2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do a piece of work in 8 days. In how many days 2 man and 1 boy can do the work?
Answers
Step-by-step explanation:
If 2 men and 3 boys can do a piece of work in 10 days, while 3 men and 2 boys can do the same work in 8 days, then in how many days can 2 men and 1 boy do the work?
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Well this question falls under a particular topic known as ‘Time And Work’ and it can approached in the following manner:_
Let us suppose that in 1 day, 1 man completes ‘x’ part of the work and 1 boy completes ‘y’ part of the work.
A/Q; 2 men and 3 boys can complete the work in 10 days i.e, in 1 day they together can complete 1/10th of the work, which can be written as:
2x + 3y = 1/10
Similarly: 3 men and 2 boys can complete the work in 8 days i.e, in 1 day they can together complete 1/8th of the work, which can be written as:
3x + 2y =1/8
After simplifying both the above equations we have;
6x + 9y =3/10;
6x + 4y =2/8.
And on solving we have;
x = 7/200; y = 1/100.
So now we know the respective amount of work completed by 1 man and 1 boy in 1 day.
Therefore in 1 day, 2 men and 1 boy can complete = 2 * (7/200) + (1/100) = 2/25th of the work i.e, the whole work can be completed in 25/2 days.