Notice that in both situations, Tank Y is fully drained while Tank X still has water left.

Situation ①
Tank X is being drained at 102 l per hour.

Situation ②
Tank X is being drained at 34 l per hour.

102 l ÷ 34 l = 3

So in ①, water in Tank X is being drained at 3x the rate in ②.

As for Tank Y, it is the opposite.
In ② , water in Tank Y is being drained at 3x the rate in ①.

This also means the rate of ① is ⅓ of ②. So Tank Y takes 3 times as long to be fully drained in ① as compared to ②.

This also means that the time that Tank X was being drained for in ① is 3x that in ②.

So when you compare Situation ① to Situation ②,

Volume of water drained from Tank X in ①

= 3 x 3 x volume of water drained in ②
(3x for the rate and 3x for the amount of time)

= 9 x volume of water drained in ②

9x - 1x = 8x
This means volume of water drained from Tank X in ① is 8 times more than in ②.

Volume of water in Tank X
= volume drained in ② + 1176 l left

Volume of water in Tank X also
= volume drained in ① + 420 l left
= 9 x volume drained in ② + 420 l left

Comparing the two,

8 times in ② = 1176 l - 420 l = 756 l
1 time in ② = 756 l ÷ 8 = 94.5 l

So this tells you at 94.5 l was drained from Tank X in ②.

Time used to fully drain Tank Y in ②
= Time that Tank X drained in ②
= 94.5 l ÷ 34 l/h
= 189/68 h

Volume of water in Tank Y
= 189/68 h x 102 l/h
= 283.5 l

(Alternatively,

since we know in ②, Tank Y is drained at 3x the rate of Tank X, and Tank Y was fully drained in both cases,

Volume of water in Tank Y
= 3 x volume of water drained in Tank X in ② = 3 x 94.5 l = 283.5 l )

Volume of water in Tank X
= 94.5l + 1176 l = 1270.5 l

Difference = 1270.5 l - 283.5 l
= 987 l