According to question ,
Total age of 14 girls + 1 teacher = 15 × 15 = 225 yrs.
Average age of 14 girls = 14 yrs.
∴ Total age of 14 girls = 14 × 14 = 196 yrs.

Correct Option: D

According to question ,
Total age of 14 girls + 1 teacher = 15 × 15 = 225 yrs.
Average age of 14 girls = 14 yrs.
∴ Total age of 14 girls = 14 × 14 = 196 yrs.
∴ Teacher’s age = 225 – 196 = 29 yrs.

The average of marks of 28 students in Mathematics = 50
Total marks of 28 students = 28 × 50 = 1400
When 8 students left , The average of marks of 20 students = 55
Total marks of 20 students = 20 × 55 = 1100

Correct Option: B

The average of marks of 28 students in Mathematics = 50
Total marks of 28 students = 28 × 50 = 1400
When 8 students left , The average of marks of 20 students = 55
Total marks of 20 students = 20 × 55 = 1100
∴ Total marks of 8 students = 1400 – 1100 = 300
∴ Average = 300 ÷ 8 = 37.5

Given that , The average of five numbers = 27
Total sum of five numbers = 27 × 5 = 135
If one number is excluded, the average of five numbers = 25

Correct Option: D

Given that , The average of five numbers = 27
Total sum of five numbers = 27 × 5 = 135
If one number is excluded, the average of five numbers = 25
Total sum of four numbers = 25 × 4 = 100
∴ Required number = 135 – 100 = 35

Let the average for first 12 innings is y
According to question ,
⇒ 12y + 96 = (y + 5) x 13
⇒ 13y - 12y = 96 - 65
⇒ y = 31

Correct Option: C

Let the average for first 12 innings is y
According to question ,
⇒ 12y + 96 = (y + 5) x 13
⇒ 13y - 12y = 96 - 65
⇒ y = 31
∴ Average after 13th inning = (31 + 5)= 36

According to question ,
Total runs scored by remaining 10 cricketers = 23 × 11 – 113
Total runs scored by remaining 10 cricketers = 253 – 113 = 140

Correct Option: C

According to question ,
Total runs scored by remaining 10 cricketers = 23 × 11 – 113
Total runs scored by remaining 10 cricketers = 253 – 113 = 140
∴ Required average = 140 ÷ 10 = 14 runs