Question

Raju can complete a work in 20 days, which Bobby, Arjun and Habib can finish Independently in 27, 30 and 36 days respectively, Raju and Arjan starts doing this work jointly and continues on it for 4 days and stops working. If one of Habib and Hobby has to complete the work, how many more days they may take respectively?

• A. 24, 18
• B. 36, 27
• C. 24, 20
• D. 30, 25

Answer 1

Answer:

A. 24, 18

Work and Time Problems Explanation

• Understanding Work and Time: This type of problem deals with the rate at which individuals or groups complete tasks. The fundamental concept is that Work = Rate × Time. The rate of work is the amount of work done per unit of time.

• Calculating Individual Rates:

  • Raju's rate: If Raju completes the work in 20 days, his rate is 1/20 of the work per day.

  • Bobby's rate: If Bobby completes the work in 27 days, his rate is 1/27 of the work per day.

  • Arjun's rate: If Arjun completes the work in 30 days, his rate is 1/30 of the work per day.

  • Habib's rate: If Habib completes the work in 36 days, his rate is 1/36 of the work per day.

• Joint Work Calculation:

  • Raju and Arjun work together for 4 days.

  • Their combined rate is Raju's rate + Arjun's rate = 1/20 + 1/30.

  • To add these fractions, find a common denominator (LCM of 20 and 30 is 60): (3/60) + (2/60) = 5/60 = 1/12 of the work per day.

  • Work done by Raju and Arjun in 4 days = Combined rate × Time = (1/12) × 4 = 4/12 = 1/3 of the total work.

• Remaining Work:

  • Total work is considered as 1 unit.

  • Remaining work = Total work - Work done = 1 - 1/3 = 2/3 of the total work.

• Calculating Time for Habib and Bobby:

  • Habib's remaining days: If Habib has to complete the remaining 2/3 work, the time taken would be Remaining Work / Habib's rate = (2/3) / (1/36).

  • To divide fractions, multiply by the reciprocal: (2/3) × 36 = 72/3 = 24 days.

  • Bobby's remaining days: If Bobby has to complete the remaining 2/3 work, the time taken would be Remaining Work / Bobby's rate = (2/3) / (1/27).

  • To divide fractions, multiply by the reciprocal: (2/3) × 27 = 54/3 = 18 days.