Let the total number of students in the class be n.
According to the question,
an = 10 × b + (n – 10) c
⇒ an = 10b + nc – 10c
⇒ an – cn = 10b – 10c
⇒ n (a – c) = 10 (b – c)

Correct Option: D

Let the total number of students in the class be n.
According to the question,
an = 10 × b + (n – 10) c
⇒ an = 10b + nc – 10c
⇒ an – cn = 10b – 10c
⇒ n (a – c) = 10 (b – c)

According to the question,
a + b + c = 3 × 20 = 60 ...(i)
b + c + d = 3 × 25 = 75 ...(ii)
By equation (i) – (ii),
a – d = 60 – 75
⇒ a – 30 = – 15

Correct Option: D

According to the question,
a + b + c = 3 × 20 = 60 ...(i)
b + c + d = 3 × 25 = 75 ...(ii)
By equation (i) – (ii),
a – d = 60 – 75
⇒ a – 30 = – 15
⇒ a = 30 – 15 = 15

If each number of a set be multiplied by m, the average gets multiplied by m.
If each number of a set be increased by p, the average gets increased by p.
Here , The average of 12 numbers = 9
m = 2 , p = 3

Correct Option: C

If each number of a set be multiplied by m, the average gets multiplied by m.
If each number of a set be increased by p, the average gets increased by p.
Here , The average of 12 numbers = 9
m = 2 , p = 3
∴ Required average = m × The average of 12 numbers + p = 2 × 9 + 3 = 21

Total correct marks of 17 students = 17 × 71 – 65 – 24 + 56 + 50
Total correct marks of 17 students = 1207 – 89 + 106 = 1224

Correct Option: C

Total correct marks of 17 students = 17 × 71 – 65 – 24 + 56 + 50
Total correct marks of 17 students = 1207 – 89 + 106 = 1224

Correct Option: B

Average height of whole class =		30 × 160 + 20 × 165		cm
		50

Average height of whole class =		4800 + 3300		cm
		50

Average height of whole class =		8100		cm
		50