#### 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

Is there an error in this question or solution?

Solution If P + R = Mq and `1/Q + 1/S = M/R` Then Prove that P : Q = R : S Concept: Proportions.