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 the number of days Aman and Bhanu require to complete \( \frac{1}{4} \) of the job collaboratively, we must first ascertain their individual work rates and subsequently aggregate them.

Step 1: Ascertain Aman's work rate.
Aman completes 50% (equivalent to \( \frac{1}{2} \)) of the job in 16 days.
His work rate is \( \frac{1/2}{16} = \frac{1}{32} \) of the job per day.

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

Step 3: Aggregate their work rates.
Combined work rate = Aman's rate + Bhanu's rate = \( \frac{1}{32} + \frac{1}{96} \).
To sum these fractions, a common denominator is required:
\[ \frac{1}{32} = \frac{3}{96} \] (as \( 32 \times 3 = 96 \)).
Consequently, \( \frac{1}{32} + \frac{1}{96} = \frac{3}{96} + \frac{1}{96} = \frac{4}{96} = \frac{1}{24} \) of the job per day.

Step 4: Determine the time to complete \( \frac{1}{4} \) of the job together.
Given their combined work rate is \( \frac{1}{24} \) of the job per day, the time to complete \( \frac{1}{4} \) of the job is calculated as:
\[\frac{\frac{1}{4}}{\frac{1}{24}} = \frac{1}{4} \times 24 = 6 \] days.

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