Question

Two taps A and B can fill a tank in x and 80 minutes respectively. To fill the empty tank, both taps are kept opened for 20 minutes and then B is turned off. If the total time to fill the tank is 45 minutes, then what is the value of x?
1. 56 minutes
2. 72 minutes
3. 60 minutes
4. 64 minutes

Answer 1

Correct Answer - Option 3 : 60 minutes

Time taken to fill the tank for tap A = x min

Time taken to fill the tank for tap B = 80 min

∴ In one min,

Tap A can fill 1/x of the tank.

Tap B can fill 1/80 of the tank.

Part of tank will be filled when both are opened = (1/x) + (1/80) = (80 + x)/80x.

Part of tank will be filled when both are opened in 20 min = 20 × (80 + x)/80x = (80 + x)/4x.

Remaining part = 1 – (80 + x)/4x. = (4x - 80 - x)/4x  = (3x - 80)/4x

Now, (3x - 80)/4x of the tank is empty and only B has to fill it.

Remaing time = 45 - 20 = 25 min

Let time taken to fill the tank only by tap A = 25 min

∴ 25 × (1/x) = (3x - 80)/4x

⇒ 100x = 3x² - 80x

⇒ 3x² = 100x + 80x

⇒ 3x² = 180x

⇒ x = 60 min

∴ tap A will fill the tank in 60 min.