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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?
- A1733
- B1619
- C1661
- D1793
Answer not set
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CCommunity
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
⇒ (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