79 vote
The average of three natural numbers, P, Q and R is 35. The average of P and Q is 42 while average of Q and R is 25. What is the average of squares of P and R?
The average of three natural numbers, P, Q and R is 35. The average of P and Q is 42 while average of Q and R is 25. What is the average of squares of P and R?
1). 1733
2). 1619
3). 1661
4). 1793
1 answers
56 vote
The average of three natural numbers, P, Q and R is 35.
⇒ (P + Q + R)/3 = 35
⇒ (P + Q + R) = 105
The average of P and Q is 42 while average of Q and R is 25.
⇒ (P + Q)/2 = 42 and (Q + R)/2 = 25
⇒ P + Q = 84 and Q + R = 50
Solving, we get Q = 84 + 50 – 105 = 29
⇒ P = 84 – 29 = 55 and R = 50 – 29 = 21
∴ Average of squares of P and R = (55× 55 + 21 × 21)/2 = 3466/2 = 1733
Other Questions
1. The average of 23, 34, x, 21, 19 and 18 is 21. What is the value of x?