Average

 Average ( SET 5 : Q21-Q25 )

21.The average age of a family is 24 years which is consisting 5 members, out of which the youngest being 6 years old. What would be the average age of the family just before his birth?
1
23 years
2
22.5 years
Correct Answer
3
20 years
Incorrect
4
18 years

Solution: 2

The average age of 5 member family is 24 years.

∴ Total age of Family i.e. Summation of age of every member = 24 × 5 = 120.

At the time of youngest member birth, which means 6 years back

Total age of family would be 120 – (6 × 5) = 120 – 30 = 90. (Because each member’s age would reduce by 6 years).

∴ Average age of family = 90/4 = 22.5.

22. In a cricket team of 11 players, one player weighing 42kg is injured and his place is taken by a new player due to which the average weight of team is reduced by 100 grams. Find weight of new player.
1
41.1 Kg
2
40.9 Kg
Correct Answer
3
42.9 Kg
4
43.1 Kg

Solution: 2

Given:

Number of players = 11

Average weight reduced by 100 gm when 1 player weighing 42 kg is injured and is replaced by a new player

Concept used:

Weight of new player = Weight of injured player – (Number of players × Average reduced by)

Calculation:

Weight of new player = 42 – (11 × 0.1) kg

⇒ (42 – 1.1) kg

⇒ 40.9 kg

∴ The weight of new player is 40.9 kg


23. The average age of 8 persons in a committee is increased by 2 years when two men whose ages are 35 years and 45 years are replaced by two new men. The average age of the two new men is (in years)

1
40
2
42
3
48
Correct Answer
4
45

Solution: 3

∵ Average = (Sum total of Ages of All the persons) ÷ (Total no. of persons)

Let the sum of age of 6 persons be x, age of 7th person = 35 & age of 8th Person = 45

⇒ Sum of ages of 8 person = x + 35 + 45 = x + 80

⇒ Average = A = (x + 80)/8

⇒ 8A = x + 80 .... (i)

Let the 7th & 8th person with ages 35 & 45 be replaced with persons having ages as "a" & "b" years respectively

∴Avg of age of the 2 new men = (a + b)/2

According to question

⇒(x+a+b)/8=A+2

⇒ x + a + b = 8A +16... (ii)

∴ From Eq. (i) &Eq (ii) we get

⇒ x + a + b = x + 80 + 16

⇒ a + b = 96

Dividing both sides by 2

⇒ (a + b)/2 = 48


24. The average of 8 numbers is 19. The average of first and sixth numbers is 17 and that of the third, fifth and seventh numbers is 2413. If the second number is less than the fourth number by 8, and greater than the eighth number by 2, then the sum of fourth number and eighth number is:
1
45
2
21
3
13
Incorrect
4
32
Correct Answer

Solution: 4

We know that, Average = Sum of all observations/Number of observations

According to the given information,

Average of 8 numbers is 19

∵ The average of first and sixth numbers is 17

first number + sixth number = 17 × 2 = 34

And, since Average of the third, fifth and seventh numbers is 

∴ third number + fifth number + seventh number 

Now, since the second number is less than the fourth number by 8, and greater than the eighth number by 2, let the second number be x thus, fourth number would be x + 8, and eighth number would be x - 2.

Thus,

19 = (sum of all eight numbers)/8


⇒ 3x + 113 = 152

⇒ 3x = 39

⇒ x = 13

Hence fourth number = 13 + 8 = 21

eighth number = 13 - 2 = 11

Required sum = 21 + 11 = 32


25. A librarian purchased 50 story books for his library. But he saw that he could get 14 more books by spending Rs. 76 more and the average price per book would be reduced by Rs. 1. The average price (in Rs.)of each book he bought, was:
1
20
2
25
3
15
Incorrect
4
10
Correct Answer

Solution: 4

Let average price of each book, a librarian bought be Rs x

Then, total price of these 50 books = Rs 50x

But he saw that he could get 14 more books by spending Rs.76 more

∴ Price of (50 + 14) = 64 books will be Rs (50x + 76)

Average price of 64 books = (50x + 76)/64

As, the average price per book would be reduced by Rs. 1


⇒ 64x – 50x -76 = 64

⇒ 14x = 140

⇒ x = 10

Hence, average price of books = Rs 10


 SET 01 : Q1 - Q5

 SET 02 : Q6 - Q10

 SET 03 : Q11 - Q15

 SET 04 : Q16 - Q20

 SET 05 : Q21 - Q25

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