Question

The average of 25 students in a class is 75. If the average of first 12 students is 74 and last 12 students is 76. What is the mark of 13th student?

Answer 1

Step-by-step explanation:

Given, ( where x1, x2,...x25 are marks of students)

(x1 + x2 + .....+ x25) ÷ 25 = 75

also,

(x1 + x2 +... + x12) ÷ 12 = 74

(x1 + x2 +... + x12) = 74 × 12

( x14+ x15+ ...+ x25) ÷ 12 = 76

( x14+ x15+ ...+ x25) = 76 × 12

now,

( (x1 + x2 +... + x12) + x13 + ( x14+ x15+ ...+ x25) ) ÷ 25 = 75

( ( 74×12) + x13 + ( 76×12) ) ÷ 25 = 75

(74×12) + x13 + (76×12) = 75 ×25

( 74 + 76) 12 + x13 = 75 × 25

x13 = (75×25) - 12( 150)

x13 = 1875 - 1800

x13 = 75

therefore, 13th student got 75 marks