Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
Two taps can fill a cistern in 2 hours and 46 hours respectively. A third tap can empty it in 46 hours. How long (in hours) will it take to fill the empty cistern, if all of them are opened together?
2
4
3
5
2
Since Tap B fills and Tap C empties in the same time (46 hours), they cancel each other out completely, leaving only Tap A to fill the cistern in 2 hours.
Tap A fills in 2 hours, Tap B fills in 46 hours, and Tap C empties in 46 hours.
T=A1тАЛ+B1тАЛтИТC1тАЛ1тАЛ
Since Tap B fills and Tap C empties in the same time (46 hours), they cancel each other out completely, leaving only Tap A to fill the cistern in 2 hours.
Many students try to calculate the LCM of 2 and 46 (which is 46) and add all rates, forgetting that the third tap is an outlet (negative work).
Calculate individual work rates
Convert time taken by each tap into work rate per hour: Rate A = 1/2, Rate B = 1/46, and Rate C = -1/46 (negative as it empties).
RAтАЛ=21тАЛ,RBтАЛ=461тАЛ,RCтАЛ=тИТ461тАЛ
Calculate net work rate
Add the rates of all three taps together. Note that Rate B and Rate C cancel out since they have equal magnitude and opposite signs.
RnetтАЛ=21тАЛ+461тАЛтИТ461тАЛ=21тАЛ
Find total time
The time taken to fill the cistern is the reciprocal of the net work rate.
Time=RnetтАЛ1тАЛ=1/21тАЛ=2┬аhours
A is correct because the inlet and outlet rates of 46 hours cancel each other, leaving only the first tap to fill the cistern in 2 hours.
This concept is identical to work-equivalence problems in Time and Work where persons working against each other (one building, one dismantling) are analyzed.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download тАв 100K+ Aspirants