Question

Ajay can complete a work in 9 days working for 8 hours a day. Vijay can complete the same work in 16 days working for 4 hours a day. If they work together to complete the work , then what is the approximate percentage of work done by Vijay?

• A. 51%
• B. 53%
• C. 55%
• D. 58%

Answer 1

The Correct Option is B

Finding the Percentage of Work Done by Vijay

Step 1: Define Total Work

Let the total work be \( L \) (in hours).

Step 2: Compute Efficiency of Ajay and Vijay

• Ajay’s total work in hours: \[ 9 \times 8 = 72 \text{ hours} \] So, his efficiency per hour: \[ \frac{L}{72} \] 
• Vijay’s total work in hours: \[ 16 \times 4 = 64 \text{ hours} \] So, his efficiency per hour: \[ \frac{L}{64} \]

Step 3: Work Done Per Hour by Both Together

\[ \frac{L}{72} + \frac{L}{64} \]

Finding the LCM of 72 and 64, which is 4608:

\[ \frac{64L + 72L}{4608} = \frac{136L}{4608} \]

Work done per hour:

\[ \frac{L}{33.88} \]

Step 4: Compute the Percentage of Work Done by Vijay

\[ \frac{L}{64} \div \frac{L}{33.88} \times 100 \]

Substituting values:

\[ \frac{136L}{4608} \times 100 \]

\[ = 53\% \]

Final Answer:

Thus, the correct answer is 53% (Option B).