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If Rajat can do a work in 35 days, Raju can do it in 21days. How many days both together can complete the work?

This question was previously asked in
MP Police Constable 2023 Official Paper (Held On: 01 Sept, 2023 Shift 1)
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  1. \(11\dfrac{1}{8} \text{ days} \\\)
  2. \(15\dfrac{1}{8} \text{ days} \)
  3. \(12\dfrac{1}{8} \text{ days} \\\)
  4. \(13\dfrac{1}{8} \text{ days} \)

Answer (Detailed Solution Below)

Option 4 : \(13\dfrac{1}{8} \text{ days} \)
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Detailed Solution

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Given:

Time taken by Rajat = 35 days

Time taken by Raju = 21 days

Formula used:

Total work = LCM of individual times

Efficiency = Total work / Time

Time to complete work together = Total work / Combined efficiency

Calculations:

Total work = LCM of (35, 21) = 105 units

⇒ Rajat's efficiency = 105 / 35 = 3 units/day

⇒ Raju's efficiency = 105 / 21 = 5 units/day

Combined efficiency = Rajat's + Raju's

⇒ Combined efficiency = 3 + 5 = 8 units/day

Time to complete work together = 105 / 8

⇒ Time = 105 / 8 or  \(13\dfrac{1}{8} \text{ days} \)

∴ Both together can complete the work in  \(13\dfrac{1}{8} \text{ days} \)

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Latest MP Police Constable Updates

Last updated on Mar 12, 2025

-> The MP Police Constable 2023 Final Merit List has been out on 12th March 2025.

-> MP Police Constable 2025 Notification will soon be released on the official website.

-> The The Madhya Pradesh Professional Examination Board (MPPEB) will announce more than 7500 Vacancies for the post of constable. 

-> Previously, the notification had invited eligible candidates to apply for 7,090 constable posts.

-> Candidates who have passed 10th or 12th are eligible to apply.

-> The final candidates selected will receive a salary between 19,500 and 62,600 INR.

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