Two pipes A and B can fill a cistern in 30 minutes and 40
minutes respectibely. Both the pipes are opened. Find when
the second pipe Bmust be turned off so the cistern may just
be full in 10 minutes.

Options

A. `26 2/3 min`
B. 25 min
C. `40 2/3 min`
D. `42 2/3 min`

Answer

(a)

Explanation

Let a and B together work for x minutes than amount of
waterr filled in the period `= x (1/30 + 1/40) = (7x)/120`
Remaining part `= 1- (7x)/120 + ((120-7x)/120)`
Work done by A in `(10 - x)` minutes `= (120 -7x)/120
`= 1- (7x)/120
`(7x)/120 + (10-x)/30 =1 or 7 x + 40 - 4 x = 120 `
`3x= 120 - 40 = 80`
`x= 26 2/3 min`