Question

12 men and 13 boys can earn 326.25 in 3 days. 5 men and 6 boys can earn 237.50 in 5 days. In how many days will 3 men and 4 boys earn 210?

• A. 7 Days
• B. 17 Days
• C. 27 Days
• D. 70 Days

Answer 1

The Correct Option is A

Finding the Number of Days Required to Earn Rs. 210 

Step 1: Define Variables

Let the daily earnings of one man be \( m \) and the daily earnings of one boy be \( b \).

Step 2: Given Equations

• From the first condition: \[ 12m + 13b = 326.25 \]
• From the second condition: \[ 5m + 6b = 237.50 \]

Step 3: Normalize the Second Equation

Dividing the second equation by 5:

\[ m + \frac{6}{5}b = \frac{237.50}{5} = 47.50 \]

Multiplying by 2 to align with the first equation:

\[ 10m + 12b = 95 \]

Step 4: Subtract the Two Equations

Subtracting the second equation from the first:

\[ (12m + 13b) - (10m + 12b) = 108.75 - 95 \]

\[ 2m + b = 13.75 \]

Step 5: Solve for \( b \)

\[ b = 13.75 - 2m \]

Step 6: Substitute into the Second Equation

\[ 5m + 6(13.75 - 2m) = 47.50 \]

\[ 5m + 82.5 - 12m = 47.50 \]

\[ -7m = -35 \]

\[ m = 5 \]

Step 7: Solve for \( b \)

\[ b = 13.75 - 2(5) = 3.75 \]

Step 8: Find Total Earnings for 3 Men and 4 Boys

\[ 3m + 4b = 3(5) + 4(3.75) \]

\[ = 15 + 15 = 30 \]

Step 9: Find the Number of Days to Earn Rs. 210

\[ \frac{210}{30} = 7 \text{ days} \]

Final Answer:

Thus, the correct answer is (A) 7 Days.