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
P and Q can complete a task in 12 days and 18 days respectively. If they work together, how many days will it take to finish the work? (Correct to one decimal place)
7.2
7.5
8.1
6.8
7.2
Use the product-over-sum formula for two workers:x+yxyтАЛ =12+1812├Ч18тАЛ =30216тАЛ = 7.2 days.
Time taken by P = 12 days, Time taken by Q = 18 days
Time=EfficiencyPтАЛ+EfficiencyQтАЛTotalWorkтАЛ
Use the product-over-sum formula for two workers:x+yxyтАЛ =12+1812├Ч18тАЛ =30216тАЛ = 7.2 days.
Students often wrongly add the days directly (12+18=30 days) or take their average instead of adding their individual work rates.
Find Total Work via LCM
Assume the total work is the LCM of 12 and 18, which is 36 units.
LCM(12,18)=36
Calculate Individual Efficiencies
P's 1-day work is 1236тАЛ=3 units/day, and Q's 1-day work is 1836тАЛ=2 units/day.
EfficiencyPтАЛ=3,EfficiencyQтАЛ=2
Calculate Combined Efficiency
When working together, their combined 1-day work is 3+2=5 units/day.
CombinedEfficiency=3+2=5
Calculate Total Time Taken
Divide the total work by the combined efficiency to get the total days required: 536тАЛ=7.2 days.
Time=536тАЛ=7.2┬аdays
A is correct because working together they take 7.2 days to complete the task.
This LCM approach is identical to pipe and cistern problems where inflow/outflow rates substitute for worker efficiencies.
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