A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done is 23 days?
Solution
Correct Answer: Option B
Ratio of times taken by A and B = 100 : 130 = 10 : 13
Suppose B takes x days to do the work.
Then,
10 : 13 :: 23 : x
⇒ x = (23 × 13)/10
⇒ x = 299/10
A's 1 day's work = 1/23
B's 1 day's work = 10/299
(A + B)'s 1day's work = 1/23 + 10/299
= 23/299
= 1/13
∴ A and B together can complete the work in 13 days.
Suppose B takes x days to do the work.
Then,
10 : 13 :: 23 : x
⇒ x = (23 × 13)/10
⇒ x = 299/10
A's 1 day's work = 1/23
B's 1 day's work = 10/299
(A + B)'s 1day's work = 1/23 + 10/299
= 23/299
= 1/13
∴ A and B together can complete the work in 13 days.
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