Average

⇒ Average = 2.2,
⇒ Number of people (n) = 20
⇒ Average = ( Total sum/n)
⇒ Total weight increased = 2.2×20 = 44 kg
⇒ Weight of new man = 44 + 53 = 97 kg

Average mark of 50 student is 92
Total marks = 92×50 = 4600
it's is given, that if 5 highest marks are removed, then the average mark reduces by 2
∴ Average of 42 = 90
Their sum is Sum of the removed 5 students is,
4600 - 4050=550
Their average is,
550/5=110

⇒ Let the odd numbers are = a-7, a-5, a-3, a-1, a+1, a+3, a+5,a+7
⇒ let the even numbers are = b-3,b-1, b+1,b+3
Now,
⇒ a-7+ a-5 + a-3 + a-1 + a+1 + a+3 + a+5 +a+7 = 8a = 256
⇒ a = 32
⇒ smallest odd number is 32-7 = 25
⇒ similarly, 4b = 100
⇒ b = 25......second largest even number is 25 + 1 = 26
⇒ Required Sum = 25+ 26 = 51

The total age of all family members = 30 × 14 = 420
New baby born and after 4 years the total age of all the members = 420 + 15 × 4 = 420 + 60 = 480
Reqd average = 480 /15 = 32 years
Hence, 32 years is correct.

Number of hours the student read in the afternoon = Number of pages/ rate
= 100 / 60
= 5/3
Number of hours the student read in the evening = Number of pages/ rate
= 100 / 40
= 5/2
Total hours of reading = (5/3) + (5/2)
= (10 + 15) / 6
= 25/6
Total pages read = 100 + 100 = 200
Average rate of reading = Total pages read / Total hours of reading
= 200 / (25/6)
= (200 × 6)/25
= 8 × 6
= 48 pages per hour

Let's boys in class be 'b'.
Average weight of a class of boys - 24 kg
So, weight of a class = 24b
New average weight of class = 23.5
So, weight of class = 23.5b
As per question,
Average weight of class - Weight of 36 kg boy leaves + Weight of 30 kg boy joins = New average weight of class
24b - 36 + 30 = 23.5b
24b - 23.5b = 6
0.5b = 6
b = 12
∴ number of boys in class = 12.

Given, average monthly income of 4 family members = ₹ 7350
⇒ Total Monthly income of 4 members = 7350 × 4 = 29,400
Average monthly income of 3 persons (excluding the dead person) = ₹ 6500
⇒ Total Monthly income of remaining 3 persons = 6500 × 3 = 19,500
∴ Monthly income of dead person = 29,400 - 19,500 = ₹ 9,900

Details

Husband age + wife age (at the time of marriage)= 23 × 2 = 46
After 5 years of marriage = Husband + wife + child
= 46 + 10 + 1 = 57 years
At the time of birth of child = 57 - 3
= 54 years
Required average age = 54/3 = 18 years

Given, C = 30% of (A + B)/2
⇒ C = (30/100) × (A + B)/2
⇒ C = (3/20) × (A + B) ⇒ eqn (i)
D = 10% of A + A
⇒ D = (10/100) × A + A
⇒ D = (1/10) × A + A
⇒ D = 11A/10 ⇒ eqn (ii)
A : B = 3 : 5
⇒ B = 5A/3 ⇒ eqn (iii)
Put value of eqn (iii) in eqn (i), to convert value of C interms of A only and to eliminate the paramater B
eqn (i) ⇒ C = (3/20) × (A + B)
⇒ C = (3/20) × (A + [5A/3])
⇒ C = (3/20) × (3A + 5A)/3
⇒ C = ($$\frac{1}{2}$$0) × (8A)
⇒ C = 2A/5 ⇒ eqn (iv)
sum of C and D = 180
⇒ C + D = 180
Put values of eqn (iv) and eqn (ii) in the above eqn,
⇒ (2A/5) + (11A/10) = 180
⇒ (4A + 11A)/10 = 180
⇒ 15A/10 = 180
⇒ 3A/2 = 180
⇒ A = 180 × ($$\frac{2}{3}$$)
⇒ A = 120
From eqn (iii), B = 5A/3 = (5 × 120)/3 = 200
From eqn (iv), C = 2A/5 = 48
From eqn (ii), D = 11A/10 = 132
Required Average = (120 + 200 + 48 + 132) / 4 = 500/4 = 125