Maths-
General
Easy

Question

A and B can do a piece of work in 12 days; B and C in 15 days; C and A in 20 days. How much time will A alone take to finish the 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 days.


    Let’s say the total work is represented as W and let’s say the work done by A in 1 day is WA, work done by B in 1 day is WB and work done by C in 1 day is WC
    Step 1 of 3:
    It is given that A and B can do a piece of work in 18 days. So we can write
    WA cross times 12 + WB cross times 12 = W
    WA  + WB = W over 12…….(1)
    It is given that B and C  can do a piece of work in 24 days. So we can write
    WB cross times 15 + WC cross times 15 = W
    WB + WC = W over 15…….(2)
    It is given that A and C  can do a piece of work in 36 days. So we can write
    WA cross times 20 + WC cross times 20 = W    …….(3)
    WA + WC = W over 20…….(3)
    Step 2 of 3:
    Now, adding equations (1), (2) and (3)
    2(WA  + WB + WC )= W over 12 + W over 15 + W over 20
    WA  + (WB + WC ) = W over 10  
    Putting the value of WB + WC from equation (2)
    WA  +  =  W over 15 = W over 10
    WA  =  W over 30
    Step 3 of 3:
    Now, we can say that time taken by A to complete W over 30 amount of work = 1 day
    So, the time taken by A to complete W amount of work = fraction numerator 1 over denominator begin display style W over 30 end style end fractioncross times = 30 days
    Final Answer:
    Hence, the time that will A alone take to finish the work is 30 days.

    Related Questions to study

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.