- 2 men and 7 boys can do a piece of work in 14 days.
- 3 men and 8 boys can do the same in 11 days.
- Days required by 8 men and 6 boys to do three times the amount of this work can be figure out as in this way.
Explanation
Let suppose
- Work done by 1 man in 1 day = y
- Work done by 1 boy in 1 day = z
According to the First given condition
2y + 7z = 1/14 ________ (i)
According to second given condition
3y + 8z = 1/11 ________ (ii)
By solving equation (i) and (ii) simultaneously, we can easily figure out the value of y and z which further leads to determine the days required by 8 men and 6 boys to finish three times the amount of this work.
To Find
Days required by 8 men and 6 boys to finish three times the amount of this work = ?
Solution
Let suppose
- Work done by 1 man in 1 day = y
- Work done by 1 boy in 1 day = z
According to the First given condition
2y + 7z = 1/14 ________ (i)
According to second given condition
3y + 8z = 1/11 ________ (ii)
Multiplying equation (i) with 3 and equation (ii) with 2 and subtracting from equation (i)
(6y + 21z) – (6y + 16z) = 3/14 – 2/11
6y + 21z – 6y – 16z = (33 – 28)/154
5z = 5/154
770z = 5
z = 5/770
z = 1/154
Work done by 1 boy in 1 day = 1/154
Work done by 6 boys in 1 day = 6/154
Putting (z = 1/154) in equation (i)
2y + 7(1/154) = 1/14
2y + 1/22 = 1/14
28y + 7/11 = 1
308y + 7 = 11
308y = 4
y = 4/308
y = 1/77
Work done by 1 man in 1 day = 1/77
Work done by 8 men in 1 day = 8/77
Work done by 8 men and 6 boys in 1 day = 8/77 + 6/154
Work done by 8 men and 6 boys in 1 day = (16 + 6)/154
Work done by 8 men and 6 boys in 1 day = 22/154
Work done by 8 men and 6 boys in 1 day = 1/7
Days required by 8 men and 6 boys to finish the work = 7 days
Days required by 8 men and 6 boys to finish three times the amount of this work = (7 x 3) days
Days required by 8 men and 6 boys to finish three times the amount of this work = 21 days
Conclusion
2 men and 7 boys can do a piece of work in 14 days; 3 men and 8 boys can do the same in 11 days. Then, 8 men and 6 boys can do three times the amount of this work in 21 days.
