Maths-
General
Easy

Question

A and B can do a piece of work in 20 days and B in 15 days. They work together for 2 days and then A goes away. In how many days will B finish the remaining work?

hintHint:

Hint:
When two quantities of different units are compared and expressed as a ratio, it is known as Rate. For example, a car travels at a speed of 100 kilometres per hour, then it means in one hour it covers 100 kilometres.
 

The correct answer is: 13 1/2 days.


    Let’s say that the total work can be represented as W.
    Step 1 of 3:
    It is given that B can do the whole work(W) in 15 days.
    So, work done by B in one day = W over 20……(1)
    It is given that A and B can do the work in 20 days
    So, work done by A and B in one day = W over 20
    Step 2 of 3:
    It is given that A and B worked together for 2 days and then A goes away.
    Work done by A and B in 2 days = W over 20 space cross times space 2 = W over 10
    Work left for B after A goes away = W - Work done by A and B in 2 days
    = W - W over 10
    = W - W over 10
    Work left for B after A goes away = fraction numerator 9 W over denominator 10 end fraction
    Step 3 of 3:
    Now, we need to find the number of days to complete fraction numerator 9 W over denominator 10 end fraction amount of work.
    From equation (1) time taken by B to complete W over 15 work = 1 day
    time taken by B to complete fraction numerator 9 W over denominator 10 end fraction work = fraction numerator 1 over denominator W over 15 end fraction cross times fraction numerator 9 W over denominator 10 end fraction equals 27 over 2 text  days  end text equals 13 1 half text  days  end text
    Final Answer:
    Hence, the time taken by B to complete the work after A after 2 days is 13 1 half days.

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