model 1 basic average questions Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (d)

If the average of remaining numbers be x, then

20 × 15 = 5 × 12 + 15x

⇒ 300 = 60 + 15x

⇒ 15x = 300 – 60 = 240

⇒ x = $240/15$ = 16

Aliter : Using Rule 13,

Here, m = 20, x = 15

n = 5, y = 12

Average of remaining Numbers = $({mx-ny}/{m-n})$

= $({20×15-5×12}/{20-5})$

= $({300-60}/15)$ = $240/15$ = 16

Answer: (a)

Number of successful students in the exam = x

∴ Number of unsuccessful students = 100 – x

According to the question,

30 = ${35x+10(100-x)}/100$

⇒ 3000 = 35x + 1000 – 10x

⇒ 3000 = 25x + 1000

⇒ 25x = 3000 – 1000 = 2000

⇒ x = $2000/25$ = 80

Answer: (b)

Let the last number be x.

According to the question,

18 × 10 + 11 × 20 + x = 30 × 15

⇒ 180 + 220 + x = 450

⇒ 400 +x = 450

⇒ x = 450 – 400 = 50

Answer: (c)

Weight of new person

= (65 + 8 × 2.5) kg

= (65 + 20) kg

= 85 kg

Aliter : Using Rule 23,

Here, x = 2.5, n = 8

Weight of new person

= weight of replaced boy + x × n

Answer: (c)

Using Rule 2,

If the given observations (x) are occuring with certain frequency (A) then,

$Average = {A_1x_1+A_2x_2+...............+A_nx_n}/{x_1+x_2+......+x_n}$

where, $A_1, A_2, A_3, .......... A_n$ are frequencies

Required average

${x_1+x_2+…+x_20}/20$ = ${101×2}/20$

= y-101

Answer: (d)

Using Rule 10,

If the average of '$n_1$' numbers is $a_1$ and the average of '$n_2$' numbers is $a_2$, then average of total numbers $n_1$ and $n_2$ is

$Average = {n_1a_1 + n_2a_2}/{n_1 + n_2}$

Required average

= ${20×30+20×30}/{30+20}$

= ${600+600}/50$

= $1200/50$ = 24