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)`