Question

A tap can empty a tank in 30 minutes. A second tap can
empty it in 45 minutes. If both the taps operate
simultaneously, how muchh time is needed to empty the tank?
A. 18 minutes
B. 14 minutes
C. 15 minutes
D. 30 minutes

Answer 1

Correct Answer - (a)
Work done by `1^(st)` tap in one minute `= 1/30`
Work done by `2^(nd)` tap in one minute `= 1/45`
Both tap one minute work `=1/30 + 1/45 = (45+30)/1350`
`= 75/1350 = 1/18`
Both tap will empty the tank in 18 minutes.
Alternate Solution:
Let total work `=90 units = LCM(30,45)`
`therefore` A can empty `90/30` units in 1 minute
B can empty `90/45` units in 1 minute
`therefore` Together they can empty 90 units in `90/(3+20)`
= 18 minutes