The ratio of the efficiencies of A, B, and C is 3 : 2 : 1. Working together, they can complete a piece of work in 4 days. A and B work together for 2 days. Then B and C worked for 2 days. The remaining work was completed in 4 days, then who would have worked for the last 4 days?

Question

The ratio of the efficiencies of A, B, and C is 3 : 2 : 1. Working together, they can complete a piece of work in 4 days. A and B work together for 2 days. Then B and C worked for 2 days. The remaining work was completed in 4 days, then who would have worked for the last 4 days?

A
B
C
A + C

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 2 : B

Given:

The ratio of efficiencies of A, B, and C is 3 : 2 : 1.

Working together they can complete the work in 4 days.

A + B worked for 2 days.

B + C worked for 2 days.

Then total work is completed in next 4 days.

Formula Used:

Efficiency = Total Work/Time taken

Total Units of Work = Efficiency × Time taken

Calculation:

Let the efficiency of A, B, and C be 3, 2, and 1 respectively.

They worked together and completed the work in 4 days.

Total Units of work = Total efficiency × 4 days

⇒ Total Units of work = (3 + 2 + 1) × 4

⇒ Total Units of work = 6 × 4

⇒ Total Units of work = 24 units

A + B worked for 2 days.

Total Units of work completed by them,

⇒ Total units of work = (A + B) × 2 days

⇒ Total units of work = (3 + 2) × 2

⇒ Total units of work = 5 × 2

⇒ Total units of work = 10 units.

B + C worked for 2 days.

Total Units of work completed by them,

⇒ Total units of work = (B + C) × 2 days

⇒ Total units of work = (2 + 1) × 2

⇒ Total units of work = 3 × 2

⇒ Total units of work = 6 units.

Total units of work completed,

⇒ 10 units + 6 units

⇒ 16 units

Remaining units of work = 24 units – 16 units

⇒ Remaining units of work = 8 units

Remaining work completed in 4 days.

8 units of work completed in 4 days.

⇒ Efficiency = Total work/Time taken

⇒ Efficiency = 8/4

⇒ Efficiency = 2

⇒ The efficiency of B was 2 units

∴ For the last 4 days, B had worked to complete the work.