model 1 basic average questions Practice Questions Answers Test with Solutions & More Shortcuts

Question : 11

If the average of x and $1/x (x ≠ 0)$ is M, then the average of $x^2$ and $1/x^2$is :

a) $1-M^2$

b) $1-2M$

c) $2M^2-1$

d) $2M^2+1$

Answer: (c)

Question : 12

If the average of m numbers is $n^2$ and that of n numbers is $m^2$, then average of (m + n) numbers is

a) $m/n$

b) m+n

c) mn

d) m-n

Answer: (c)

The average of m numbers = n2

Total number of ‘m’ numbers = m × n²

And the average of n numbers = m2

Total number of ‘n’ numbers = n × m²

∴ Average of (m + n) numbers

= ${mn² + m²n}/{m + n} = {mn(n + m)}/{m + n} = mn$

Question : 13

Numbers of boys and girls are ‘x’ and ‘y’ respectively. Ages of a girl and a boy are ‘a’ years and ‘b’ years respectively. The average age (in years) of all boys and girls is

a) $\text"x+y"/\text"bx+ay"$

b) $\text"x+y"/\text"bx+ay"$

c) $\text"bx+ay"/\text"x+y"$

d) $\text"x+y"/\text"ax+by"$

Answer: (c)

According to question,

Total age of boys = ap years

Total age of girls = bq years

∴ Required average =${ap + bq}/{p +q}$

Question : 14

Six friends have an average height of 167 cms. A boy with height 162 cm leaves the group. Find the new average height.

a) 169 cm

b) 167 cm

c) 166 cm

d) 168 cm

Answer: (d)

Total height of 5 friends

= (6 × 167 – 162) cm.

= (1002 – 162) cm.

= 840 cm.

∴ Required average = $840/ 5$

= 168 cm.

Question : 15 [SSC CGL Tier-I 2015]

The average weight of 15 oarsmen in a boat is increased by 1.6 kg when one of the crew, who weighs 42 kg is replaced by a new man. Find the weight of the new man (in kg).

a) 66

b) 43

c) 65

d) 67

Answer: (a)

Using Rule 18,

If in the group of N persons, a new person comes at the place of a person of ‘T’ years, so that average age, increases by ‘t’ years

Then, the age of the new person = T + N.t

If the average age decreases by ‘t’ years after entry of new person, then the age of the new person = T – N.t

Here, N = 15, T = 42, t = 1.6

Weight of new oarsman

= (42 + 15 × 1.6) kg.

= (42 + 24) kg. = 66 kg.

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