Bodhee Prep-CAT Online Preparation

CAT 2018 [SLOT 1] Quant Question with Solution 09

Question:
In an apartment complex, the number of people aged 51 years and above is 30 and there are at most 39 people whose ages are below 51 years. The average age of all the people in the apartment complex is 38 years. What is the largest possible average age, in years, of the people whose ages are below 51 years?

  1. 27
  2. 28
  3. 26
  4. 25
Show Answer
Correct Answer: 2

Let the average age of people aged 51 years and above be x years.

Let the average age of people aged below 51 years be y years.

Let the number of people aged below 51 years be N.

Given, the average age of all the people in the apartment complex is 38 years.

Therefore,

$\frac{x\times 30+y\times N}{30+N}=38$ ….(1)

We want to maximize y, which occurs when x is minimum i.e. for x=51.

Substituting the value of x in (1) we get

390=N×(38-y)

Again, when y is maximum, N is also maximum i.e. 39

Therefore maximum value of y = 28.


CAT Online Course
Also Check: 841+ CAT Quant Questions with Solutions

CAT 2018 Slot-1


CAT 2018 Slot-2


CAT Quant Questions with Video Solutions

30 must do CAT Quant Questions with Video Solutions

CAT 2023
Classroom Course

We are starting classroom course for CAT 2023 in Gurugram from the month of December.
Please fill the form to book your seat for FREE Demo Classes

CAT 2023 Classroom Course starts in Gurgaon