Explanation

Tap X can fill the tank in 10 hours, which means it fills 1/10 of the tank per hour.

Tap Y can fill the tank in 15 hours, which means it fills 1/15 of the tank per hour.

When both taps are opened together, their combined rate of filling the tank is the sum of their individual rates:

(1/10 + 1/15) of the tank per hour

To add these fractions, we need a common denominator, which is 30. So we get:

(3/30 + 2/30) = 5/30 = 1/6 of the tank per hour

Since they fill 1/6 of the tank per hour together, they will fill the entire tank in 6

hours.