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 $\frac{1}{4}^{th}$ of the job working together ?
The correct answer is
6 days
This problem involves calculating the combined work rate of two individuals, Aman and Bhanu, to determine the time needed to complete a specific portion of a job.
Calculate Individual Work Rates
First, find the rate at which each person works per day.
- Aman's Rate: Aman completes 50% (or $\frac{1}{2}$) of the job in 16 days. Aman's daily work rate = $\frac{\text{Work Done}}{\text{Time Taken}} = \frac{1/2 \text{ job}}{16 \text{ days}} = \frac{1}{32}$ job per day.
- Bhanu's Rate: Bhanu completes 25% (or $\frac{1}{4}$) of the job in 24 days. Bhanu's daily work rate = $\frac{\text{Work Done}}{\text{Time Taken}} = \frac{1/4 \text{ job}}{24 \text{ days}} = \frac{1}{96}$ job per day.
Calculate Combined Work Rate
When working together, their rates add up.
- Combined daily work rate = Aman's rate + Bhanu's rate
- Combined rate = $\frac{1}{32} + \frac{1}{96}$
- To add these fractions, find a common denominator, which is 96.
- Combined rate = $\frac{3}{96} + \frac{1}{96} = \frac{4}{96}$
- Simplify the combined rate: $\frac{4}{96} = \frac{1}{24}$ job per day.
Calculate Time for Target Job Portion
They need to complete $\frac{1}{4}^{th}$ of the job.
- Time = $\frac{\text{Target Work}}{\text{Combined Rate}}$
- Time = $\frac{1/4 \text{ job}}{1/24 \text{ job per day}}$
- Time = $\frac{1}{4} \times 24$ days
- Time = 6 days.
Therefore, Aman and Bhanu can complete $\frac{1}{4}^{th}$ of the job working together in 6 days.
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Important Questions from Time & Work (Notes)
- If 6 men and 8 boys can do a piece of work in 10 days and 26 men and 48 boys can do the same work in 2 days, then the time taken by 15 men and 20 boys to do the same work will be
- A fresh water tap fills a fish tank in 40 minutes. The same tank is filled by a salt water tap in 120 minutes. If both the taps are open, how many minutes will it take to fill the tank?
- A completes $\frac{7}{10}$ of a work in 15 days and then he completes the remaining work with the help of B in 5 days. In how many days can A and B together complete the entire work?
- If 15 workers can build a wall in 10 days, how many workers are needed to build it in 6 days?
- A can finish a work in 5 days and B can do the same work in 50 days. B worked alone for 10 days and left the job. In how many days can A alone finish the remaining work?
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