UPSC CAPF Assistant Commandant Model Paper 7

Short trick:
∵ Total is always same
∴ nX = (n – 1)Y + A ---- (1)
⇒ 30Y – 15X = 16Y – A
⇒ 15X = 14Y + A ---- (2)
Comparing equation (1) and (2)
⇒ n = 15
Detailed solution:
Given, 30Y – 15X = 16Y – A
Subtracting 15Y from both the sides
⇒ 15Y – 15X = Y – A
⇒ (Y – A)/(Y – X) = 15 ---- (1)
Average of all ‘n’ numbers = Sum of ‘n’ numbers/n
nX = Sum of ‘n’ numbers
Average of all numbers except A = (Sum of ‘n’ numbers – A)/(n – 1)
⇒ Y = (nX – A)/(n – 1)
⇒ n(Y – X) = Y – A
⇒ n = (Y – A)/(Y – X) = 15 [From equation 1]
∴ The set contains 15 numbers.