Bihar Police Constable Model Paper 5

Given:
The average of thirteen number = 9
The average of the first seven numbers = 10
The average of the last seven numbers = 9
Formula used:
The sum of total numbers = the average of all numbers × total numbers
Calculation:
Let the thirteen number be x1,x2,x3,x4,x5, x6,x7,x8,x9,x10, x11,x12 and x13
The sum of the first seven numbers = 10 × 7
⇒ x1+x2+x3+x4+x5 + x6+x7 = 70 ----(i)
The sum of the last seven numbers = 9 × 7
⇒ x7+x8+x9+x10+x11 + x12+x13 = 63 ----(ii)
The sum of thirteen numbers = 13 × 9
⇒ x1+x2+x3+x4+x5 + x6+x7+x8+x9+x10+x11 + x12+x13 = 117 ----(iii)
After adding equation (i) and (ii), we get,
x1+x2+x3+x4+x5 + x6+x7+x8+x9+x10+x11 + x12+x13 = 70 + 63
⇒ x1+x2+x3+x4+x5 + x6+2x7+x8+x9+x10+x11 + x12+x13 = 133 ----(iv)
After subtracting equation (iii) from equation (iv), we get
x7 = 133 – 117
⇒ 16
∴ The 7th number is 16.