From a group of 15 casting directors of a Bollywood film, four directors aged 18 years, 19 years, 17 years and 15 years were removed and replaced by four new directors, the average age of the group increased by 4 months it occurs. Find the average age of the newly joined directors.?

1. A

   18 years 6 months

2. B

   17 years 6 months

3. C

   18 years 5 months

4. D

   17 years 4 months

Appeared in: UP CHO - 10 September 2021

Explanation

• The total age of the four new directors must compensate for the age of the four removed directors and also account for the total increase in the group's age.
• The total age increase for the group is calculated by multiplying the number of members (15) by the average age increase (4 months), which equals 60 months or 5 years.
• The total age of the four removed directors is 18 + 19 + 17 + 15 = 69 years.
• Therefore, the total age of the four new directors is 69 years (removed age) + 5 years (total increase) = 74 years.
• The average age of the new directors is 74 years divided by 4, which is 18.5 years or 18 years and 6 months.

Why Other Options Were Wrong

• Option B: This answer is incorrect. An average age of 17 years and 6 months (17.5 years) for four directors would mean their total age is 70 years (17.5 × 4). This does not correctly account for the required total age of 74 years.
• Option C: This answer is incorrect. It likely results from a calculation error, either in dividing the total age (74) by 4 or in converting the decimal part of the year into months.
• Option D: This answer is mathematically incorrect and does not align with the data provided. An average age of 17 years and 4 months is significantly lower than the calculated correct average.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating average age after replacement of members in a group as background academic context rather than a clinical decision trigger.
• This question tests quantitative aptitude, a skill often evaluated in competitive examinations, including those for nursing.
• The ability to perform accurate, multi-step calculations is a foundational skill for nurses, especially in critical tasks like medication dosage calculation and fluid balance monitoring, where precision is paramount.
• What if? If the average age had decreased by 4 months, the total age of the new directors would be the age of the removed directors minus the total decrease. The calculation would be: 69 years - 5 years = 64 years. Their average age would then be 64 ÷ 4 = 16 years.

How to Approach the Question

• First, identify all the key numerical values given in the problem: total members in the group (15), number of members replaced (4), the ages of the removed members (18, 19, 17, 15), and the change in the group's average age (+4 months).
• Calculate the total age of the members who were removed from the group by summing their individual ages: 18 + 19 + 17 + 15 = 69 years.
• Next, calculate the total change in the sum of ages for the entire group. This is found by multiplying the total number of members by the change in the average age: 15 members × 4 months = 60 months.
• Convert the total change in age from months to years for consistency: 60 months ÷ 12 = 5 years.
• Determine the total age of the new members. Since the average age increased, the new members' total age must be the old members' total age plus the total increase: 69 years + 5 years = 74 years.
• Finally, calculate the average age of the new members by dividing their total age by their number: 74 years ÷ 4 members = 18.5 years.

Concept Tested & Keywords

• Concept Tested: Calculating average age after replacement of members in a group.
• Stem keywords: group of 15, casting directors, four directors removed, replaced by four new, average age increased by 4 months
• Lead-in keywords: Find the average age

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Q5_bqym0iaEjZcpEiXehC7

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