Question

A father can do a job as fast as his two sons working together. If one son does the job in 24 days and the other in 40 days, how many days will the father take to do the job?

Answer 1

Work done by Son1 in one day=1/24
Work done by Son2 in one day=1/40
Work done by both in one day=1/24+1/40 =8/120 = 1/15
Therefore, Time takby both sons to complete work=Time taken by father to complete work=15

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Answer 2

Son 1 takes 24 days to complete

⇒ 1 day = 1/24 of the work

Son 2 takes 40 days to complete

⇒ 1 day = 1/40 of the work

Father is as fast as his sons working together

⇒ 1 day = 1/24 + 1/40 = 1/15 of the work

Number of days the Father needs to complete the work:

1/15 of the work = 1 day

15/15 of the work = 1 x 15 = 15 days

Answer: The Father needs 15 days to do the job