In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: Pipe A takes thrice the time taken by Pipe B to fill a tank. Together they can fill the tank in 15 hours, tank A and B is opened together for 4 hours and then Pipe A is closed and after 2 more hours Pipe B is closed and an outlet Pipe C is opened which when working alone can empty the tank in 10 hours. Calculate the time taken by C to empty the tank. Quantity B: A pipe A can fill the tank in 10 hours another pipe B can fill the tank in 15 hours and with the help of third pipe C they can fill the tank in 5 hours. Pipe A is opened for 4 hours then it is closed, pipe B is closed 3 hours before filling of tank and tank C is opened the whole time. Calculate the time taken to fill the tank?

Question

In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: Pipe A takes thrice the time taken by Pipe B to fill a tank. Together they can fill the tank in 15 hours, tank A and B is opened together for 4 hours and then Pipe A is closed and after 2 more hours Pipe B is closed and an outlet Pipe C is opened which when working alone can empty the tank in 10 hours. Calculate the time taken by C to empty the tank. Quantity B: A pipe A can fill the tank in 10 hours another pipe B can fill the tank in 15 hours and with the help of third pipe C they can fill the tank in 5 hours. Pipe A is opened for 4 hours then it is closed, pipe B is closed 3 hours before filling of tank and tank C is opened the whole time. Calculate the time taken to fill the tank?

Quantity A > Quantity B
Quantity A < Quantity B
Either Quantity A = Quantity B or no relation can be established
Quantity A ≥ Quantity B
Quantity A ≤ Quantity B

LohaHridoy

6 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 2 : Quantity A < Quantity B

Quantity A:

Let the time taken by B be x

Tank filled by B in 1 hour = 1/x

Then, time taken by A is 3x

Tank filled by B in 1 hour = 1/x

∴ According to question

⇒ (1/x) + (1/3x) = 1/15

⇒ 4/3x = 1/15

⇒ x = 20

Pipe B takes 20 hours to fill the tank

Pipe A takes = 20 × 3 = 60 hours to fill the tank

Now, pipe B is opened for 4 hours and A is opened for 6 hours

⇒ 4/20 + 6/60 = 1/5 + 1/10 = 3/10

An outlet pipe C can empty the tank alone in 10 hours

Tank emptied by C in 1 hour = 1/10

⇒ Time taken to empty the tank = (3/10) – (1/10) = 2/10 = 1/5

∴ Tank will be emptied in 5 hours

Quantity B:

Time taken by A to fill the tank = 10 hours

Tank filled by A in 1 hour = 1/10

Time taken by B to fill the tank = 15 hours

Tank filled by B in 1 hour = 1/15

Let the time taken by C be x

Tank filled by C in 1 hour = 1/x

Together they can fill the tank in 5 hours

⇒ (1/10) + (1/15) + (1/x) = 1/5

⇒ 1/10 + 1/15 – 1/5 = 1/x

⇒ 1/x = 1/30

Time taken by B to fill the tank = 30 hours

Pipe A is opened for 4 hours then it is closed, pipe B is closed 3 hours before filling of tank and tank C is opened the whole time

Let the time taken in which tank will completely filled be x

⇒ 4/ 10 + (x – 3)/15 + x/30 = 1

⇒ (3x + 6)/30 = 1

⇒ 3x = 24

⇒ x = 8

∴ Time taken to fill the tank 8 hours

Hence Quantity A < Quantity B