Three persons X, Y, Z are hired to do a particular job. (X + Y) can do the same job in 16 days while (Y + Z) can do the same job in 10 days. To complete the job X worked on the job for 6 days, Y worked for 11 days and Z worked for 7 days respectively. Find how much time will X take to complete the work alone?

Three persons X, Y, Z are hired to do a particular job. (X + Y) can do the same job in 16 days while (Y + Z) can do the same job in 10 days. To complete the job X worked on the job for 6 days, Y worked for 11 days and Z worked for 7 days respectively. Find how much time will X take to complete the work alone? Correct Answer 40 days

Given:

Out of the three persons (X + Y) can do the job in 16 days, and (Y + Z) can do the job in 10 days. X has worked on the job for 6 days, Y worked for 11 days, and Z worked for 7 days.

Concept Used:

LCM method: In this, we try to find the LCM of the given data and consider that LCM as our work is done and the multiples that we found here is the efficiency of the persons. As shown below in the answer.

Total work done = (Time taken)×(Total Efficiency)

Calculation:

As we can find in the answer the total efficiency of (X +Y) and (Y + Z) is 5, 8 unit/day

Now, as given X worked for 6 days, Y for 11 days, and Z for 7 days.

⇒ Total work done = (X + Y)6 + (Y + Z)5

⇒ Total work done = 5×6 + 8×5 = 30 + 40 = 70 unit

Now, the work left after X has worked for 6 days and Y for 11 days but Z worked only for 5 days will be

⇒ Work left = 80 – 70 = 10 unit

This work is done by Z in 2 days, So the efficiency of Z will be

⇒ Efficiency of Z = 10/2 = 5 unit/day

As the efficiency of (X + Y) is 5 units/day and of (Y + Z) is 8 units/day the efficiency of X and Y will be

⇒ Y = 8 – 5 = 3 units/day

⇒ X = 5 – 3 = 2 units/day

Now the time taken by X alone to complete the work will be

⇒ Time taken by X = 80/2 = 40 days

∴ The time taken by X alone to complete the work is 40 days