A takes double time than C to complete a work and C is thrice efficien

1.	A takes double time than C to complete a work and C is thrice efficient as B. A takes 22 days to complete a work alone. If they work in pairs (i.e. AB, BC, CA) starting with AB on the 1st, BC on 2nd and CA on 3rd day and so on, then how many days are required to finish the work?1. 6 days2. 9 days3. 8 days4. 12 days
Answer» Correct Answer - Option 2 : 9 days Given: A's time is double to C's time to complete a work. C is three times as efficient as B. Time taken by A to complete the work alone = 22 days Concept used: Time is inversely proportional to efficiency. Formula used: Total work = Efficiency × Total time Calculation: Ratio of time taken by A to C = 2 ∶ 1 ⇒ Ratio of efficiency of A to C = 1 ∶ 2 ----(1) Ratio of efficiency of B to C = 1 ∶ 3 (Given) ----(2) On comparing (1) and (2), we get ⇒ A ∶ B ∶ C = 3 ∶ 2 ∶ 6 Let the efficiency of A, B and C be 3 units, 2 units and 6 units respectively. According to question, Total work = Efficiency of A × Time ⇒ 3 × 22 ⇒ 66 units Efficiency of (A + B), (B + C) and (C + A) is 5 units, 8 units and 9 units respectively. ⇒ 3 days work = 22 units ↓_{× 3} ↓× 3 ⇒ 9 days work = 66 units ∴ The number of days to finish the work in the given pattern is 9 days.

A takes double time than C to complete a work and C is thrice efficient as B. A takes 22 days to complete a work alone. If they work in pairs (i.e. AB, BC, CA) starting with AB on the 1st, BC on 2nd and CA on 3rd day and so on, then how many days are required to finish the work?1. 6 days2. 9 days3. 8 days4. 12 days

Answer» Correct Answer - Option 2 : 9 days

Given:

A's time is double to C's time to complete a work.

C is three times as efficient as B.

Time taken by A to complete the work alone = 22 days

Concept used:

Time is inversely proportional to efficiency.

Formula used:

Total work = Efficiency × Total time

Calculation:

Ratio of time taken by A to C = 2 ∶ 1

⇒ Ratio of efficiency of A to C = 1 ∶ 2 ----(1)

Ratio of efficiency of B to C = 1 ∶ 3 (Given) ----(2)

On comparing (1) and (2), we get

⇒ A ∶ B ∶ C = 3 ∶ 2 ∶ 6

Let the efficiency of A, B and C be 3 units, 2 units and 6 units respectively.

According to question,

Total work = Efficiency of A × Time

⇒ 3 × 22

⇒ 66 units

Efficiency of (A + B), (B + C) and (C + A) is 5 units, 8 units and 9 units respectively.

⇒ 3 days work = 22 units

↓_{× 3} ↓× 3

⇒ 9 days work = 66 units

∴ The number of days to finish the work in the given pattern is 9 days.