A is 40% more efficient than B. How much time will both, working together, take to finish the work, which B alone can finish in 36 days?

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SSC CGL 2022 Tier-I Official Paper (Held On : 12 Dec 2022 Shift 3)
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  1. 18 days
  2.  days
  3. 15 days
  4.  days

Answer (Detailed Solution Below)

Option 3 : 15 days
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PYST 1: SSC CGL - General Awareness (Held On : 20 April 2022 Shift 2)
25 Qs. 50 Marks 10 Mins

Detailed Solution

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Given:

A is 40% more efficient than B

B can complete the task in 36 days.

Concept used:

Total work = Efficiency of the worker × time taken by the worker

Calculation:

Let the efficiency of B be 10a

So, efficiency of A = 10a × 140%

⇒ 14a

So, total work = 10a × 36

⇒ 360a

Now,

If they both work then time = 360a/(14a + 10a)

⇒ 360a/24a

⇒ 360/24

⇒ 15

∴ The required answer is 15 days.

Shortcut Trick

A is 40% more efficient than B, then the efficiency of A : B = 140 : 100 = 7 : 5

B alone can finish in 36 days, then total work = (5 × 36) = 180 unit

If A & B both working together, time taken = 180/(7 + 5) = 180/12 = 15 days

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