# Average Questions

FACTS  AND  FORMULAE  FOR  AVERAGE QUESTIONS

1. Average =

2. Suppose a man covers a certain distance x kmph and an equal distance at y kmph. Then, the average speed during the whole journey is$\frac{2xy}{x+y}$Kmph

Q:

The average age of a husband and his wife was 23 years at the time of their marriage. After  five years they have a one-year old child. The average age of the family now is :

 A) 25 B) 23 C) 19 D) 18

Explanation:

Sum of the present ages of husband, wife and child = (23 * 2 + 5 * 2) + 1 = 57 years.

Required average = (57/3) = 19 years.

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Q:

After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member ?

 A) 12 B) 13 C) 14 D) 15

Explanation:

i) Let the ages of the five members at present be a, b, c, d & e years.

And the age of the new member be f years.

ii) So the new average of five members' age = (a + b + c + d + f)/5 ------- (1)

iii) Their corresponding ages 3 years ago = (a-3), (b-3), (c-3), (d-3) & (e-3) years

So their average age 3 years ago = (a + b + c + d + e - 15)/5 = x ----- (2)

==> a + b + c + d + e = 5x + 15

==> a + b + c + d = 5x + 15 - e ------ (3)

iv) Substituting this value of a + b + c + d = 5x + 15 - e in (1) above,

The new average is: (5x + 15 - e + f)/5

Equating this to the average age of x years, 3 yrs, ago as in (2) above,

(5x + 15 - e + f)/5 = x

==> (5x + 15 - e + f) = 5x

Solving e - f = 15 years.

Thus the difference of ages between replaced and new member = 15 years.

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Q:

Of the four numbers, whose average is 60, the first is one-fourth of the sum of the last three. The first number is :

 A) 17 B) 29 C) 36 D) 48

Explanation:

Let the first number be x,

Then, sum of the four numbers = x + 4x = 5x.

so,  5x/4 = 60 or x = (60 * 4) / 5 = 48.

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Q:

A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17th innings ?

 A) 34 B) 36 C) 35 D) 37

Explanation:

16x + 85 = 17(x + 3)

x = 34 + 3 = 37

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Q:

A certain factory employed 600 men and 400 women and the average wager was Rs. 25.50 per day, If a woman got Rs. 5 less than a man, then what are their daily wages ?

 A) m:25.50 w:27.50 B) m:27.50 w:22.50 C) m:26.50 w:27.50 D) m: 24.50 w:26.50

Explanation:

Let the daily wage of a man be Rs. x.

Then, daily wage of a woman = Rs. (x - 5).

Now, 600x + 400 (x - 5) = 25.50 * (600 + 400) <=>  1000x = 27500 <=>  x = 27.50.

Man's daily wages = Rs. 27.50; Woman's daily wages = (x - 5) = Rs. 22.50.

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Q:

The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is :

 A) 20 B) 21 C) 23 D) 24

Explanation:

Lot the total number of workers be v Then,

8OOOv = (12000 * 7) + 6000 (v - 7) <=>  2000v = 42000  <=>  v = 21.

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Q:

A team of 8 persons joins in a shooting competition. The best marksman scored 85 points. If he had scored 92 points, the average score for the team would have been 84. The number of points, the team scored was :

 A) 665 B) 657 C) 658 D) 678

Explanation:

Let the total score be x.

(x + 92 - 85) / 8 = 84.

So,  x + 7 = 672   => x = 665.

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Q:

The average age of 36 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?

 A) 35 years B) 45 years C) 51 years D) 54 years