Question

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

Answer 1

Number of hours A takes alone to fill the tank = 12 hrs.

∴ Amount of water filled by trap A in 1 hr = `(1)/(12)`

Number of hours tap B takes alone to fill the tank = x

∴ Amount of water filled by tap B in 1 hr = `(1)/x`

No o hours Tap A and B take together to fill the tank = 6 hrs and 40 minutes

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

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

∴ Amount of work done by both Tap A and B in 1 hr = `(1)/(4)`

⇒ `(1)/(12) + (1)/x = (1)/(4)`

⇒ `(1)/x = (1)/(4) - (1)/(12)`

= `(3 - 1)/(12)`

= `(2)/(12)`

= `(1)/(6)`
⇒ x = 6 days.
Thus, the number of  Days B working alone = 6 days.