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Average age of an ABC party leader and 9 of its followers is 29.7 years. All the followers have the same age and the difference between ages of a leader and a follower is 47 years. The average age of the leader and a follower is A. Which of the following is/are correct? I. A is an integer. II. A – 19 = 32.3 III. A/5 = 9.7 IV. Age of the leader is 47 years more than the age of the follower.

Average age of an ABC party leader and 9 of its followers is 29.7 years. All the followers have the same age and the difference between ages of a leader and a follower is 47 years. The average age of the leader and a follower is A. Which of the following is/are correct? I. A is an integer. II. A – 19 = 32.3 III. A/5 = 9.7 IV. Age of the leader is 47 years more than the age of the follower. Correct Answer III and IV

Given:

Average age of an ABC party leader and 9 followers = 29.7 years

Difference of ages of a leader and a follower = 47 years

The average age of the leader and a follower = A

Formula Used:

Average = Sum of values/Number of values

Calculation:

Let the age of leader be L years and the age of one follower be F years

Sum of ages of an ABC party leader and 9 followers = Average age of an ABC party leader and 9 followers × Number of persons

⇒ L + 9F = 29.7 × 10

⇒ L + 9F = 297      ---- (1)

L – F = 47      ---- (2)

Subtracting equation (2) from (1)

⇒ 10F = 250

⇒ F = 25 years

Put the value of F in equation (2)

L – 25 = 47

⇒ L = 72 years

Average age of leader and a follower = (L + F)/2

⇒ (72 + 25)/2

⇒ 97/2

⇒ 48.5

A = 48.5 years.

I. A is an integer

48.5 is not an integer

I is not correct

II. A – 19 = 32.3 

48.5 – 19 = 29.5

II is not correct

III. A/5 = 9.7

48.5/5 = 9.7

III is correct

IV. Age of leader is 47 years more than the age of the follower.

L – F = 72 – 25

47

IV is correct.

∴ III and IV are correct.

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