Question

A can complete a work in 15 days and B can complete the same work in 45 days . Together, they can complete the same work in

• A. 12.25 days
• B. 11.5 days
• C. 12.5 days
• D. 11.25 days

Hint:

Alternatively, use the LCM method:
Assume the total work is the LCM of 15 and 45, which is 45 units.
- A's daily efficiency = $45 \div 15 = 3$ units/day.
- B's daily efficiency = $45 \div 45 = 1$ unit/day.
- Combined daily efficiency = $3 + 1 = 4$ units/day.
- Time taken = $\frac{\text{Total Work}}{\text{Combined Efficiency}} = \frac{45}{4} = 11.25$ days.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
This is a standard Time and Work problem.
We are given that person A can complete a task in 15 days, and person B can complete the same task in 45 days.
We need to determine how many days they will take to finish the work working together.

Step 2: Key Formula or Approach:
We can use the work-rate method or the direct product-sum formula:
1.

Work Rate Method:
- Rate of work of A = $\frac{1}{15}$ of the work per day.
- Rate of work of B = $\frac{1}{45}$ of the work per day.
- Combined rate = $\frac{1}{A} + \frac{1}{B}$
2.

Product-Sum Formula:
\[ \text{Total Days} = \frac{A \times B}{A + B} \]

Step 3: Detailed Calculation:
Let's use the product-sum formula as it is highly efficient:
- $A = 15$
- $B = 45$
\[ \text{Total Days} = \frac{15 \times 45}{15 + 45} \]
Calculate the numerator:
\[ 15 \times 45 = 675 \]
Calculate the denominator:
\[ 15 + 45 = 60 \]
Substitute back to find Total Days:
\[ \text{Total Days} = \frac{675}{60} \]
Divide both numerator and denominator by 15:
\[ \text{Total Days} = \frac{45}{4} \]
Convert the improper fraction to a decimal:
\[ \frac{45}{4} = 11.25 \text{ days} \]
Thus, working together, they complete the work in 11.25 days.

Step 4: Final Answer:
This matches Option (D).