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The rate at which A,B & C work together is \(\frac{1}{2}\) [i.e. half of one work is done in one hour by A, B & C working together]
The rate at which B & C work together is \(\frac{1}{4}\) [i.e. one-fourth of one work is done in one hour by B & C working together]
The rate at which A works is \(\frac{1}{2}-\frac{1}{4} = \frac{1}{4}\) [i.e. one-fourth of one work is done in one hour by Machine A alone]
Therefore the time taken by A alone is 4 hours.
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LCM Method:-

A, B & C working together take 2 hours
B & C working together take 4 hours
A alone ?

LCM of 2 & 4 is 4 therefore:-
A, B & C working together make 4/2, i.e. 2 units per hour
B & C working together make 4/4, i.e. 1 units per hour
There A alone will make 1 units per hour. To make 4 units, Machine A will take 4 hours at the rate of 1 units per hour
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Rate of work of A,B & C together=1/2 (work/hr)
Rate of work of B & C together=1/4 (work/hr)
Rate of work of A=1/2-1/4= 1/4 (work/hr)
So, time taken by A to finish job alone= 4 hrs

Ans-(C)
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Solve Time and Work Problems Efficiently using Efficiency Method! - Exercise Question #1

Three copying machines A, B, and C, working together at their respective constant rates, can do a copying work in 2 hours. B and C, working together at their respective constant rates, can do the same copying job in 4 hours. How many hours would it take A, working alone at its constant rate, to do the same job?

    A. 2 hours
    B. 3 hours
    C. 4 hours
    D. 5 hours
    E. 6 hours



Let a, b, and c be the number of hours A, B, and C take to finish the job alone, respectively. Their respective rates are 1/a, 1/b, and 1/c. We have:

1/a + 1/b + 1/c = 1/2

and

1/b + 1/c = 1/4

Subtracting the second equation from the first, we have:

1/a = 1/4

a = 4

Answer: C
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