To do a certain task X would take 3 times as long as Y and Z together; and Z would takes 4 times as long as Y and X together. Three of them together can complete the task in 10 days. How much time is taken by X and Z to complete the task?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. .
Given that
X would take 3 times as long as Y and Z together
Z would take 4 times as long as X and Y together
Formula used
Efficiency is inversely proportional to the time taken
Calculation
If, The efficiency of X = 1 unit
So, The efficiency of Y and Z = 3 units
The net efficiency of X, Y, and Z = 1 + 3 = 4 units
If, The efficiency of Z = 1 unit
So, the efficiency of X and Y = 4 units
The net efficiency of X, Y, and Z = 1 + 4 = 5 units
To make same net efficiency of X, Y,and Z = LCM (4, 5) = 20 units
Now, the efficiency of X and Z is 5 and 4 respectively
Total work = 20 × 10 = 200 units
Hence, work completed by X and Z in = 200/(5 + 4) = 200/9 =