Subject
Quantitative Aptitude
Topic
Time and Work
Consider three pipes P, Q and R. The pipes P and Q can fill the cistern in 2 and 2.5 hours respectively. The pipe R can empty the cistern in 1 hour. If these pipes were opened at an interval of half an hour at 6:00am, 6:30am and 7:00am respectively. When the cistern will get empty?
Consider three pipes P, Q and R. The pipes P and Q can fill the cistern in 2 and 2.5 hours respectively. The pipe R can empty the cistern in 1 hour. If these pipes were opened at an interval of half an hour at 6:00am, 6:30am and 7:00am respectively. When the cistern will get empty?
ক)
7:00 amখ)
10:00 amগ)
12:00 pmঘ)
2:00 pmঙ)
1:00 pmExplanation
Amount emptied by pipe R in one hour = 1 As pipe P fills the entire cistern in 2 hours, Part of cistern filled by pipe P in one hour = ½ As pipe Q fills the entire cistern in 2.5 hours, Amount filled by pipe Q in one hour = 1/2.5 For the first half an hour only pipe P is open. ∴ Part of cistern filled by pipe P in starting ½ hour = ½ × ½ = ¼ For the next half an hour, pipe P and pipe Q both are open. ∴ Part of cistern filled by pipe P and pipe Q in next half an hour ∴ Total pat of cistern filled after one hour After 1 hour all three pipes are open. Let x be the number of hours for which all 3 pipes are open ∴ At the end of x hours, the cistern will be completely empty ⇒ x = 7 ∴ All three tanks are open for 7 hours. ⇒ Tank will get empty 7 hours after 7:00 am. ⇒ Tank will get empty at 2:00 pm.Related questions
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