1. The average height of 25 boys is 1.4 m. When 5 boys leave the group, then the average height increased by 0.15 m. What is the average height of the 5 boys who leave ?

a) 0.8 m

b) 0.9 m

c) 0.95 m

d) 1.05 m

Explanation: Sum of height of the 5 boys

= (25 × 1.4 - 20 × 1.55) m

= 4 m

Required average = $$\left( {\frac{4}{5}} \right)$$ = 0.8 m

2. The average monthly income of a family of four earning members was Rs. 15130. One of the daughters in the family got married and left home, so the average monthly income of the family came down to Rs. 14660. What is the monthly income of the married daughter?

a) Rs. 12000

b) Rs. 15350

c) Rs. 16540

d) Cannot be determined

Explanation: Monthly income of the married daughter

= Rs. (15130 × 4 - 14660 × 3)

= Rs. (60520 - 43980)

= Rs. 16540

3. The average marks obtained by 22 candidates in an examination are 45. The average marks of the first ten are 55 and that of the last eleven are 40. The number of marks obtained by the 11^{th} candidates is

a) 0

b) 45

c) 47.5

d) 50

Explanation: Mark obtained by the 11th candidate

= [(45 × 22) - (55 × 10 + 40 × 11)]

= (990 - 990) = 0

4. The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly added. The first is 18 greater than the actual number and the second number added is 13 instead of 33. Find the correct average.

a) 40.2

b) 40.4

c) 40.6

d) 40.8

Explanation: Correct sum

= (40.2 × 10 - 18 + 33 - 13)

= 404

Correct average = $$\left( {\frac{{404}}{{10}}} \right)$$ = 40.4

5. The average height of 35 girls in a class was calculated as 160 cm. It was later found that the height of one of the girls in the class was wrongly written as 144 cm, whereas her actual height was 104 cm. What is the actual average height of the girls in the class? ( rounded off to 2 digits after decimal)

a) 158.54 cm

b) 158.74 cm

c) 159.56 cm

d) None of these

Explanation: Correct sum

= (160 × 35 + 104 - 144) cm

= 5560 cm

Actual average height

= $$\left( {\frac{{5560}}{{35}}} \right)$$ cm

= 158.857 cm $$ \approx $$ 158.86 cm

6. The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?

a) 0

b) 1

c) 10

d) 19

Explanation: Average of 20 numbers = 0

Sum of 20 numbers (0 x 20) = 0

It is quite possible that 19 of these numbers may be positive and if their sum is a then 20

^{th}number is (-a)

7. The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

a) 76 kg

b) 76.5 kg

c) 85 kg

d) Data inadequate

Explanation: Total weight increased = (8 x 2.5) kg = 20 kg.

Weight of new person = (65 + 20) kg = 85 kg.

8. The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

a) 23 years

b) 24 years

c) 25 years

d) None of these

Explanation: Let the average age of the whole team by x years

11x - (26 + 29) = 9(x - 1)

11x - 9x = 46

2x = 46

x = 23

9. The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:

a) 3500

b) 4000

c) 4050

d) 5000

Explanation: Let P, Q and R represent their respective monthly incomes.

P + Q = (5050 x 2) = 10100 .... (i)

Q + R = (6250 x 2) = 12500 .... (ii)

P + R = (5200 x 2) = 10400 .... (iii)

Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv)

Subtracting (ii) from (iv), we get P = 4000

P's monthly income = Rs. 4000

10. The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:

a) 35 years

b) 40 years

c) 50 years

d) None of these

Explanation: Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years

= 90 years

Sum of the present ages of wife and child = (20 x 2 + 5 x 2) years

= 50 years

Husband's present age = (90 - 50) years

= 40 years