Question:medium
A can do a piece of work in 6 days while B alone can do it in 8 days. With the help of C, they can complete the work in 2 days. If they are paid Rupees 720 for the whole work, how much money A gets?
A can do a piece of work in 6 days while B alone can do it in 8 days. With the help of C, they can complete the work in 2 days. If they are paid Rupees 720 for the whole work, how much money A gets?
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In work and wages problems, always reduce the data to "1-day work" (or unit work). Then compare each person's contribution over the total period and divide wages in the same ratio.
Updated On: Jul 16, 2026
- Rupees 180
- Rupees 240
- Rupees 300
- Rupees 420
Show Solution
The Correct Option is B
Solution and Explanation
Step 1: Take the whole work as 24 units (LCM of 6, 8 and 2). A's rate \(=24/6=4\) units/day, B's rate \(=24/8=3\) units/day, and A+B+C together \(=24/2=12\) units/day, so C's rate \(=12-4-3=5\) units/day.
Step 2: In 2 days, A does \(2\times4=8\) units, B does \(2\times3=6\) units, C does \(2\times5=10\) units, totalling \(8+6+10=24\) units, which checks out.
Step 3: Payment is split in the ratio of work done, \(8:6:10=4:3:5\), with total parts \(12\). A's share \(=\dfrac{4}{12}\times720=240\). \[ \boxed{240} \]
Step 2: In 2 days, A does \(2\times4=8\) units, B does \(2\times3=6\) units, C does \(2\times5=10\) units, totalling \(8+6+10=24\) units, which checks out.
Step 3: Payment is split in the ratio of work done, \(8:6:10=4:3:5\), with total parts \(12\). A's share \(=\dfrac{4}{12}\times720=240\). \[ \boxed{240} \]
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