Question

4 men and 6 boys can finish a work in 5 days while 3men and 4boys can finish it in 7 days. find the time taken by 1 men and 1 boy alone

Answer 1

4M + 6B = 5D

3M + 4B = 7D

Find the ratio of boys to men:

(4 x 5)M + (6 x 5)B = (3 x 7)M + (4 x 7)B

20M + 30B = 21M + 28B

30B - 28B = 21M - 20M

2B = 1M

Find the number of days 1 boy take to do the job:

4M + 6B = 5D

4(2B) + 6B = 5D

8B + 6B = 5D

14B = 5D

1B = 5 x 14 = 70 days

Find the amount of work 1 boy can do in a day:

1 Boy takes 70 days to do the work

⇒ 1 day = 1/70 of the work

Find the amount of work one man can do in a day:

1M = 2B

1 boy = 1/70 of the work

1 man = 1/70 x 2 = 1/35 of the work

Find the number of days needed:

1 boy = 1/70 of the work

1 man = 1/35 of the work

1 boy + 1 man = 3/70 of the work

3/70 of the work = 1 day

1/70 of the work = 1/3

70/70 of the work = 1/3 x 70 = 23 1/3 days

Answer: 1 man and 1 boy will need 23 1/3 days to finish the work