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

To determine in how many days Aman and Bhanu can complete \( \frac{1}{4} \) of the job working together, we first need to find their individual work rates and then combine them. 

Step 1: Calculate Aman's work rate.
Aman can complete 50% (or \( \frac{1}{2} \)) of the job in 16 days.
His rate of work is \( \frac{1/2}{16} = \frac{1}{32} \) of the job per day.

Step 2: Calculate Bhanu's work rate.
Bhanu can complete 25% (or \( \frac{1}{4} \)) of the job in 24 days.
His rate of work is \( \frac{1/4}{24} = \frac{1}{96} \) of the job per day.

Step 3: Combine their work rates.
Combined work rate = Aman's rate + Bhanu's rate = \( \frac{1}{32} + \frac{1}{96} \).
To add these, find a common denominator:
\[ \frac{1}{32} = \frac{3}{96} \] (since \( 32 \times 3 = 96 \)).
Thus, \( \frac{1}{32} + \frac{1}{96} = \frac{3}{96} + \frac{1}{96} = \frac{4}{96} = \frac{1}{24} \) of the job per day.

Step 4: Find the time to do \( \frac{1}{4} \) of the job together.
Since their combined work rate is \( \frac{1}{24} \) of the job per day, the time taken to do \( \frac{1}{4} \) of the job is:
\[\frac{\frac{1}{4}}{\frac{1}{24}} = \frac{1}{4} \times 24 = 6 \] days.

Therefore, Aman and Bhanu together can complete \( \frac{1}{4} \) of the job in 6 days.

Answer 2

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.