Question

# A, B, and C together earn Rs. 300 per day, while A and C together earn Rs. 188 and B and C together earn Rs. 152. The daily earning of C is:(a) Rs. 40(b) Rs. 30(c) Rs. 50(d) Rs. 60

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Hint: We are given earnings of A, B, and C together for each day as Rs. 300. Also, the earning of (A + C) for each day is Rs. 188, we subtract the two to get the earning of B for each day. Once, we have B’s every day earning, we will subtract the value from each day earning of (B + C) and get the earning of C alone.

Complete step-by-step solution:
We are given that the earning of A, B and C together is Rs. 300 per day. That is, we have, (A + B + C)’s one day earning as
$A+B+C=Rs.300.......\left( i \right)$
Also, we have that earning of A and C together is Rs. 188 for each day. So, we have,
$A+C=Rs.188.......\left( ii \right)$
Now, we will use (i) and (ii) to find the one day earning of B alone. Subtracting (ii) from (i), we get,
$\left( A+B+C \right)-\left( A+C \right)=B$
$\Rightarrow B=Rs.300-Rs.188$
$\Rightarrow B=Rs.112$
So, we get B’s alone per day earning Rs. 112.
We also have the per day earning of (B + C) as Rs. 152.
Therefore, we have,
$B+C=Rs.152$
Substituting the value of B in the above equation we get,
$\Rightarrow Rs.112+C=Rs.152$
$\Rightarrow C=Rs.152-Rs.112$
$\Rightarrow C=Rs.40$
So, we get the earning per day of C as Rs. 40.
Hence, option (a) is the right answer.

Note: We first find the per day earning of B alone because it is clubbed with C as per day earning of B + C which is 152. So, once we have B, we can get the daily wages of C by subtracting the daily wages of B from 152. If we go for finding the daily wages of A first, the solution becomes lengthy as we have to find the daily wages of B in the next step.