model 4 find nth average from 1st & last number Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

Using Rule 1,

Average of two or more numbers/quantities is called the mean of these numbers, which is given by

$\text"Average(A)" = \text"Sum of observation / quantities"/\text"No of observation / quantities"$

∴ S = A × n

Last number = Sum of 20 numbers

– sum of first 12 numbers – sum of next 7 numbers

= 20 × 12 – 11 × 12 – 7 × 10

= 240 – 132 – 70 = 38

Answer: (d)

Using Rule 1,

Sum of remaining two numbers

= 6 × 3.95 – 2 × 3.4 – 2 × 3.85

= 23.7 – 6.8 – 7.7 = 9.2

∴ Required average = ${9.2}/2$= 4.6

Answer: (a)

Sum of remaining 10 numbers

= 12 × 15 – 2 × 14

= 180 – 28 = 152

∴ Required average =$152/10$

= $76/5$ = 15$1/5$

Answer: (d)

Let three numbers be a,b and c respectively.

∴ a + b + c = 16 × 3 = 48 ---(i)

b + c + 20 = 15 × 3 = 45

⇒ b + c = 45 – 20 = 25 ---(ii)

By equation (i) - (ii),

a = 48 – 25 = 23

Aliter : Using Rule 16,

Here, n = 3, F = 16, L = 15

l = 20, f= ?

f – l= n (F – L)

f – 20= 3 (16 – 15)

f = 3 + 20

f = 23

Answer: (a)

Using Rule 1,

According to the question,

195 + x + x + 20 = 135 × 3

⇒ 2x + 215 = 405

⇒ 2x = 405 – 215 = 190

∴ x =$190/2$ = 95

x = Smallest number

Answer: (c)

Using Rule 1,

Sum of 8 numbers = 20 × 8 = 160

Sum of the first two numbers =$31/2$ ×2 = 31

Sum of next three numbers = $64/3$×3=64

Sum of the remaining three numbers = 160 – (31 + 64) = 160 – 95 = 65

Let 6th number = x

∴ 7th number = x + 4,

8th number = x + 7

⇒ x + x + 4 + x + 7 = 65

⇒ 3x = 65 – 11

⇒ x = $54/3$ =18

∴ Eighth number = 18 + 7 = 25