Let the number of papers = x.
According to the question,
64x + 18 + 4 = 66x

Correct Option: A

Let the number of papers = x.
According to the question,
64x + 18 + 4 = 66x
∴ 2x = 22
∴ x = 22/2 = 11

Let number of passed students = N
Total marks = 120 x 30

According to the question,
40N + (120 - N) x 10 = 120 x 30

Correct Option: B

Let number of passed students = N
Total marks = 120 x 30

According to the question,
40N + (120 - N) x 10 = 120 x 30
⇒ 3600 = 40N + 1200 - 10N
⇒ 30N = 2400
∴ N = 2400/30 = 80
∴ 25% of 80 = 80/4 = 20

Here n₁ = 20, n₂ = 30, a₁ = 80%, a₂ = 70%
∴ Total average = (n₁a₁ + n₂a₂) / (n₁ + n₂)

Correct Option: B

Here n₁ = 20, n₂ = 30, a₁ = 80%, a₂ = 70%
∴ Total average = (n₁a₁ + n₂a₂) / (n₁ + n₂)
= (20 x 80 + 30 x 70) / (20 + 30)
= (1600 + 2100) / 50
= 74%

Total age of all members of the family (at present) = 20 x 4 = 80
4yr ago, total age of all members = 80 - ( 4 x 4) = 80- 16 = 64 yr.

As 4 yr ago, there were only 3 members in the family

Correct Option: C

Total age of all members of the family (at present) = 20 x 4 = 80
4yr ago, total age of all members = 80 - ( 4 x 4) = 80- 16 = 64 yr.

As 4 yr ago, there were only 3 members in the family

∴ Average age of the family at the time of the birth of the youngest member
= 64/3
= 21¹/₃ yr

3 yr ago, total age of 5 members of the family = 17 x 5 = 85 yr
Present age of all the members of the family = 85 + 3 x 5 = 100 yr
Let the age of the child = N yr
Present avrage age of family = (100 + N) / 6
[At present total number of members = 5 + 1 = 6]

Correct Option: D

3 yr ago, total age of 5 members of the family = 17 x 5 = 85 yr
Present age of all the members of the family = 85 + 3 x 5 = 100 yr
Let the age of the child = N yr
Present avrage age of family = (100 + N) / 6
[At present total number of members = 5 + 1 = 6]
17 = 100N / 6
⇒ 102 = 100 + N
∴ N = 2 yr