Question 828271
10 men or 18 boys can do a piece of work in 15 days, 
in how many days will 25 men and 15 boys do the same 
piece of work?
<pre>
Let the answer be x days.

10 men can do 1 job in 15 days. Therefore
 1 man can do {{{1/10}}}th of the job in 15 days.
 1 man can do {{{1/15}}}th of {{{1/10}}}th of the job in 1 day
Since {{{1/15}}}th of {{{1/10}}}th is {{{1/150}}}th of the job,
 1 man can do {{{1/150}}}th of the job in 1 day.
25 men can do {{{25/150}}}ths of the job in 1 day.
Reduce the fraction:
25 men can do {{{1/6}}}th of the job in 1 day.
25 men can do {{{x/6}}}ths of the job in x days. 

18 boys can do 1 job in 15 days, so
 1 boy can do {{{1/18}}}th of the job in 15 days.
 1 boy can do {{{1/15}}}th of {{{1/18}}}th of the job in 1 day
Since {{{1/15}}}th of {{{1/18}}}th is {{{1/270}}}th of the job,
 1 boy can do {{{1/270}}}th of the job in 1 day.
15 boys can do {{{15/270}}}ths of the job in 1 day.
Reduce the fraction:
15 boys can do {{{1/18}}}th of the job in 1 day.
15 boys can do {{{x/18}}}ths of the job in x days. 

The equation comes from:

{{{(matrix(14,1,
the, fraction, of, the, job, which, the, 25, men, can, do, in, x, days))}}}{{{""+""}}}{{{(matrix(14,1,
the, fraction, of, the, job, which, the, 15, boys, can, do, in, x, days))}}}  {{{""=""}}} {{{(matrix(3,1,one,whole,job))}}}

{{{x/6}}}{{{""+""}}}{{{x/18}}} {{{""=""}}} 1

Multiply through by LCD of 18

3x + x = 18
    4x = 18
     x = {{{18/4}}}
     x = {{{9/2}}}
     x = {{{4&1/2}}} days.

Edwin</pre>