Question

The average marks of three students P, Q, and R is 75. Another student S joins the group and makes the average 70. Now, a man X whose marks are 8 more than that of S, replaces Q, and the average of P, R, S, and X becomes 68. What are the marks of Q?
1. 71
2. 68
3. 72
4. 77
5. 56

Answer 1

Correct Answer - Option 1 : 71

Given:

(P + Q + R)'s average = 75

(P + Q + R + S)'s average = 70

X's marks = 8 + S' marks

(P + R + S + X)'s average = 68

Formula used:

Average = sum of observations/total number of observations

Calculation:

(P + Q + R)/3 = 75

⇒ (P + Q + R) = 225

also, (P + Q + R + S)/4 = 70

⇒ (P + Q + R + S) = 280      ----(1)

S = 280 - 225 = 55

so, X's marks = 55 + 8 = 63

(P + R + S + X)/4 = 68

⇒ (P + R + S + X) = 272      ----(2)

subtracting (1) - (2), we get

Q - X = 280 - 272 = 8

Q = 8 + X

Q's marks = 8 + 63 = 71

∴ The answer is 71