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# If P + R = Mq and 1/Q + 1/S = M/R Then Prove that P : Q = R : S - Mathematics

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#### Question

If p + r = mq and 1/q + 1/s = m/r then prove that p : q = r : s

#### Solution

1/q + 1/s = m/r

(s + q)/(qs) = m/r

(s + q)/s = (mq)/r

(s + q)/s = (p + r)/r     (∵ p + r = mq)

1 + q/s = p/r + 1

q/s = p/r

p/q = r/s

Hence proved

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