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A and B complete a work in 18 days. If A alone can do it in 54 days then, B alone can do in______________(days).
29
27
26
28
27
Use the formula: time = (A * B) / (A - B). Here, 18 * 54 / (54 - 18) = 18 * 54 / 36 = 27 days.
Combined work rate of A and B is 18 days. A's individual work time is 54 days.
B1тАЛ=(A+B)1тАЛтИТA1тАЛ
Use the formula: time = (A * B) / (A - B). Here, 18 * 54 / (54 - 18) = 18 * 54 / 36 = 27 days.
Students often incorrectly add the days (18+54) or subtract them without considering the reciprocal nature of work rates.
Define Rates
Let the total work be 1 unit. A and B together do 1/18 work per day. A alone does 1/54 work per day.
(A+B)=181тАЛ,A=541тАЛ
Isolate B's Rate
Subtract A's rate from the combined rate to find B's daily work rate.
B1тАЛ=181тАЛтИТ541тАЛ
Calculate and Invert
Finding a common denominator of 54, we get (3тИТ1)/54=2/54=1/27. Thus, B takes 27 days.
B=27
B is correct because the individual work rate of B is found to be 1/27, meaning B completes the work in 27 days.
This concept is fundamentally identical to Pipe and Cistern problems, where 'filling' is positive work and 'emptying' is negative work.
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