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A is 50% more efficient than B, B is 25% less efficient than C. If C can complete a work in 30 days, how many days will A and B take to complete the same work together if they work on alternate days with A starting the work?


1. 48 days
2. 12 days
3. 20 days
4. 32 days

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Correct Answer - Option 4 : 32 days

Given:

A is 50% more efficient than B, B is 25% less efficient than C. If C can complete a work in 30 days

Concept Used:

Total Work = Efficiency × Time

Calculation:

50% more = + 1/2, 25% less = - 1/4

 Take efficiency of C= 2 × 4 = 8

 Suppose efficiency of C = 8

The efficiency of B (EB) = 75% of C = 3/4 × 8 = 6

The efficiency of A (EA)  = 150% of B = 3/2 × 6 = 9

Days taken by C to complete the work = 30

⇒ Total Work = Efficiency × Days = 8 × 30 = 240

Now, EA = 9, EB = 6      

Work on the first day by A = 9     [∵ A starts the work]

Work on the second day = 6

Thus, Work in 2 days = 9 + 6 = 15

Total time to complete the work (240/15) × 2   [∵ 15 unit work done in 2 days]

⇒ 16 × 2 = 32 days

∴ The work will complete in 32 days.

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