Math Problem Statement

यदि 18 आदमी एक काम को 13 दिनों में पूरा कर सकते हैं, तो 54 आदमी उसी काम को कितने दिनों में पूरा करेंगे?

Solution

The problem presented in the image is in Hindi and translates to the following:

Question: If 18 people can complete a task in 13 days, how many days will 54 people take to complete the same task?

Answer Choices:

  1. 133\frac{13}{3} days
  2. 85\frac{8}{5} days
  3. 9 days
  4. 184\frac{18}{4} days

Solution:

This is a classic "Work and Time" problem, where the relationship between the number of workers and the time taken to complete the same task is inversely proportional. The formula to solve this problem is:

Work=Number of People×Time\text{Work} = \text{Number of People} \times \text{Time}

Let’s apply the formula:

  • For 18 people to complete the task in 13 days: W=18×13W = 18 \times 13
  • Now, for 54 people, let the number of days taken be xx. So the work done will be: W=54×xW = 54 \times x Since the total work remains constant, we equate both expressions: 18×13=54×x18 \times 13 = 54 \times x Solving for xx: x=18×1354=133x = \frac{18 \times 13}{54} = \frac{13}{3}

Thus, 54 people will complete the work in 133\frac{13}{3} days.

Answer:

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Math Problem Analysis

Mathematical Concepts

Work and Time
Inverse Proportionality

Formulas

Work = Number of People × Time

Theorems

Inverse Proportionality Theorem in Work and Time Problems

Suitable Grade Level

Grades 6-8