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Question

A carpenter can do a job in eight hours. His assistant can do the same job in ten hours. How long would it take them to do the job together?


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Solution

Step-1: Find the work done in one hour:

It is given that a carpenter can do a job in 8hour .

Thus, the carpenter can do 18 of a job in 1hour.

Similarly, it is given that carpenter's assistant can do a job in 10hour.

Thus, the carpenter's assistant can do 110 of a job in 1hour.

Step-2: Find the time:

Let us assume that the carpenter and his assistant can do the job in xhour.

Thus, the carpenter and his assistant can do 1x of the job in 1hour.

Thus,

1x=18+1101x=5+440L.C.Mof(8,10)is401x=94040=9xCrossmultiplytheequation409=9x9Dividebothsideoftheequationby9409=xx=409x=449hour

Hence, the time taken by the carpenter and his assistant to do the job is 449hour.


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