Aptitude - Time and Work - Discussion

Solving these two equations, we get: x =1and y =1.
100 200,

Please explain above the line.

Why are we taking days in x/y form?

Can we solve by 6x+8y=10 doing this if not then why, please help me out?

Thanks for explaining the solution.

Very well explained @Siddharth.

Let M denotes the work done by a man in 1 day and B denotes the work done by a boy in 1 day.

Now, 6 men and 8 boys do the work in 10 days means 10(6M+8B) = 1.

Similarly, 26 men and 48 boys do the work in 2 days means 2(26M+48B) = 1.
=> 10(6M+8B) = 2(26M+48B),
=> 60M + 80B = 52M + 96B,
=> 8M = 16B,
=> 1M = 2B.

Thus, if we employ 15 men and 20 boys, we mean to say; 15M + 20B.
= 30B + 20B = 50B.

Now, (6M + 8B) do the work in 10 days.
=> (12B + 8B) do the work in 10 days.
=> 20B do the work in 10 days.
=> 1B do the work in 10*20 = 200 days.
=> 50B will do the work in 200/50 = 4 days.

Thank you all for explaining the solution.

1st
6men+8boy=1/10days.

Take 2 common from above eq.
2(3men+4boy)=1/10days.
3men+4boy=1/(10*2)
3men+4boy=1/20.
15men+20 boys= ??days.
3men+4boy=1/20.---->multiply this term with 5.
5(3men+4boy)=(1/20)*5.

Now solve:
15men+20boy=4days.

Then apply x value into 1st equation.
6x+8y=1/10.
6*1/10+8y=1/10,
8y=4/100,
y=1/200.

In the above solution;
How come 6*1/10+8y=1/10?
Please explain the above line.

@All.

M1D1=M2D2.
M1=6men+8boys=14
D1=10,M2=15men+20boys=35
D2=?

or,D2=(M1XD1)/M2.
or,D2=(14X10)/35=4.
So the answer will be 4 days.

According to me,

6men + 8boys = 10 days = 60md + 80bd -----> 1 (md = men and days).

26men + 48boys =2 days = 52md + 96bd ----->2

So,
60md + 80bd = 52md + 96bd,
60md - 52md=96bd - 80bd,
8md = 16bd.

1md = 2bd reciprocal of this so we can get 2boys=1men or 1 men = 2boys.
So 15 men and 20 boys in doing the same type of work will be;
40/7.5 = 4.