People and Days Inverse Proportion Calculation
This problem involves an inverse relationship between the number of people working and the time taken to complete a job. If the time decreases, the number of people must increase proportionally to finish the same work.
Understanding Inverse Proportion
- The total work is constant.
- Work = (Number of People) × (Number of Days).
- If the number of days is reduced, the number of people must increase.
Applying the Formula
Let $P_1$ be the initial number of people and $D_1$ be the initial number of days. Let $P_2$ be the new number of people and $D_2$ be the new number of days.
Given:
- $P_1 = 45$ people
- $D_1 = 18$ days
- $D_2 = 15$ days
- $P_2 = ?$
For inverse proportion, the product of people and days remains constant:
$P_1 \times D_1 = P_2 \times D_2$Calculating the New Number of People
Substitute the known values into the formula:
$45 \times 18 = P_2 \times 15$Solve for $P_2$:
$P_2 = \frac{45 \times 18}{15}$Simplify the calculation:
$P_2 = \frac{(3 \times 15) \times 18}{15}$ $P_2 = 3 \times 18$ $P_2 = 54$Therefore, 54 people need to be employed to dig the pond in 15 days.
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?
- 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.
- 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?
