Question

25 20 50 48. If Tarun and Arun are excluded, the average age of a group of n people increases by 12 more. The total age of two newcomers, Rohit and Mohit, is same as that of Tarun and Arun. If Rohit and Mohit are included in a group of n people, the average age becomes 4 less. find n?​

Answer 1

Answer:

N = 4

The average age of a group of n people increases by 12 if Tarun and Arun are excluded

The total age of two new people, Rohit and Mohit, is the same as that of Tarun and Arun

If Rohit and Mohit are added to the group of n people, the average age decreases by 4

Calculation:

Let Average of the group of n people be n

⇒ Total age of the group = n

Excluding Tarun and Arun,

(nx - (Tarun + Arun))/(n - 2) = x + 12

⇒ nx - (Tarun + Arun) = nx + 12n - 2x -24

⇒ (Tarun + Arun) = 2x - 12n + 24 --(1)

Now, Adding Rohit and Mohit

⇒ (nx + (Rohit + Mohit))/(n+ 2) = x - 4

⇒ nx + (Rohit + Mohit) = nx - 4n + 2x - 8

⇒ (Rohit + Mohit) = 2x - 4n -8 --(2)

The total age of two new people, Rohit and Mohit, is the same as that of Tarun and Arun

∴ 2x - 12n + 24 = 2x - 4n -8

⇒ 8n = 32

∴ n = 4

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

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Question:

The average age of a group of n people increases by 12 if Tarun and Arun are excluded. The total age of two new people, Rohit and Mohit, is the same as that of Tarun and Arun. If Rohit and Mohit are added to the group of n people, the average age decreases by 4. Find n?

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Options:

4

5

6

2

Correct Answer: Option 1 (Solution Below)

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Solution:

Given:

The average age of a group of n people increases by 12 if Tarun and Arun are excluded

The total age of two new people, Rohit and Mohit, is the same as that of Tarun and Arun

If Rohit and Mohit are added to the group of n people, the average age decreases by 4

Calculation:

Let Average of the group of n people be x

⇒ Total age of the group = nx

Excluding Tarun and Arun,

(nx - (Tarun + Arun))/(n - 2) = x + 12

⇒ nx - (Tarun + Arun) = nx + 12n - 2x -24

⇒ (Tarun + Arun) = 2x - 12n + 24 --(1)

Now, Adding Rohit and Mohit

⇒ (nx + (Rohit + Mohit))/(n+ 2) = x - 4

⇒ nx + (Rohit + Mohit) = nx - 4n + 2x - 8

⇒ (Rohit + Mohit) = 2x - 4n -8 --(2)

The total age of two new people, Rohit and Mohit, is the same as that of Tarun and Arun

∴ 2x - 12n + 24 = 2x - 4n -8

⇒ 8n = 32

∴ n = 4