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Mohan is twice as good as Kamlesh and together, they finish a task in 22 days. Mohan alone can finish the task in:
Question

Mohan is twice as good as Kamlesh and together, they finish a task in 22 days. Mohan alone can finish the task in:

A.

35 days

B.

31 days

C.

33 days

D.

37 days

Correct option is C

Given:
Mohan is twice as efficient as Kamlesh.
Together, they complete the task in 22 days.
Concept Used:
Total Work=Efficiency×Time\text{Total Work} = \text{Efficiency} \times \text{Time}
Solution:
Let Kamlesh’s efficiency = 1 unit/day.
Mohan’s efficiency = 2 units/day (twice as efficient).
Total Efficiency = 2 ( Mohan ) + 1 ( Kamlesh ) = 3 units/day
Total Work=Efficiency×Time=3×22=66 units\text{Total Work} = \text{Efficiency} \times \text{Time} = 3 \times 22 = 66 \text{ units}​​
TimeMohan=Total WorkMohan’s Efficiency=662=33 days\text{Time}_{\text{Mohan}} = \frac{\text{Total Work}}{\text{Mohan’s Efficiency}} = \frac{66}{2} = 33 \text{ days}​​

Alternate Method :
Let Mohan’s time alone = m days.
Kamlesh’s time alone = 2m days (since Mohan is twice as efficient).

1m+12m=122 32m=122 2m=66\frac{1}{m} + \frac{1}{2m} = \frac{1}{22} \\ \ \\\frac{3}{2m} = \frac{1}{22}\\ \ \\2m = 66

m = 33 days

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