Ram can do a work in 20 days. Ram and Shyam together can do the same work in 15 days. If they are paid Rs.400 for that work, what is the share of Shyam (in Rs.).

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  1. 100
  2. 200
  3. 150
  4. 50

Answer (Detailed Solution Below)

Option 1 : 100
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Given:

Ram alone can do the work in = 20 days

Ram and Shyam together can do the work in = 15 days

Total payment for the work = Rs.400

Formula used:

Efficiency = Total work / Days 

Shyam’s share = (Shyam's efficiency / Total efficiency) × Total payment

Calculations:

Total work (LCM of 20, 15) = 60 units

Efficiency of Ram = 60 / 20 = 3 units/day

Efficiency of (Ram + Shyam) = 60 / 15 = 4 units/day

Efficiency of Shyam = Efficiency of (Ram + Shyam) - Efficiency of Ram

Efficiency of Shyam = 4 - 3 = 1 unit/day

Share of payment is divided based on efficiency:

Total efficiency = 4 units/day

Shyam’s share = (Shyam's efficiency / Total efficiency) × Total payment

Shyam’s share = (1 / 4) × 400 = Rs.100

Shyam's share is Rs.100.

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