Work Time : Share of wage

This aptitude practice question is a Work Time problem solving question. Concept tested: Share of wages to 3 people working together to complete a task.

Question

X alone can do a piece of work in 15 days and Y alone can do it in 10 days. X and Y undertook to do it for Rs. 720. With the help of Z they finished it in 5 days. How much is paid to Z?

1. Rs.360
2. Rs.120
3. Rs.240
4. Rs.300

  Correct Answer      Choice (2). Z is paid Rs.120.

Explanatory Answer

Step 1: Find the time taken by Z to complete the task

In one day X can finish \\frac{1}{15}^{th}) of the work.
In one day Y can finish \\frac{1}{10}^{th}) of the work.
Let us say that in one day Z can finish \\frac{1}{Z}^{th}) of the work.
When all three work together, they finish the work in 5 days. Or they finish \\frac{1}{5}^{th}) of the work in a day.
When all the three work together, in one day, they can finish \\frac{1}{15}) + \\frac{1}{10}) + \\frac{1}{Z}) = \\frac{1}{5}^{th}) of the work.
Therefore, \\frac{1}{Z}) = \\frac{1}{5}) - \\frac{1}{15}) - \\frac{1}{10})
Or \\frac{1}{Z}) = \\frac{6 - 2 - 3}{30}) = \\frac{1}{30})

Step 2: Find the share of Rs.720 paid to Z

Wages are shared in the ratio of work done or in the ratio of individual efficiencies.
Wages are NOT shared in the ratio of time taken by them to complete the job. The rate of work done is the reciprocal of the time taken by them.
Ratio of work done = \\frac{1}{15}) : \\frac{1}{10}) : \\frac{1}{30})
Rewriting the ratio with a common denominator, \\frac{2}{30}) : \\frac{3}{10}) : \\frac{1}{30}) = 2 : 3 : 1.
Therefore, total wages of Rs.720 is divided among X, Y, and Z in the ratio 2 : 3 : 1
Z receives \\frac{1}{6}^{th}) of the total money.

So, Z will receive \\frac{1}{6})* 720 = Rs.120

X will get \\frac{2}{6}) * 720 = Rs.240
Y will get \\frac{3}{6}) * 720 = Rs.360

  The correct answer is Choice (2).