A and B working together can complete a job in 30 days. The ratio of their efficiencies is 3 : 2. In how many days can the faster person complete the job?
50
Understanding Work and Efficiency Ratio
This problem requires calculating the time the most efficient person takes to finish a job, given their combined work duration and efficiency ratio.
Calculating Individual Efficiencies
Let the efficiencies of person A and person B be $E_A$ and $E_B$. The ratio $E_A : E_B$ is given as 3:2.
- Assume $E_A = 3x$
- Assume $E_B = 2x
The combined efficiency is $E_{Total} = E_A + E_B = 3x + 2x = 5x$.
Calculating Total Work
The total work ($W$) equals the combined efficiency multiplied by the time they took working together.
Given time together = 30 days:
$W = E_{Total} \times 30$
$W = (5x) \times 30 = 150x$ units of work.
Finding Time for the Faster Person
The faster person has the higher efficiency. Here, A (with $3x$ efficiency) is faster than B (with $2x$ efficiency).
The time taken by the faster person (A) is:
$Time_A = \frac{W}{E_A}$
$Time_A = \frac{150x}{3x}$
$Time_A = 50$ days.
The faster person can complete the job in 50 days.
Important Questions from Work Efficiency
A takes 15 days to complete \(\frac{5}{7} \) of a work. With the help of B, they finish the whole work in 12 days. In how many days, B alone will complete the same work
A alone can complete a work in 14 days and B alone can complete the same work in 21 days. A and B start the work together but A leaves the work after 4 days of the starting of work. In how many days B will complete the remaining work?
For completing a certain work, A is 50% less efficient than B and B is 50% more efficient than C. Working together A, B and C can complete the work in 48 days. A alone can complete the same work in:
30 persons can do a piece of work in 24 days. How many more persons are required to complete the work in 20 days?
X is twice as good as workman as Y. Together, they finish the work in 18 days. In how many days can it be done by each separately?
