X, Y and Z can do a piece of work in 4 days, 5 days and 7 days, respectively. They get Rs. 415 for completing the work. If X, Y and Z have worked together to complete the work, what is X's share?

Wages are distributed in the ratio of the work efficiencies of the individuals when they work together for the same amount of time.
Step 1: Determine the individual efficiencies
The ratio of times taken by X, Y, and Z is 4:5:7.
The ratio of their efficiencies is the reciprocal of the ratio of time taken:

Efficiency Ratio=
4
1
​
:
5
1
​
:
7
1
​

To clear the fractions, multiply each term by the LCM of 4, 5, and 7, which is 140:

Efficiency Ratio=(
4
1
​
×140):(
5
1
​
×140):(
7
1
​
×140)=35:28:20
Step 2: Calculate X's share
Total parts =35+28+20=83

X’s Share=
83
35
​
×415
Since
83
415
​
=5:

X’s Share=35×5=Rs. 175