Question:
Two persons A and B agreed to complete a work for Rs.1600. A can do that work in 6 days and B can do it in 8 days. With the help of another person C, if they completed that work in 3 days, then the share of C (in Rs.) is
Two persons A and B agreed to complete a work for Rs.1600. A can do that work in 6 days and B can do it in 8 days. With the help of another person C, if they completed that work in 3 days, then the share of C (in Rs.) is
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In work-payment problems, payment is always divided according to the amount of work done.
Updated On: Jul 15, 2026
- \(500\)
- \(400\)
- \(300\)
- \(200\)
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The Correct Option is D
Solution and Explanation
Concept:
Work done is proportional to efficiency.
Total payment is divided according to work contribution.
Step 1: Find efficiencies.
A’s one day work: \[ \frac16 \] B’s one day work: \[ \frac18 \] Together: \[ \frac16+\frac18 \] LCM \(=24\): \[ =\frac4{24}+\frac3{24} \] \[ =\frac7{24} \]
Step 2: Find total one-day work with C.
They finish in 3 days. So total one-day work: \[ \frac13 \] Thus C’s one-day work: \[ \frac13-\frac7{24} \] LCM \(=24\): \[ =\frac8{24}-\frac7{24} \] \[ =\frac1{24} \]
Step 3: Find work ratio.
A : B : C \[ =\frac16:\frac18:\frac1{24} \] Multiply by 24: \[ 4:3:1 \] Total ratio: \[ 4+3+1=8 \]
Step 4: Find C’s share.
\[ \frac18 \times 1600 \] \[ =200 \] Thus, C’s share is: \[ \boxed{200} \]
Step 1: Find efficiencies.
A’s one day work: \[ \frac16 \] B’s one day work: \[ \frac18 \] Together: \[ \frac16+\frac18 \] LCM \(=24\): \[ =\frac4{24}+\frac3{24} \] \[ =\frac7{24} \]
Step 2: Find total one-day work with C.
They finish in 3 days. So total one-day work: \[ \frac13 \] Thus C’s one-day work: \[ \frac13-\frac7{24} \] LCM \(=24\): \[ =\frac8{24}-\frac7{24} \] \[ =\frac1{24} \]
Step 3: Find work ratio.
A : B : C \[ =\frac16:\frac18:\frac1{24} \] Multiply by 24: \[ 4:3:1 \] Total ratio: \[ 4+3+1=8 \]
Step 4: Find C’s share.
\[ \frac18 \times 1600 \] \[ =200 \] Thus, C’s share is: \[ \boxed{200} \]
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