Question

A tap can fill an Empty tank in 48 minutes and another tap can empty the full tank in 2 hours if both taps are opened at 11:40 a.m. will the empty tank can be filled

Answer 1

Efficiency is work done per minute here
efficiency of First Tap = 1/48
efficiency of Second Tap = 1/120 (convert 2 hr in minutes)
total work done/efficiency in 1 minute if both taps opened simultaneously
=1/48 +1/120
=7/240
This implies
7* 33 = 238 (just less than 240, unit of 33 is minutes)
2/240 work will remain undone , which will be done under 34 th minute after 11:40 am
so
remaining work/efficiency of doing work per minute
=(2/238)/(7/240)
=2/7 minutes
which is equal to approx 17 seconds)
so
time after 11:40 minutes at which tank will be filled is
=33 minutes+ 17 seconds
or
=33 whole2/7
this implies
after adding 33 minutes and 17 seconds to 11:40 am, it will be
12:13:17 pm