Question

Amit can complete a piece of work in 20 days and Sumit can complete the same in 24 days. They decide to complete the work by working on alternate days. If Sumit starts the work, how long will it take to complete the work?

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Answer 1

Answer:

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In 1- day A and B can do= 1/20+ 1/25 = 9/100.

In 5- days both can do= 9/100 x 5 =45/100.

Number days required by A to finish the remaining work= (55/100)÷(1/20) = 11- days.

========================== Another method A does the work till the end and B does the work for 5- days only.

If the total work if finished in X- days, then

So X/20 + 5/25= 1

5X+ 20= 100

X= 80/5= 16.

So complete work is done in 16- days.

A alone does after B- left= 16–5= 11- days

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Answer 2

Answer:

There is no complete number of days in which the work will be completed

Step-by-step explanation:

There are two possibilities that the work will be done in either in Odd number of day or in Even Number of day.

Case : 1

If work is completed in odd number of days

Let the number of days for work to be complete in 2x + 1.

If Amit and Sumit work alternatively

Amit will work for x  days and Sumit will work for x + 1 days because Sumit started the work first and if work is ended on odd days then Sumit will work one more day.

Thus

Work done by Amit  = x/20

Work done by Sumit = (x+1)/24

Thus,

$\frac{x}{20}+\frac{x+1}{24}=1\\\;\\\frac{6x+5x+5}{120}=1\\\;\\11x+5=120\\\;\\11x=120-5\\\;\\11x=115\\\;\\x=\frac{115}{11}$

Which is not a perfect number of days.

Case : 2

If work is completed in even number of days

Let the number of days for work to be complete in 2x.

If Amit and Sumit work alternatively

Amit will work for x  days and Sumit will work for x days because Sumit started the work first and if work is ended on even days thus both will work for equal number of days

Thus

Work done by Amit = x/20

Work done by Sumit = x/24

Hence,

$\frac{x}{20}+\frac{x}{24}=1\\\;\\\frac{6x+5x}{120}=1\\\;\\11x=120\\\;\\x=\frac{120}{11}$

Which is not a perfect number of days.

Hence we can see that in both we couldn't find a perfect number of days.

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