The pipes A and B can together fill a tank in 8 hours, pipes B and C c

1.	The pipes A and B can together fill a tank in 8 hours, pipes B and C can together fill the tank in 12 hours, and all the three pipes A, B and C can fill the tank working together for 6 hours. Then find the time taken (in hours) by the pipes A and C to fill the tank working together.1. 82. 63. 44. 55. 9
Answer» Correct Answer - Option 1 : 8 Given: Time taken by the pipes A and B to together fill the tank = 8 hours Time taken by the pipes B and C to together fill the tank = 12 hours Time taken by the pipes A, B, and C to together fill the tank = 6 hours Formula Used: If a pipe takes x hours to fill an empty tank completely, the part of the pipe filled by the tank in one hour = 1/x Calculation: Part of the tank filled by A and B working together in 1 hour = 1/8 So, 1/A + 1/B = 1/8 Similarly, 1/B + 1/C = 1/12 And 1/A + 1/B + 1/C = 1/6 We know that, we can obtain the part of the work all the three complete working together for 1 hour as (1/A + 1/B) + (1/B + 1/C) + (1/A + 1/C) = 2 (1/A + 1/B + 1/C) ⇒ 1/8 + 1/12 + (1/A + 1/C) = 2 × 1/6 ⇒ (1/A + 1/C) = 1/3 – 1/8 – 1/12 ⇒ (1/A + 1/C) = 1/8 So, the time taken by A and C to complete the work working together = 1/(1/8) = 8 hours ∴ The time taken by A and C to complete the work working together is 8 hours

The pipes A and B can together fill a tank in 8 hours, pipes B and C can together fill the tank in 12 hours, and all the three pipes A, B and C can fill the tank working together for 6 hours. Then find the time taken (in hours) by the pipes A and C to fill the tank working together.1. 82. 63. 44. 55. 9

Answer» Correct Answer - Option 1 : 8

Given:

Time taken by the pipes A and B to together fill the tank = 8 hours

Time taken by the pipes B and C to together fill the tank = 12 hours

Time taken by the pipes A, B, and C to together fill the tank = 6 hours

Formula Used:

If a pipe takes x hours to fill an empty tank completely, the part of the pipe filled by the tank in one hour = 1/x

Calculation:

Part of the tank filled by A and B working together in 1 hour = 1/8

So, 1/A + 1/B = 1/8

Similarly, 1/B + 1/C = 1/12

And 1/A + 1/B + 1/C = 1/6

We know that, we can obtain the part of the work all the three complete working together for 1 hour as

(1/A + 1/B) + (1/B + 1/C) + (1/A + 1/C) = 2 (1/A + 1/B + 1/C)

⇒ 1/8 + 1/12 + (1/A + 1/C) = 2 × 1/6

⇒ (1/A + 1/C) = 1/3 – 1/8 – 1/12

⇒ (1/A + 1/C) = 1/8

So, the time taken by A and C to complete the work working together = 1/(1/8) = 8 hours

∴ The time taken by A and C to complete the work working together is 8 hours