Pipes A and B can fill a tank in 10 hours and 15 hours respectively. If both are opened together into an empty tank, how long will they take to fill it?
Aptitude
Pipes and Cistern
Difficulty: Easy
Choose an option
Answer
Correct Answer: 6 hours
Explanation
Introduction / Context:When two inlets run together, their rates add. The time to complete one tank equals the reciprocal of the combined rate.
Given Data / Assumptions:
- A fills in 10 h ⇒ 1/10 tank/h.
- B fills in 15 h ⇒ 1/15 tank/h.
Concept / Approach:Combined rate = 1/10 + 1/15. Time = 1 ÷ (combined rate).
Step-by-Step Solution:LCM(10, 15) = 30 ⇒ 1/10 = 3/30; 1/15 = 2/30.Total rate = (3 + 2)/30 = 5/30 = 1/6 tank/h.Time to fill = 1 ÷ (1/6) = 6 hours.
Verification / Alternative check:In 6 hours, A fills 6/10 = 3/5 and B fills 6/15 = 2/5; total = 1 tank.
Why Other Options Are Wrong:12 1/2 hours is slower than either pipe alone; 5 hours is too optimistic for these rates.
Common Pitfalls:Adding times instead of rates; arithmetic errors in LCM.
Final Answer:6 hours