A is 1.5 times efficient than B therefore takes 8 days less than B to complete a work. If A and B work on alternate days and A works on first day, then in how many days the work will be completed?a)17b)19c)19.5d)21Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Given, A is 1.5 times efficient than B and takes 8 days less than B to complete the work.

Let’s assume that B takes x days to complete the work.

Therefore, A takes 0.67x days to complete the work. (as A is 1.5 times efficient than B)

Also, given A and B work on alternate days and A works on the first day.

So, in two days A and B would have worked for (0.67x+ x) = 1.67x days.

Let’s assume that the work is completed in n days.

Now, we can write the equation as per the given information i.e.

A works for (n+1)/2 days and B works for n/2 days.

So, (n+1)/2 * 0.67x + n/2 * x = 1 (as the work is completed)

Solving this equation, we get n = 19 days.

Therefore, the work will be completed in 19 days.

Hence, option B is the correct answer.

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