Work Efficiency Calculation
The problem involves calculating the time taken by person B to complete a piece of work, given the time taken by person A and the relative efficiency between A and B.
Understanding Efficiency and Time
Key concepts:
- Efficiency is the rate at which work is done.
- The number of days required to complete a fixed amount of work is inversely proportional to the efficiency. If efficiency increases, the number of days decreases, and vice versa.
Analyzing the Efficiency Relationship
We are given that B is 25% more efficient than A. Let $E_A$ represent the efficiency of A and $E_B$ represent the efficiency of B.
This means:
$E_B = E_A + 0.25 \times E_A$ $E_B = 1.25 \times E_A$We can express the ratio of their efficiencies:
$\frac{E_B}{E_A} = 1.25 = \frac{125}{100} = \frac{5}{4}$This implies the ratio of A's efficiency to B's efficiency is:
$\frac{E_A}{E_B} = \frac{4}{5}$Calculating Days Taken by B
Since the number of days is inversely proportional to efficiency, the ratio of days taken by B to days taken by A is equal to the inverse ratio of their efficiencies:
$\frac{\text{Days}_B}{\text{Days}_A} = \frac{E_A}{E_B}$We know:
- $\text{Days}_A = 1455$ days
- $\frac{E_A}{E_B} = \frac{4}{5}$
Substitute these values into the equation:
$\frac{\text{Days}_B}{1455} = \frac{4}{5}$Now, solve for $\text{Days}_B$:
$\text{Days}_B = 1455 \times \frac{4}{5}$Perform the calculation:
$\text{Days}_B = \frac{1455}{5} \times 4$ $\text{Days}_B = 291 \times 4$ $\text{Days}_B = 1164$Therefore, B takes 1164 days to complete the same piece of work.
Important Questions from Work Efficiency
- M is thrice as efficient as workman as N and therefore is able to finish a job in 264 days less than N. Then in how many days can N finish the entire work?
- 45 people take 18 days to dig a pond. If the pond would have to be dug in 15 days, then the number of people to be employed will be
- A stock of food is enough for 240 men for 48 days. How long will the same stock last for 160 men?
One contractor had undertaken a construction work. To complete the given job, he sought labour comprising 24 men for 12 days for working 10 hours a day. But due to festival season, as the labour had gone to their respective hometowns, he could get only 15 men and they too were willing to work 8 hours a day. With this much labour, in how many days would he be able to complete the same job?
Rajender engages Sunil and Vijay to do some construction work in his office. Sunil is highly skilled and is $3\frac{1}{2}$ times as good a workman as Vijay. Therefore, he is able to finish his work in 45 days less than Vijay. In how many days they both working together, can finish the work?
