Average

-⇒ Let's passed students be x,
-⇒ 45 × 12 = 14x + (45 - x) × 5
-⇒ 540 = 14x + 225 - 5x
-⇒ 540 - 225 = 9x
-⇒ 9x = 315
-⇒ X = 35
-⇒ Total number of passed students = 35

The average weight of class = x
If the strength of old students = 100
The new students strength = 100 + 100×(1/4)
= 100 + 25 = 125
New students weight = 200 kgs
125(x - 1) = 100x + 200
125x - 125 = 100x + 200
125x - 100x = 200 + 125
25x = 325
x = 13
Required average =×- 1
= 13 - 1 = 12 kgs

Let total no. of workers =×
Total salary =×× 75 ..... (i)
again, as per the question
Total salary = 25 × 625 + (x - 25) × 65 ..... (ii)
From (i) & (ii)
x × 75 = 25 × 625 + (x - 25) × 65
75x - 65x = 15625 - 1625
10x =14000
x = 1400
Hence, Total numbers of workers is 1400.

Given, the average age of A, B, C and D = 5 years
⇒ (A + B + C + D) / 4 = 5
⇒ A + B + C + D = 5 × 4
⇒ A + B + C + D = 20 years ⇒ eqn (i)
Also, given that, average age of A, B, D, E = 6 years
⇒ (A + B + D + E) / 4 = 6
⇒ A + B + D + E = 6 × 4
⇒ A + B + D + E = 24 years ⇒ eqn (ii)
On Solving eqn (i) - eqn (ii) [ie., subtracting], we get
C - E = - 4
age of C = 8 years
⇒ 8 - E = -4
⇒ E = 8 + 4 = 12 years
Hence, the age of E = 12 years.

Difference of numbers = 23 - 32
= -9
There are 9 integers
So, the average of -9 = -9 / 9 = -1
The new average = 11 - 1 = 10

Given Mean of 11 numbers = 35
Formula:- Mean (or) Average = Sum of numbers/Total no. of elements
So, sum of 11 numbers = 35 × 11 = 385
Similarly, sum of first 6 numbers = 32 × 6 = 192
and sum of last six numbers = 37 × 6 = 222
Now, the sixth number = (192 + 222) - 385
= 414 - 385
= 29

No. of employees = 100
Given, average age of all the 100 employees = 29 years
⇒ Total age of all the 100 employees = 29 × 100 = 2900
Total No. of female employees = ($$\frac{2}{5}$$) × 100 = 40
So, Total No. of Male employees = 100 - 40 = 60
Ratio of average age of men to women = 5 : 7
⇒ Average age of men = 5x
and, Average age of women = 7x
Now, Total age of male employees + Total age of female employees = Total age of all the 100 employees
⇒ (5x × 60) + (7x + 40) = 2900
⇒ 300x + 280x = 2900
⇒ 580x = 2900
⇒ x = 5
So, average age of female employees = 7x = 7 × 5 = 35 years

Weight of 40 students = 40×75
New weight = 40×75 - 74-66 + 66 + 54
= 40×75 - 20
∴ the new average = (40×75-20)/40
= 74.50 kg

Let the average height of 4 mens be 'X'.
So, total height of 4 mens = 4X
Total height of 24 mens = 24×6 = 144 feet.
we know that,
4X + 144 = 28(6 + 0.2)
4X + 144 = 168 + 5.6
4X = 173.6 - 144
4X = 29.6
X = 7.4 feet
∴ average height of 4 mens is 7.4 feet:

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