Manoj can do a piece of work in 20 days, while Chandu can do the same work in 30 days.
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Manoj can do a piece of work in 20 days, while Chandu can do the same work in 30 days. They work together and finish the work, receiving a total wage of Rs. 600. What is Manoj's share of the wages?
Show answer & explanation
Wages are distributed in proportion to the efficiency (work done per day) of the workers. Since Manoj is faster than Chandu, he does more work in the same amount of time and thus receives a larger share of the total payment.
Step-by-step Derivation:
Step 1: Determine the efficiency of Manoj and Chandu.
Efficiency of Manoj = 1/20 of the work per day.
Efficiency of Chandu = 1/30 of the work per day.
Step 2: Find the ratio of their efficiencies.
Ratio (Manoj : Chandu) = (1/20) : (1/30)
To simplify, multiply both sides by the LCM of 20 and 30, which is 60.
Ratio = (60/20) : (60/30) = 3 : 2.
Step 3: Divide the total wage based on this ratio.
Total parts = 3 + 2 = 5 parts.
Total wage = Rs. 600.
Value of one part = 600 / 5 = Rs. 120.
Step 4: Calculate Manoj's share.
Manoj's share = 3 parts * Rs. 120 = Rs. 360.