A alone can finish a work in 15 days. A works only for the first two days and last two days. The rest work is done by B and the work is completed in 20 days. In how many days A and B together can finish the work?

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 18 Jul 2023 Shift 3)

Answer 1

Shortcut Trick

A works for a total 4 days and B works for a total (20 - 4) = 16 days.

A can complete alone in 15 days.

So, on comparing total works

4A + 16B = 15A

16B = 11A

A/B = 16/11

Total work = 15A = 15×16 = 240

A + B = 240/(16 + 11) = 240/27 = 80/9

∴ The correct answer is 80/9.

Alternate Method

Given:

A alone can finish a work in 15 days.

A works only for the first two days and last two days.

The rest work is done by B and the work is completed in 20 days.

Concept used:

Efficiency = (Total work / Total time taken)

Efficiency = work done in a single day

Calculation:

Let total work is 60 units ( Lcm of 20 and 15)

The efficiency of A is

⇒ 60 / 15 = 4 unit

A does total 4 × 4 = 16 units

Remainig work , 60 - 16 = 44 units does by B in 16 days

Again, the Efficiency of B is,

⇒ 44 / 16 = 11/4 units

Total efficiency is 4+11/4 = 27/4

A and B does the work in,

60×4/ 27 = 80/9 days

∴ The correct option is 3

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