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
A pipe can fill a tank in 18 hours. Another pipe can empty the filled tank in 21 hours. If both the pipes are opened simultaneously, then the time (in hours) in which the tank will be filled is:
126
128
129
127
126
Use direct product-over-difference formula: T=bтИТaa├ЧbтАЛ=21тИТ1818├Ч21тАЛ=3378тАЛ=126 hours.
Time taken by filling pipe A=18 hours, Time taken by emptying pipe B=21 hours
Time┬аtaken=Net┬аEfficiencyTotal┬аWork┬а(LCM)тАЛ
Use direct product-over-difference formula: T=bтИТaa├ЧbтАЛ=21тИТ1818├Ч21тАЛ=3378тАЛ=126 hours.
Adding the rates of both pipes instead of subtracting the emptying pipe's rate, leading to 181тАЛ+211тАЛ instead of 181тАЛтИТ211тАЛ.
Find Total Capacity (LCM)
Assume the total capacity of the tank is the LCM of 18 and 21. LCM(18,21)=126 units.
Total┬аCapacity=126┬аunits
Calculate Individual Efficiencies
Efficiency of filling pipe A=18126тАЛ=+7 units/hour. Efficiency of emptying pipe B=21126тАЛ=тИТ6 units/hour.
Efficiency┬аof┬аA=+7,Efficiency┬аof┬аB=тИТ6
Calculate Net Efficiency
When both pipes are opened simultaneously, the net efficiency is the sum of their individual efficiencies.
Net┬аEfficiency=7тИТ6=+1┬аunit/hour
Calculate Total Time Taken
Divide total tank capacity by net efficiency to find total time required to fill the tank.
Time=1126тАЛ=126┬аhours
A is correct because the net rate of filling is 181тАЛтИТ211тАЛ=1261тАЛ of the tank per hour, taking 126 hours to fill completely.
Pipes filling/emptying a tank behave identically to positive and negative work in Time & Work problems, where filling is positive work and emptying/destroying is negative work.
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