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Two pipes can fill a tank in 20 hours and 90 hours, respectively. The time (in hours) required to fill the tank when both pipes are opened simultaneously is:
9179
8183
13177
11180
11180
Use the formula (product/sum) for two pipes: (20 * 90) / (20 + 90) = 1800 / 110 = 180/11 hours.
Pipe 1 can fill the tank in 20 hours (A = 20), Pipe 2 in 90 hours (B = 90).
T=A+BA×B
Use the formula (product/sum) for two pipes: (20 * 90) / (20 + 90) = 1800 / 110 = 180/11 hours.
Students often add the rates incorrectly by adding the hours directly (20 + 90) instead of their reciprocals (1/20 + 1/90).
Calculate individual work rates
Rate of Pipe 1 is 1/20 of the tank per hour, and Rate of Pipe 2 is 1/90 of the tank per hour.
R1=201,R2=901
Add the work rates
When working together, the combined rate is the sum of individual rates.
Rcombined=201+901=1809+2=18011
Determine total time
The time required is the reciprocal of the combined rate.
T=11180
D is correct because the time taken for both pipes is 180/11 hours.
This formula is equivalent to the 'Efficiency Method' used in work-time problems where total work is assumed to be the LCM of individual times (e.g., LCM(20, 90) = 180 units).
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