Question:
A certain number of persons were hired to complete a job in 60 days. If 8 more persons are hired then the job could be completed in 10 days less. How many persons were hired originally?
A certain number of persons were hired to complete a job in 60 days. If 8 more persons are hired then the job could be completed in 10 days less. How many persons were hired originally?
Show Hint
For a fixed amount of work, if the number of workers increases, the time decreases proportionally. Use the relation:
\[
M_1D_1=M_2D_2.
\]
Updated On: Jun 12, 2026
- \(50\)
- \(48\)
- \(45\)
- \(40\)
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The Correct Option is D
Solution and Explanation
Concept:
For the same amount of work,
\[
\text{Men} \times \text{Days}
=
\text{Constant}
\]
This is the principle of inverse proportion.
Step 1: Assume the original number of persons is \(x\). Initially, \[ x \text{ persons} \] complete the work in \[ 60 \text{ days} \] Hence total work: \[ 60x \] man-days.
Step 2: Form the second condition. After hiring 8 additional persons, \[ x+8 \] persons complete the work in \[ 60-10=50 \] days. Thus, \[ 50(x+8) \] man-days. Since total work remains unchanged, \[ 60x=50(x+8) \]
Step 3: Solve the equation. \[ 60x=50x+400 \] \[ 10x=400 \] \[ x=40 \] Therefore, the number of persons originally hired was \[ \boxed{40} \]
Step 1: Assume the original number of persons is \(x\). Initially, \[ x \text{ persons} \] complete the work in \[ 60 \text{ days} \] Hence total work: \[ 60x \] man-days.
Step 2: Form the second condition. After hiring 8 additional persons, \[ x+8 \] persons complete the work in \[ 60-10=50 \] days. Thus, \[ 50(x+8) \] man-days. Since total work remains unchanged, \[ 60x=50(x+8) \]
Step 3: Solve the equation. \[ 60x=50x+400 \] \[ 10x=400 \] \[ x=40 \] Therefore, the number of persons originally hired was \[ \boxed{40} \]
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