Problem Solving

Hi, I found this question in another forum and was not convinced with the solution. Can you please solve? Thanks!
I do not have the OA.

13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 women can finish the same job in 6 days. In how many days can 1 man, 1 boy and 1 woman working together finish the same job (assume constant rates each for men, women, and boys)?

A. 32
B. 54
C. 21
D. 63
E. 24

ace_gre wrote:Hi, I found this question in another forum and was not convinced with the solution. Can you please solve? Thanks!
I do not have the OA.

13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 women can finish the same job in 6 days. In how many days can 1 man, 1 boy and 1 woman working together finish the same job (assume constant rates each for men, women, and boys)?

A. 32
B. 54
C. 21
D. 63
E. 24

say 1 man can finish the work in m days he does 1/m in 1 day, 1 boycan finish the work in b days he does 1/b in 1 day; 1 woman can finish the work in w days he does 1/w in 1 day

13/m+7/b =1/7
6/b+13/w = 1/6

13/m+13/b+13/w = 13/42
1/m+1/b+1/w =1/42

So it would take 42 days for a man, a woman and a boy together to complete the work

Group 1: 13M+7B = 7 days
Group 2 : 13W+6B = 6 days

The amount of work done by G1 in 1 day : 1/7 and by G2 in 1 day : 1/6

So, total work done by G1 and G2 together in 1 day, = 1/7 + 1/6

1 day work by 13(M+B+W) = 13/42 of work

1 day work by ( M+B+W) = 1/42 of work

so, altogether it would take 42 days for ( M+B+W) to finish the entire work.

Ans : 42

Hi..

I've worked on the problem. But, am getting 42 days.

13 Men + 7 Boy = 7 days. So, 1 day's work of 13 Men + 7 Boy = 1/7 --(1)

6 Boy + 13 Women = 6 days. So, 1day's Work of 6 Boy + 13 Women = 1/6 --(2)

(1) + (2) = 13 Men + (6+7) Boy + 13 Women = 1/6+1/7
13 Men + 13 Boy + 13 Women = 13/42 work in 1 day
So, 1Man + 1 Boy + 1 Woman = 1/42 work

So, 1Man + 1 Boy + 1 Woman will take 42 days to complete the whole job

(13m+7b)*7=(13w+6b)*6
--->7m+b=6w
---->1w=(7m+b)/6
1m+1b+1w=(13m+b)/6

now (13m+7b)*7=(13m+b)*x
x=42 days
which is not in option so cheers!!!!

Thanks for replying. It could have been a typo. Looking at your approaches and given that all your answers coincide, I think 42 is the answer.