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Quantitative Reasoning – Practice – Time and Work:How many days will Hans take!

PSA_PRACTICE_QNR25. It takes Jose 12 days to complete a task. The same task would take Hans 24 days. After the two men work on the task for 4 days, Jose leaves for vacation and Hans continues. In how many more days will Hans finish the work? 

Ans:
Method 1:

Let, the task be of 1 unit.
Jose finishes the task in 12 days.

Jose’s one day work= 1/12
Similarly, Hans’s one day work= 1/24

When two men work together, both complete (1/12 + 1/24) units in one day.

1/12 + 1/24 = 1/8

In 4 days, both complete 4*(1/8) or 1/2 of the work. Remaining work is 1/2 units. Hans can finish it in 12 days.

Method 2:
Let the total work comprises of 24 units.

Jose does 2 units every day and Hans 1 unit every day.
Both do 3 units every day.

In 4 days, 4*3=12 units every day.

Remaining work=24-12=12 units. Hans can finish it in 12 days.

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