- 20 men complete one-third of a piece of work in 20 days.
- More men needed to finish the rest of work in 25 more days can be figure out in this way.
Explanation
Three given entities here are
- Work
- Days
- Men
To determine the relation here, let suppose; Men needed to finish the rest of work in 25 more days = y
Case I
20 men complete work in 20 days = 1/3
Remaining work = 2/3
Work Men
1/3 20
2/3 y
- More work mean more men.
- Less work mean less men.
This clearly indicates that there is direct relation.
Direct/Indirect relation tells how the equation will be written.
1/3 : 2/3 :: 20 : y ________ (i)
Case II
Days Men
20 20
25 y
- More days mean less men.
- Less days mean more men.
This clearly indicates that there is inverse relation.
Direct/Indirect relation tells how the equation will be written.
25 : 20 :: 20 : y ________ (ii)
By (i) and (ii)
1/3 : 2/3 :: 20 : y
25 : 20
1/3 x 25 x y = 2/3 x 20 x 20 ________ (A)
After simplifying equation (A), we can easily figure out the value of y (y = 32) and more men = 32 – 20 = 12 men
To Find
More men needed to finish the rest of work in 25 more days = ?
Solution
Method I
Let suppose
Men needed to finish the rest of work in 25 more days = y
Work Days Men
1/3 20 20
2/3 25 y
- Relation between work and men is direct.
- Relation between days and men is inverse.
So
1/3 : 2/3 :: 20 : y
25 : 20
1/3 x 25 x y = 2/3 x 20 x 20
25y = 2 x 20 x 20
y = 2 x 4 x 4
y = 2 x 16
y = 32
Men needed to finish the rest of work in 25 more days = 32 men
More men needed to finish the rest of work in 25 more days = 32 – 20
More men needed to finish the rest of work in 25 more days = 12 men answer
Method II
Men needed to finish one-third of a work in 20 days = 20 men
Men needed to finish one-third of a work in 1 day = (20 x 20) men
Men needed to finish one-third of a work in 1 day = 400 men
Men needed to finish entire work in 1 day = (400 x 3) men
Men needed to finish entire work in 1 day = 1200 men
Men need to finish entire work in 25 days = 1200/25 men
Men needed to finish entire work in 25 days = 48 men
Men needed to finish 2/3 of work in 25 days = (48 x 2/3) men
Men needed to finish 2/3 of work in 25 days = 32 men
Men needed to finish the rest of work in 25 more days = 32 men
More men needed to finish the rest of work in 25 more days = 32 – 20
More men needed to finish the rest of work in 25 more days = 12 men answer
Conclusion
20 men complete one-third of a piece of work in 20 days. 12 more men should be employed to finish the rest of work in 25 more days.
