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    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 effici
    Question

    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?

    A.

    100%

    B.

    150%

    C.

    300%

    D.

    200%

    Correct option is D

    1. Given:

    A completes 34\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 EAE_A​ and B's efficiency be EBE_B ​.​

    2. Solution:

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

    A completes 34\frac{3}{4}​ of the work in 9 days. Work completed per day by A: EA=349=336=112 work/day.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 (EA+B)( E_{A+B} )​​

    A and B together complete the whole work in 9 days: EA+B=19 work/day.E_{A+B} = \frac{1}{9} \text{ work/day.}

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

    From EA+B=EA+EB:19=112+EBE_{A+B} = E_A + E_B : \frac{1}{9} = \frac{1}{12} + E_B

    Subtract 112\frac{1}{12}​ from both sides: EB=19112=436336=136 work/day.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: Percentage Increase=EAEBEB×100\text{Percentage Increase} = \frac{E_A - E_B}{E_B} \times 100

    Substitute EA=112andEB=136:Percentage Increase=112136136×100E_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: 112136136=336136136=236136=2\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, Percentage Increase=2×100=200%.\text{Percentage Increase} = 2 \times 100 = 200\%.

    Final Answer:

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

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