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Theorems on Integration

If P : Q : R ...

Question

If P : Q : R = 6 : 5 : 4 and $P^{2} + Q^{2} + R^{2} = 192500$ then find $\frac{(P + Q - R)}{2}$

A

175

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B

165

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C

185

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D

200

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Solution

The correct option is A 175
$: Q : R = 6 : 5 : 4 L e t P = 6 x Q = 5 x R = 4 x P^{2} + Q^{2} {+ R}^{2} = 192500 {(6 x)}^{2} + {(5 x)}^{2} + (4 x)^{2} = 192500 77 x^{2} = 192500 x^{2} = 2500 x = 50 \frac{P + Q - R}{2} = \frac{6 x + 5 x - 4 x}{2} = \frac{7 x}{2} = \frac{7 \times 50}{2} = 175$

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