A completes three-fourth of a work in 9 days while A and B complete the whole work in 9 days. The efficiency of A is what percent more than the efficiency of B?

Correct option is D

1. Given:

A completes $$\frac{3}{4}$$​ of the work in 9 days.

A and B together complete the whole work in 9 days.

Let A's efficiency be $$E_A$$​ and B's efficiency be $$E_B$$​.​

2. Solution:

Step 1: Calculate A's efficiency $$( E_A )$$​​

A completes $$\frac{3}{4}$$​ of the work in 9 days. Work completed per day by A: $$E_A = \frac{\frac{3}{4}}{9} = \frac{3}{36} = \frac{1}{12} \text{ work/day.}$$​

Step 2: Calculate combined efficiency of A and B $$( E_{A+B} )$$​​

A and B together complete the whole work in 9 days: $$E_{A+B} = \frac{1}{9} \text{ work/day.}$$​

Step 3: Calculate B's efficiency $$( E_B )$$​​

From $$E_{A+B} = E_A + E_B : \frac{1}{9} = \frac{1}{12} + E_B$$​

Subtract $$\frac{1}{12}$$​ from both sides: $$E_B = \frac{1}{9} - \frac{1}{12} = \frac{4}{36} - \frac{3}{36} = \frac{1}{36} \text{ work/day.}$$​

Step 4: Calculate percentage increase in A's efficiency compared to B's efficiency

Using the formula: $$\text{Percentage Increase} = \frac{E_A - E_B}{E_B} \times 100$$​

Substitute $$E_A = \frac{1}{12} and E_B = \frac{1}{36} : \text{Percentage Increase} = \frac{\frac{1}{12} - \frac{1}{36}}{\frac{1}{36}} \times 100$$​

Simplify: $$\frac{\frac{1}{12} - \frac{1}{36}}{\frac{1}{36}} = \frac{\frac{3}{36} - \frac{1}{36}}{\frac{1}{36}} = \frac{\frac{2}{36}}{\frac{1}{36}} = 2$$​

So, $$\text{Percentage Increase} = 2 \times 100 = 200\%.$$​

Final Answer:

A's efficiency is $$\boxed{200\%}$$​ more than B's efficiency.