P varies directly as the sum of the two quantities Q and R. Q in turn varies directly as x and R varies inversely as x. When x = 4, P = 12 and when x = 8, P = 18. Find the value of P when x = 16.
Explanation:
P α (Q+R)
⇒ P = k(Q+R)
Also,Q α x ⇒ Q =k1x
and, R α 1/x ⇒ R = k2/x
P = kk1x + kk2/x
= p1x + p2/x (where p1 and p2 are constants)
⇒ 4p1 + p2/4 = 12
⇒ 16p1 + p2 = 48 …(1)
and, 8p1 + p2/8 = 18
⇒ 64p1 + p2 = 144 …(2)
Solving (1) and (2),
we get∶ p1 = 2 and, p2 = 16
∴ A = 2x + 16/x
When, x = 16, A = 32 + 1 = 33
Hence, option (d).
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