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A and B together can complete a work in 2 days. If A works for 1 day and B works for 4 days, the work is completed. How long would B alone take to complete the work?
4 days
10 days
8 days
6 days Question ID : 4410091622543 Option 1 ID : 4410096408948 Option 2 ID : 4410096408951 Option 3 ID : 4410096408950 Option 4 ID : 4410096408949 Status : Answered Chosen Option : D
6 days Question ID : 4410091622543 Option 1 ID : 4410096408948 Option 2 ID : 4410096408951 Option 3 ID : 4410096408950 Option 4 ID : 4410096408949 Status : Answered Chosen Option : D
Observe the trade-off: decreasing A's time by 1 day requires increasing B's time by 2 days (from 2 to 4). Since 1 day reduction in A requires 2 days increase in B, B's total work takes 3 times the original remaining effort.
Combined work rate of A and B is such that they finish in 2 days. A works for 1 day and B works for 4 days to complete the work.
1=(A+B)├Ч2=A├Ч1+B├Ч4
Observe the trade-off: decreasing A's time by 1 day requires increasing B's time by 2 days (from 2 to 4). Since 1 day reduction in A requires 2 days increase in B, B's total work takes 3 times the original remaining effort.
Students often add the days directly (1+4=5) or fail to realize that the total work unit is constant, equating work rates instead of time.
Define Efficiency
Let A and B be the daily work rates. Given they finish together in 2 days, total work is 2(A+B). Given the second scenario, total work is 1A+4B.
2(A+B)=A+4B
Solve for Ratio of Efficiencies
Expand the equation: 2A+2B=A+4B. Subtract A and 2B from both sides to find the ratio A/B.
A=2BтЯ╣BAтАЛ=12тАЛ
Calculate Total Work
Using efficiency ratio A=2,B=1, total work is 2(A+B)=2(2+1)=6 units.
Total┬аWork=6┬аunits
Calculate Time for B
Time taken by B alone = Total┬аWork/BтАЩs┬аefficiency=6/1=6 days.
TBтАЛ=16тАЛ=6┬аdays
D is correct because solving the work equation 2A+2B=A+4B results in A=2B, leading to a total work of 6 units which takes B exactly 6 days to complete.
This ratio-based logic is identical to mixture and allegation problems where the balance of two components (A and B) determines the total composition.
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