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
8 men and 12 women can build a wall in 10 days. 6 men and 8 women can build the same wall in 14 days. How long will it take for 1 woman to build it alone?
280 days
140 days
350 days
700 days
280 days
Set up the simultaneous work equations, equate total work in both scenarios to find the efficiency ratio of a man to a woman (M:W), then substitute back to find the time taken by 1 woman alone.
8 men and 12 women can build a wall in 10 days. 6 men and 8 women can build the same wall in 14 days.
M1тАЛ=Work┬аdone┬аby┬а1┬аman┬аin┬а1┬аday,W1тАЛ=Work┬аdone┬аby┬а1┬аwoman┬аin┬а1┬аday
Set up the simultaneous work equations, equate total work in both scenarios to find the efficiency ratio of a man to a woman (M:W), then substitute back to find the time taken by 1 woman alone.
Confusing the time taken by a group with individual worker efficiencies, or making calculation errors when equating total work units (8M+12W)├Ч10=(6M+8W)├Ч14.
Step 1: Set up the total work equations
Since the amount of work in both cases is the same, we can equate the total work done in both scenarios: (8M+12W)├Ч10=(6M+8W)├Ч14
(8M+12W)├Ч10=(6M+8W)├Ч14
Step 2: Find the efficiency relation between men and women
Expanding both sides of the equation: 80M+120W=84M+112W Simplifying the terms gives: 4M=8WтЯ╣M=2W
M=2W
Step 3: Calculate total work in terms of women
Substitute M=2W into the first scenario to find total work units: Total┬аWork=(8(2W)+12W)├Ч10=(16W+12W)├Ч10=280┬аwoman-days
Total┬аWork=280┬аwoman-days
Step 4: Calculate time taken by 1 woman alone
To find the number of days required for 1 woman to build the wall alone, divide the total work by the 1-woman daily capacity: Days=1┬аwoman280┬аwoman-daysтАЛ=280┬аdays
280┬аdays
A is correct because equating the work rates yields M=2W, and substituting this into the total work gives 280 woman-days, meaning 1 woman will take 280 days to build the wall alone.
This method is universally applicable to pipes and cisterns problems as well as combined efficiency problems in quantitative aptitude.
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