- If 3 men or 6 boys can do a piece of work in 10 days working 7 hours a day.
- Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work twice as large can be figure out in this way.
Explanation
Three given entities here are
- Boys
- Hours
- Days
To determine the relation here, let suppose; days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work = y
Case I
As
3 men = 6 boys
1 man = 2 boys
6 men = 12 boys
6 men and 2 boys = 14 boys
Boys Days
6 10
14 y
- Less boys mean more days.
- More boys mean less days.
This clearly indicates that there is inverse relation.
Direct/Indirect relation tells how the equation will be written.
14 : 6 :: 10 : y ________ (i)
Case II
Hours Days
7 10
8 y
- Less hours mean more days.
- More hours mean less days.
This clearly indicates that there is inverse relation.
Direct/Indirect relation tells how the equation will be written.
8 : 7 :: 10 : y ________ (ii)
By (i) and (ii)
14 : 6 :: 10 : y
8 : 7
14 x 8 x y = 6 x 7 x 10 ________ (A)
After simplifying equation (A), we can easily figure out the value of y (y = 7.5 days)
To Find
Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work twice as large = ?
Solution
Method I
Let suppose
Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work = y
Boys Hours Days
6 7 10
14 8 y
- Relation between boys and days is inverse.
- Relation between hours and days is also inverse.
So
14 : 6 :: 10 : y
8 : 7
14 x 8 x y = 6 x 7 x 10
112y = 420
y = 420/112
y = 3.75 days
Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work = 3.75 days
Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work twice as large = (3.75 x 2) days
Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work twice as large = 7.5 days
Method II
As
3 men = 6 boys
1 man = 2 boys
6 men = 12 boys
6 men and 2 boys = 14 boys
Days required by 6 boys working for 7 hours a day to complete a piece of work = 10 days
Days required by 6 boys working for 1 hour a day to complete a piece of work = (10 x 7) days
Days required by 6 boys working for 1 hour a day to complete a piece of work = 70 days
Days required by 1 boy working for 1 hour a day to complete a piece of work = (70 x 6) days
Days required by 1 boy working for 1 hour a day to complete a piece of work = 420 days
Days required by 1 boy working for 8 hours a day to complete a piece of work = 420/8 days
Days required by 1 boy working for 8 hours a day to complete a piece of work = 52.5 days
Days required by 14 boys working for 8 hours a day to complete a piece of work = 52.5/14 days
Days required by 14 boys working for 8 hours a day to complete a piece of work = 3.75 days
Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work twice as large = (3.75 x 2) days
Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work twice as large = 7.5 days
Conclusion
If 3 men or 6 boys can do a piece of work in 10 days working 7 hours a day; 7.5 days it will take to complete a piece of work twice as large with 6 men and 2 boys working together for 8 hours a day.
