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?

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Accepted Answer

#### Step 1: Calculate Aman's Total Work
Aman completes **50% of the job in 16 days**, meaning he can complete the entire job in:  
$$
16 	imes 2 = 32 \, 	ext{days}.
$$  
Thus, Aman's work rate is:  
$$
\frac{1}{32} \, 	ext{of the job per day}.
$$

#### Step 2: Calculate Bhanu's Total Work
Bhanu completes **25% of the job in 24 days**, meaning he can complete the entire job in:  
$$
24 	imes 4 = 96 \, 	ext{days}.
$$  
Thus, Bhanu's work rate is:  
$$
\frac{1}{96} \, 	ext{of the job per day}.
$$

#### Step 3: Combined Work Rate
The combined work rate of Aman and Bhanu is:  
$$
\frac{1}{32} + \frac{1}{96}.
$$  
Find a common denominator (96):  
$$
\frac{1}{32} = \frac{3}{96}, \quad 	ext{so} \quad \frac{1}{32} + \frac{1}{96} = \frac{3}{96} + \frac{1}{96} = \frac{4}{96} = \frac{1}{24}.
$$

#### Step 4: Time to Complete **1/4** of the Job
To complete **1/4** of the job together:  
$$
	ext{Time required} = \frac{	ext{Work}}{	ext{Rate}} = \frac{\frac{1}{4}}{\frac{1}{24}} = 6 \, 	ext{days}.
$$

Thus, Aman and Bhanu can complete **1/4** of the job together in **6 days**.

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