Suppose, ‘A’ can complete a job in 10 days, and ‘A’ and ‘B’ together can complete the same job in 6 days. In how many days can ‘B’ alone complete the job ?
15 days
12 days
18 days
20 days
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CISF-AC-EXE – 2022
A completes the job in 10 days. A’s work rate per day = W / 10.
A and B together complete the job in 6 days. Their combined work rate per day = W / 6.
Let B alone take x days to complete the job. B’s work rate per day = W / x.
The combined work rate of A and B is the sum of their individual work rates:
(A’s rate) + (B’s rate) = (A+B)’s rate
(W / 10) + (W / x) = (W / 6)
Since W represents the same job and is non-zero, we can divide the entire equation by W:
1 / 10 + 1 / x = 1 / 6
Now, solve for 1/x:
1 / x = 1 / 6 – 1 / 10
To subtract the fractions, find a common denominator for 6 and 10. The least common multiple is 30.
1 / 6 = 5 / 30
1 / 10 = 3 / 30
So, 1 / x = 5 / 30 – 3 / 30
1 / x = (5 – 3) / 30
1 / x = 2 / 30
1 / x = 1 / 15
Therefore, x = 15.
B alone can complete the job in 15 days.
– The combined work rate is the sum of individual work rates.
– Set up an equation based on work rates and solve for the unknown time.
A does 30 units in 10 days, so A’s rate = 30/10 = 3 units/day.
A and B together do 30 units in 6 days, so their combined rate = 30/6 = 5 units/day.
B’s rate = (A+B)’s rate – A’s rate = 5 units/day – 3 units/day = 2 units/day.
Time taken by B alone = Total Work / B’s rate = 30 units / (2 units/day) = 15 days.
Both methods yield the same result.