Ratios & Proportion
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Q.

$A$, $B$ and $C$, each of them working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn Rs.2340, what will be $C$’s share of the earnings?

 A.

Rs.520

 B.

Rs.1080

 C.

Rs.1170

 D.

Rs.630

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Solution:
Option(A) is correct

$A$, $B$ and $C$ will share the amount of Rs. 2340 in the ratio of the amounts of work done by them.

As $A$ takes 6 days to complete the job, if $A$ works alone, $A$ will be able to complete \(\dfrac{1}{6}\) th of the work in a day.

Similarly, $B$ will complete \(\dfrac{1}{8}\) th and $C$ will complete \(\dfrac{1}{12}\)  th of the work.
So, the ratio of the work done by $A:B:C$ when they work together will be equal to \(\dfrac{1}{6}, \dfrac{1}{8}, \dfrac{1}{12}\)

Multiplying the numerator of all 3 fractions by 24, the LCM of 6, 8 and 12 will not change the relative values of the three values

We get \(\dfrac{24}{6}, \dfrac{24}{8}, \dfrac{24}{12}=4:3:2\)

i.e., the ratio in which $A:B:C$ will share Rs.2340 will be $4:3:2$.

Hence, $C$’s share will be \(\dfrac{2}{9}\times 2340=\text{Rs }520\)


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