A can do 20% of a work in 4 days, and B can do 33\(\frac{1}{3}\)% of the same work in 10 days. They worked together for 9 days and then C completed the remaining work in 6 days. B and C together will complete 75% of the same work in:

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SSC CGL 2023 Tier-I Official Paper (Held On: 21 Jul 2023 Shift 3)
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  1. 12 days
  2. days
  3. 11 days
  4. 10 days

Answer (Detailed Solution Below)

Option 4 : 10 days
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A does total work in 4 × 5 = 20 days

B does total work in 10 × 3 = 30 days

F1 SSC  Priya 30 4 24 D2

As per question,

  A + B C
Days of work done 9 days 6 days
Work done 9 × 5 = 45 60 - 45 =15
Efficiency 5 15/6 = 2.5

 

Efficiency of B + C = 2 + 2.5 = 4.5

75% of work = 60 × (3/4) = 45

Time taken by B and C to complete the 75% work = 45/4.5 = 10 days.

∴ The correct answer is 10 days.

Given: 

A can do 20% of a work in 4 days, and B can do 33\(\frac{1}{3}\)% of the same work in 10 days.

They worked together for 9 days and then C completed the remaining work in 6 days.

Concept used:

Efficiency = (Total work / Total time taken)

Efficiency = work done in a single day 

Calculation:

A does total work in 4 × 5 = 20 days

B does total work in 10 × 3 = 30 days

Let total work is 60 units ( Lcm of 20 and 30)

The efficiency of A is

⇒ 60 / 20 = 3 unit

The efficiency of B is

⇒ 60 / 30 = 2 unit

They does together in 9 days 

9 × (3+2) = 45 units

The remaining 60 - 45 = 15 unit done by C in 6 days

Total work done by C in 6 × 4 = 24 days

Efficiency of C is 60 /24 = 2.5 unit

75% of the total work is 60 × 3/4 = 45 units

Combined efficiency of B and C = 4.5

The number of days required is 45 / 4.5 = 10 days

∴ The correct option is 4

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