Question

Average of 9 observations is 79. First two
observations average is 75, next four observations
average is 87. 8th observation is 5 more than 7th
observation and 1 more than 9th observation. Find
the 9th observation ?
a) 65
b) 66
c) 67
d) 68​

Answer 1

Answer:

9th = 72

Step-by-step explanation:

Let the 9 observations be a, b, c, d, e, f, g, h, i

Avg. of 9 observations = 79

(a+b+c+d+e+f+g+h+i) ÷ 9 = 79

Sum of the 9 observations (a+b+c+d+e+f+g+h+i) = 711   (eqn.1)

First two observations average is 75

(a+b) ÷ 2 = 75

(a+b) = 150     (eqn.2)

next four observations average is 87

(c+d+e+f) ÷ 4 = 87

(c+d+e+f) = 348     (eqn.3)

8th observation is 5 more than 7th observation and 1 more than 9th observation

h = g+5 and h = i+1    (eqn.4)

Make the values of g, h, i in terms of 'i'.

h = g+5

g = h-5  

put the 'h' value  (in terms of i) here

g = i+1-5

g = i-4   (eqn.5)

Substitute all values (eqn. 2, 3, 4, 5) in eqn.1

(a+b+c+d+e+f+g+h+i) = 711

[150+348+ (i-4) + (i+1) + i] = 711

495 + 3i = 711

3i = 216

i = 72

So, h = i+1 = 72+1 = 73

g = i-4 = 72-4 = 68

For check,

(a+b+c+d+e+f+g+h+i) = 711

150 + 348 + 68 + 73 + 72 = 711

711 = 711

So, the 7th observation (g) = 68

8th observation (h) = 73

9th observation (i) = 72

Answer 2

Let us suppose the nine observations are $a,b,c,d,e,f,g,h,i$

Average of $9$ observations $=79$

$\frac{a+b+c+d+e+f+g+h+i}{9} =79$

∴ $a+b+c+d+e+f+g+h+i=79\times 9$

Sum of $9$ observations $=711$      

Average of first two observations $=75$

$\frac{a+b}{2}=75$

∴ $a+b=150$

Average of next four observations $=87$

$\frac{c+d+e+f}{4} =87$

$c+d+e+f=348$

∵ $8^{th}$ observation is $5$ more than $7^{th}$ observation and $1$ more than $9^{th}$ observation

$h=g+5=i+1$

$g=h-5$

substituting all the values ofthe equations we get

$150+348+(i-4)+(i+1)+i=711$

$495+3i=711$

$3i=216\\i=72$

So the $9^{th}$ observatiion will be $72$

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