c) = b+3/16c ;`
`75%c-(25%×75%c)=75%c-3/16c`
`+)` There was `90 ml` more water in cup `A` than cup `B` at the end.
`⇒ (a+25%c)-(b+3/16c) = 90 (ml)`
`⇒ a + 1/4c-b-3/16c = 90 (ml)`
`⇒ a-b+1/16c = 90`
`⇒ 16a-16b+c = 1440`
`+)` Tuan poured water into cup `A, B, C` in the ratio of `9 : 7 : 16.`
`⇒ a/9 = b/7 = c/16 (1)`
Using theorem on equal ratios:
`a/9 = b/7 = c/16 = (16a)/144 = (16b)/112 = {16a - 16b + c}/{144-112+16}`
`= 1440/48 (∵16a-16b+c=1440)`
`=30`
`∴ a = 270; b = 210; c = 480`
`∴` Total water in `3` cups: `270+210+480=960 (ml)`
