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
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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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Question : The average of p, q, r, and s is 30. If the average of p and q is 12, then what will be the average of r and s?
Option 1: 50
Option 2: 52
Option 3: 48
Option 4: 56
Question : The average height of 40 sticks is 156 cm. Some sticks of average height 162 cm are taken out. If the new average height is 150 cm, how many sticks remain?
Option 1: 25
Option 2: 20
Option 3: 16
Option 4: 32
Question : If p : q = 4 : 7 and q : r = 3 : 5, then what is the value of 2p : 3q : 5r ?
Option 1: 36 : 60 : 181
Option 2: 25 : 72 : 180
Option 3: 24 : 63 : 175
Option 4: 28 : 79 : 188
Question : If p : q : r = 2 : 5 : 3 and r : s = 6 : 5, then what is the value of p : q : r : s?
Option 1: 4 : 12 : 7 : 3
Option 2: 4 : 10 : 6 : 5
Option 3: 6 : 5 : 8 : 10
Option 4: 8 : 12 : 7 : 8
Question : The average age of P, Q, and R is 19 years and that of P and Q is 20 years. R's present age is:
Option 1: 17 years
Option 2: 15 years
Option 3: 20 years
Option 4: 22 years
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