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If A and B together can complete a work in 18 days. A and C together in 12 days, and B and C together in 9 days, then B alone can do the work in-

18 days

24 days

30 days

40 days

ANSWER : 2

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Let's denote the work done by A in one day as "a," the work done by B in one day as "b," and the work done by C in one day as "c."We are given the following information:<ol><li>A and B together can complete a work in 18 days, so their combined work rate is 1/18 per day.</li><li>A and C together can complete a work in 12 days, so their combined work rate is 1/12 per day.</li><li>B and C together can complete a work in 9 days, so their combined work rate is 1/9 per day.</li></ol>Now, we can set up a system of equations based on these work rates:<ol><li>a + b = 1/18</li><li>a + c = 1/12</li><li>b + c = 1/9</li></ol>We need to find the work rate of B alone, which is "b." To do that, we can subtract equation (2) from equation (1):(a + b) - (a + c) = (1/18) - (1/12) b - c = (1/18) - (1/12)Now, we can solve for "b":b = (1/18) - (1/12) + c b = (2/36) - (3/36) + c b = (-1/36) + cNow, we'll use equation (3) to express "c" in terms of "b":b + c = 1/9 c = (1/9) - bSubstitute this expression for "c" back into the equation for "b":b = (-1/36) + [(1/9) - b]Now, solve for "b":b + b = (-1/36) + (1/9) 2b = (-1/36) + (4/36) 2b = 3/36 b = (3/36) / 2 b = 1/24So, B alone can do the work in 24 days.

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