Question : The average height of P, Q, and R is 160 cm. If the average height of P and Q is 140 cm and that of Q and R is 129 cm, then what is the height of Q?
Option 1: 72 cm
Option 2: 62 cm
Option 3: 58 cm
Option 4: 78 cm
Correct Answer: 58 cm
Solution :
According to the question
Average = $\frac{P+Q+R}{3}$ = 160
⇒ P + Q + R = 480
Also, $\frac{P+Q}{2}$ = 140
⇒ P + Q = 280
The average height of Q and R is 129 cm,
⇒ $\frac{Q+R}{2}$ = 129
⇒ Q + R = 258
Now, from the above two conditions
(P + Q + R) − (P + Q) = 480 − 280
⇒ R = 200 cm
So, Q = (Q + R) − R = 258 − 200 = 58 cm
Therefore, the height of Q is 58 cm.
Hence, the correct answer is 58 cm.
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