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

Answer: (c)

Sum of first n odd natural numbers = $n^2$

∴ Their average = ${n^2}/n$ = n

∴ Required average = 25

because n = 25

Aliter : Using Rule 7,

Average = 25

Answer: (a)

D’s weight = 80 × 4 – 84 × 3

= 320 – 252 = 68 kg.

E’s weight = 68 + 3 = 71 kg.

Total weight of (A + B + C + D + E)

= 84 × 3 + 68 + 71

= 252 + 68 + 71 = 391 kg.

Total weight of (B + C + D + E)

= 79 × 4 = 316 kg.

∴ A’s weight= 391 – 316 = 75 kg.

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

Answer: (b)

Number of natural numbers = x

∴ Their sum = 15x

According to the question,

15x + 30 – 5 = x × 17.5

⇒ 17.5x – 15x = 25

⇒ 2.5x = 25

⇒ x = $25/2.5$ = 10

Answer: (a)

Mean of Ten observations – Mean of nine observations

Tenth observation

= 10 × 17 – 16 × 9

= 170 – 144 = 26

Aliter : Using Rule 19,

Here, N = 9, T = 16

n = 1, t = 1

10th observation

= T+ $({N/n}+1)$t

= 16+$(9/1+1) ×1$

= 16 + 10 = 26

Answer: (c)

Required average weight

= ${42×25+28×40}/{42+28}$

= ${1050+1120}/70$ = $2170/70$ = 31kg

Aliter : Using Rule 10,

Here, $n_1$ = 42, $a_1$ = 25

$n_2$ = 28, $a_2$ = 40

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