Question

A tap can fill a tank in 12 hours while another tap can fill the same tank in x hours. Both the taps if opened together can fill the tank in 6 hours and 40 minutes. Find the time the second tap will take to fill the tank.

Answer 1

Let the time taken by the second tap be x hours.

So, the second tap can fill `(1)/x` part of the tank in an hour.

Given that the time taken by the first tap to fill the tank is 12hours.

So, the first tap can fill `(1)/(12)` part of the tank in an hour.

Together they can fill the tank in 6hours 40minutes

= `(6 + 40/60)"hours"`

= `(6 + 2/3)"hours"`

= `(20)/(3)"hours"`

So, together they can fill `(3)/(20)` part of the tank in an hour.

As per the given condition.

`(1)/x + (1)/(12) = (3)/(20)`

⇒ `(12 + x)/(12x) = (3)/(20)`

⇒ 20(12 + x) = 36x
⇒ 240 + 20x = 36x
⇒ 16x = 240
⇒ x = 15
Hence, the time taken by the second tap is 15hours.