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Three taps A, B and C together can fill an empty cistern in 11 minutes. Tap A alone can fill it in 66 minutes and tap B can fill it in 33/2 minutes. How much time will tap C alone take to fill it?

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ITBP Constable Tradesman Official Paper (Held On: 27 Sept, 2023 Shift 1)
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  1. 66 minutes
  2. 60 minutes
  3. 40 minutes
  4. 55 minutes

Answer (Detailed Solution Below)

Option 1 : 66 minutes
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Detailed Solution

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Given:

A, B, and C together fill the cistern in 11 minutes.

A alone fills the cistern in 66 minutes.

B alone fills the cistern in 33/2 minutes.

Calculations:

Let the total capacity of the cistern be the LCM of 11, 66, and 33/2 = 66.

Efficiency of A, B, and C together = 66 / 11 = 6 units/minute

Efficiency of A = 66 / 66 = 1 unit/minute

Efficiency of B = 66 / (33/2) = 66 × (2/33) = 4 units/minute

Efficiency of C = (Efficiency of A, B, and C together) - (Efficiency of A) - (Efficiency of B)

Efficiency of C = 6 - 1 - 4 = 1 unit/minute

Time taken by C alone to fill the cistern = Total capacity / Efficiency of C

Time taken by C = 66 / 1 = 66 minutes

∴ Tap C alone will take 66 minutes to fill the cistern.

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Last updated on Jul 31, 2024

-> ITBP Constable Tradesman 2024  Notification has been released for the position of Constable (Pioneer) Group 'C', Non-Gazetted (Non-Ministerial).

-> A total number of 202 Vacancies have been announced for the post of Constable (Carpenter), Constable (Plumber), Constable (Mason) & Constable (Electrician). Interested Candidates can apply from 12th August 2024 to 10th September 2024.  

-> Earlier, Application Link was released for Cobbler and Tailor. Candidates can apply for the said post from 20th July 2024 to 18th August 2024. 

-> Also, Indo-Tibetan Border Police Force invites online applications from eligible Male & Female Indian citizens to fill up 51 vacancies of Constable/Tradesman (Tailor & Cobbler). 

-> The ITBP Constable Tradesman is a Group C Non-Gazetted post, and the salary of the finally appointed candidates will be in the pay scale of INR 21,700 - INR 69,100. 

-> Candidates can check the ITBP Constable Tradesman Previous Year Papers which helps them to get the difficulty level of the exam.

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