Work problem

[hey_thr67]

2 men and 7 boys can do a work in 14 days. 3 men and 8 boys can do the same work in 11 days. Then 8 men and 6 boys can do 3 times the work in how many days ?

A: 12
B: 21
C: 27
D: 15
E: 18


How can I approximate the answer fast ?

[Anurag@Gurome]

2 men and 7 boys can do a work in 14 days. 3 men and 8 boys can do the same work in 11 days. Then 8 men and 6 boys can do 3 times the work in how many days ?

2 men and 7 boys does 1/14 of the job in one day.
3 men and 8 boys does 1/11 of the job in one day.

Hence, in one day,

• (2m + 7b) = 1/14
  (3m + 8b) = 1/11
  
  So, (2m + 7b)/(3m + 8b) = 11/14
  --> (28m + 98b) = (33m + 88b)
  --> 10b = 5m
  --> m = 2b

Hence, in one day one man works twice of a boy.

Now, (2m + 7b) = (4b + 7b) = 11b
And, (8m + 6b) = (16b + 6b) = 22b

As, 2men and 7 boys, i.e. 11 boys completes the work in 14 days, 8 men and 6 boys, i.e. 22 boys will complete the work in 14/2 = 7 days.

Hence, 8 men and 6 boys can do 3 times the work in 3*7 = 21 days.

The correct answer is B.

[hey_thr67]

Thanks Anurag, is there any shorter way . I tend to commit calculation errors when I am specifically solving arithmatic problems