Maths-
General
Easy

Question

A, B and C working together can do a piece of work in 8 hours. A alone can do it in 20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same work?

Hint:

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: 30 hours.


    Let’s say the total work is represented as w
    Step 1 of 2:
    It is given that A alone can do the full work in 20 hours and B alone can do the full work in 24 hours and Let’s say that C alone can do the full work in t hours
    So, work done by A in 1 hour = w over 20
    Work done by B in 1 hour = w over 24
    Work done by C in 1 hour = w over t
    Step 2 of 2:
    It is also given that A, B and C working together can do a piece of work in 8 hours. So we can write
    Work done by A in 8 hours + Work done by B in 8 hours + Work done by C in 8 hours = w
    w over 20 cross times8 + w over 24 cross times 8 + w over t cross times 8 = w
    8w(1 over 20 + 1 over 24 + 1 over t) = w
    11 over 120 plus 1 over t equals 1 over 8
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 1 over t equals 1 over 8 minus 11 over 120 end cell row blank end table
    1 over t equals 1 over 30
    t = 30 hours
    Final Answer:
    Hence, C alone can do the same work in 30 hours.

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