1 questions from actual SSC GD Constable papers · all shown free · click option to reveal solution
If a pipe fills a tank in 'n' hours, it fills 1/n part in 1 hour. This is the pipe's rate of work. When pipes work together, ADD their rates. For outlet pipes, SUBTRACT their rates from inlet rates.
The combined rate tells you the net filling or emptying speed
- Pipe Rate = 1/Time taken to fill/empty alone - Combined Rate = Sum of individual rates (+ for inlet, - for outlet) - Time with combined rate = 1/Combined rate - Work done = Rate × Time
SSC loves asking about 2-3 pipes working together, pipes opened at different times, and alternating pipe problems. Questions often mix inlet and outlet pipes to test your positive/negative rate concept.
Take LCM of all individual times. This becomes tank capacity. Each pipe's rate becomes LCM/individual time.
This eliminates fractions completely and makes calculations super fast.
Find individual rates A's rate = 1/12 per hour B's rate = 1/15 per hour C's rate = -1/20 per hour (negative for outlet)
Combined rate = 1/12 + 1/15 - 1/20
Take LCM of 12,15,20 = 60 A fills 60/12 = 5 units/hour B fills 60/15 = 4 units/hour C empties 60/20 = 3 units/hour
Net rate = 5 + 4 - 3 = 6 units/hour
Time = 60/6 = 10 hours Worked Example 2: Two pipes fill tank in 6 hours when opened together. First pipe alone takes 5 hours more than second pipe. Find individual times.
Let second pipe take x hours, first takes (x+5) hours
Combined rate = 1/6 per hour
1/(x+5) + 1/x = 1/6
Cross multiply: 6x + 6(x+5) = x(x+5)
6x + 6x + 30 = x² + 5x
12x + 30 = x² + 5x
x² - 7x - 30 = 0
(x-10)(x+3) = 0, so x = 10 hours
Second pipe = 10 hours, First pipe = 15 hours Shortcut Trick 1 - Efficiency Method: Instead of fractions, use efficiency. If A completes work in 4 hours and B in 6 hours, their efficiencies are in ratio 6:4 = 3:2. Total work = LCM(4,6) = 12 units. Shortcut Trick 2 - Alternating Pipes Formula: If two pipes work alternately starting with first pipe, and their individual times are a and b hours, then cycles needed = Total work/(work in 2 hours) and check remainder. The #1 Most Common Trap: Students forget to make outlet pipe rates NEGATIVE. They add all rates as positive and get wrong answers. Always remember: Inlet = +, Outlet = -, then calculate combined rate. Another major mistake is not converting 'part of tank filled' back to actual time. If question asks when tank will be full and you calculated rate, don't forget the final division step.