Work Efficiency Problem: Calculating Job Time
This problem involves calculating the time taken to complete a job based on the relative efficiency of two workmen, M and N.
Understanding Efficiency and Time
Let $T_N$ be the number of days N takes to finish the work, and $T_M$ be the number of days M takes.
Efficiency is inversely proportional to the time taken. If M is thrice as efficient as N, it means M does 3 times the work N does in the same amount of time, or M takes 1/3rd the time N takes to complete the same work.
Therefore, we can write the relationship between their times as:
$T_N = 3 \times T_M$This can also be written as:
$T_M = \frac{T_N}{3}$Calculating Time Difference
The problem states that M finishes the job in 264 days less than N. This gives us the equation:
$T_N - T_M = 264 \text{ days}$Solving for N's Time ($T_N$)
Now, substitute the expression for $T_M$ from the efficiency relationship into the time difference equation:
$T_N - \frac{T_N}{3} = 264$To solve for $T_N$, combine the terms on the left side:
$\frac{3T_N - T_N}{3} = 264$ $\frac{2T_N}{3} = 264$Now, isolate $T_N$:
$2T_N = 264 \times 3$ $2T_N = 792$ $T_N = \frac{792}{2}$ $T_N = 396$Conclusion
N can finish the entire work in 396 days.
Important Questions from Work Efficiency
- A can do a piece of work in $1455$ days. B is $25\%$ more efficient than A. Find the number of days taken by B to do the same piece of 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?
