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 ?
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.
Important Questions from Time & Work (Notes)
- 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?
- X can finish a job in $141$ days. He worked for $57$ days alone and the remaining work was completed by Y, in $84$ days. How many days would both together take to complete the entire job?
Ravina, Sujata, and Saroj can complete a work of painting separately in 32, 48, and 64 hours, respectively. They started working together, but Saroj left after 5 hours. From the 6th hour, Ravina and Sujata decided to work on alternate hours starting with Ravina. In how much time will the entire work of painting be completed?
A and B complete a work in 6 days. If A alone can do it in 9 days, then B alone can do $\frac{1}{3}$ of the same work in ________ (days).
