Question

Aman can do 50% of the job in 16 days, and Bhanu can do 25% of the job in 24 days. In how many days can they do 1/4 of the job working together?

• A. 8 days
• B. 6 days
• C. 10 days
• D. 12 days

Answer 1

The Correct Option is B

Let's break down this problem step-by-step:

1. Aman's Work Rate:

• Aman does 50% (1/2) of the job in 16 days.
• Aman does 100% (1) of the job in 16 * 2 = 32 days.
• Aman's work rate is 1/32 of the job per day.

2. Bhanu's Work Rate:

• Bhanu does 25% (1/4) of the job in 24 days.
• Bhanu does 100% (1) of the job in 24 * 4 = 96 days.
• Bhanu's work rate is 1/96 of the job per day.

3. Combined Work Rate:

• Their combined work rate is (1/32) + (1/96) per day.
• To add these fractions, find a common denominator (96):
• (3/96) + (1/96) = 4/96 = 1/24 of the job per day.

4. Time to Complete 1/4 of the Job:

• Let 'x' be the number of days they take to complete 1/4 of the job.
• Their combined work rate multiplied by the number of days should equal 1/4 of the job:
• (1/24) * x = 1/4
• x = (1/4) / (1/24)
• x = (1/4) * (24/1)
• x = 24/4
• x = 6 days

Therefore, they can do 1/4 of the job working together in 6 days.

The correct answer is Option.