NIMCET 2018 Logical Reasoning PYQ — Two pipes A and B can fill a cistern in 37.5 minutes and 45 minut… | Mathem Solvex | Mathem Solvex
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NIMCET 2018 — Logical Reasoning PYQ
NIMCET | Logical Reasoning | 2018
Two pipes A and B can fill a cistern in 37.5 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after
Choose the correct answer:
A.
5 minutes
B.
9 minutes
(Correct Answer)
C.
10 minutes
D.
15 minutes
Correct Answer:
9 minutes
Explanation
Given: Correct Option - 2 PipeA can fill the tank in 37.5 minutes PipeB can fill the tank in 45 minutes A cistern is filled in 1/2 hour i.e. 30 minutes Formula Used: The capacity of cistern = LCM of time taken by PipeA and PipeB The efficiency of Pipe = Capacity of cistern/time taken to fill the cistern Calculation: The capacity of cistern = LCM of time taken by PipeA and PipeB ⇒ The capacity of cistern = LCM of 37.5 minutes and 45 minutes ⇒ The capacity of cistern = 225 units The efficiency of PipeA = Capacity of cistern/time taken to fill the cistern ⇒ The efficiency of PipeA = Capacity of cistern/time taken to fill the cistern by PipeA ⇒ The efficiency of Pipe = 225/37.5 ⇒ The efficiency of Pipe A = 6 The efficiency of PipeB = Capacity of cistern/time taken to fill the cistern by PipeB ⇒ The efficiency of PipeB = 225/45 ⇒ The efficiency of PipeB = 5 The cistern filled in just half an hour ⇒ PipeA runs for 30 minutes ⇒ 6× 30 = 180 units i.e. 180 units filled by PipeA in 30 minutes Remaining cistern filled by B, ⇒ Remaining quantity = 225 - 180 ⇒ Remaining quantity = 45 units To fill the 45 units PipeB will have to run for, ⇒ Quantity/ Efficiency of PipeB = total time taken by PipeB ⇒ total time taken by Pipe = 45/5 ⇒ total time taken by Pipe = 9 minutes ∴ PipeB is turned off after 9 minutes.
Explanation
Given: Correct Option - 2 PipeA can fill the tank in 37.5 minutes PipeB can fill the tank in 45 minutes A cistern is filled in 1/2 hour i.e. 30 minutes Formula Used: The capacity of cistern = LCM of time taken by PipeA and PipeB The efficiency of Pipe = Capacity of cistern/time taken to fill the cistern Calculation: The capacity of cistern = LCM of time taken by PipeA and PipeB ⇒ The capacity of cistern = LCM of 37.5 minutes and 45 minutes ⇒ The capacity of cistern = 225 units The efficiency of PipeA = Capacity of cistern/time taken to fill the cistern ⇒ The efficiency of PipeA = Capacity of cistern/time taken to fill the cistern by PipeA ⇒ The efficiency of Pipe = 225/37.5 ⇒ The efficiency of Pipe A = 6 The efficiency of PipeB = Capacity of cistern/time taken to fill the cistern by PipeB ⇒ The efficiency of PipeB = 225/45 ⇒ The efficiency of PipeB = 5 The cistern filled in just half an hour ⇒ PipeA runs for 30 minutes ⇒ 6× 30 = 180 units i.e. 180 units filled by PipeA in 30 minutes Remaining cistern filled by B, ⇒ Remaining quantity = 225 - 180 ⇒ Remaining quantity = 45 units To fill the 45 units PipeB will have to run for, ⇒ Quantity/ Efficiency of PipeB = total time taken by PipeB ⇒ total time taken by Pipe = 45/5 ⇒ total time taken by Pipe = 9 minutes ∴ PipeB is turned off after 9 minutes.
