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Question
If A and B together can complete a piece of work in 15 days and B alone in 20 days, in how many days can A alone complete the work?
60
45
40
30
ANSWER : 1
Descrption
<p style="margin-left:0px;">Let's denote the work done by A in one day as "a" and the work done by B in one day as "b."</p><p style="margin-left:0px;">We are given the following information:</p><ol><li>A and B together can complete a piece of work in 15 days, so their combined work rate is 1/15 per day.</li><li>B alone can complete the same work in 20 days, so B's work rate is 1/20 per day.</li></ol><p style="margin-left:0px;">Now, we can set up an equation based on their combined work rate:</p><p style="margin-left:0px;">a + b = 1/15</p><p style="margin-left:0px;">We need to find the work rate of A alone, which is "a." To do that, we can solve for "a" in the equation:</p><p style="margin-left:0px;">a = 1/15 - b</p><p style="margin-left:0px;">Now, we'll substitute the value of "b" from the second piece of information (B's work rate) into this equation:</p><p style="margin-left:0px;">a = 1/15 - 1/20</p><p style="margin-left:0px;">To subtract these fractions, we need a common denominator, which is 60:</p><p style="margin-left:0px;">a = (4/60) - (3/60) a = (1/60)</p><p style="margin-left:0px;">So, A's work rate is 1/60 per day.</p><p style="margin-left:0px;">Now, we can find how many days A alone would take to complete the work:</p><p style="margin-left:0px;">A alone would take 1 work unit per (1/60) days.</p><p style="margin-left:0px;">1 work unit per (1/60) days = 60 work units per day.</p><p style="margin-left:0px;">Therefore, A alone can complete the work in 60 days.</p>
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