Average

Let number of girls = x
Given, Average weight of boys = 42 kg
Number of boys = 25
Then, Total weight of boys = Average weight of boys × Number of boys
= 42 × 25
= 1050
Given, Average weight of girls = 33 kg
Then, Total weight of girls = 33 x ×= 33x
Now, Total weight of boys and girls = 1050 + 33x ⇒ eqn (1)
Given, Average weight of a group of boys and girls = 38 kg
⇒ Total weight of boys and girls = Average weight of a group of boys and girls × (No. of boys + No. of girls)
⇒ Total weight of boys and girls = 38 (25 + x) ⇒ eqn (2)
From eqn (1) and (2),
1050 + 33x = 38 (25 + x)
⇒ 1050 + 33x = 950 + 38x
⇒ 38x - 33x = 1050 - 950
⇒ 5x = 100
⇒ x = 100/5
⇒ x = 20
Thus, number of girls =×= 20

Let's clerks in the organisation be x.
Given, average salary of officers = ₹ 800 per day
Number of officers = 30
⇒ Total salary of officers = Average salary × Number of officers
= 800 × 30
= ₹ 24,000
Given, average salary of clerks = ₹ 240 per day
Then, Total salary of clerks = 240 × x
= 240x
Given, average salary of whole employees = ₹ 300 per day
⇒ Total salary of whole employees = Average salary × [Number of officers + Number of clerks]
= 300 × [30 + x]
Now, Total salary of whole employees = Total salary of officers + Total salary of clerks
⇒ 300 × [30 + x] = 24000 + 240x
⇒ 9000 + 300x = 24000 + 240x
⇒ 300x - 240x = 24000 - 9000
⇒ 60x = 15000
⇒ x = 250
Thus, the number of clerks in the organisation =×= 250 members:

Given, average age of 20 girls = 15 yr
Average age of 25 boys = 24 yr
Age of 20 girls = 15 × 20 = 300 yr
Similarly, age of 25 boys = 24 × 25 = 600 yr
Now, the average age of the two groups = (Age of girls + Age of boys)/(Total number of boys and girls)
= (300 + 600)/(20 + 25)
= 900/45 = 20 yr

Average of C & D = 29 years
⇒ (C + D) /2 = 29
⇒ C + D = 29 × 2 = 58 years ⇒ eqn (1)
Also given that, D is 12 years elder than C
⇒ D = C + 12
So eqn (1) becomes, C + C + 12 = 58
⇒ 2C = 58 - 12
⇒ 2C = 46
⇒ C = 23 years
and D = 23 + 12 = 35 years
Now, Sum of age of A & B is 12 years more than sum of age of B, C & D
⇒ A + B = 12 + B + C + D
⇒ A + B = 12 + B + 23 + 35
⇒ A = 70 years
Then, average age of A & D = (70 + 35) / 2
= 105/2
= 52.5 years

Total members in the family = 6
Average age of the family = 22 years
Total present age of the family of 6 members = 6×22 = 132 years
age of the youngest member = 7 years
Total age of the family of 6 members 7 years ago (ie.,) at
the birth of the youngest member = (132 - 7 × 6)
= 90 years
∴ at the birth of the youngest member, Total members in the family =5.
Average age of the family at the birth of the youngest member = 90 / 5
= 18 years

Let number of pencils taken out be 'X'.
Total number of pencils = 40
Average height of 40 pencils = 154 cm
Average height of taken out pencils = 160 cm.
As per question,
Total height of 40 pencils - Total height of pencils that taken out = Total height of remaining pencils
(40×154) - 160X = 150(40 - X)
6160 - 160X = 6000 - 150X
160 = 10X
X = 16
Remaining pencils = 40 - X = 40 - 16 = 24:

Present age of family of 5 members = (17×5) + (5×3)
= 85 + 15 = 100 years
Given, average age of family is same 17 yrs.
Total age of family of 6 members(including baby) = 6×17 = 102 years
∴ present age of baby = 102 - 100 = 2 years.

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