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If P + R = Mq and `1/Q + 1/S = M/R` Then Prove that P : Q = R : S - ICSE Class 10 - 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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APPEARS IN

 Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Ex.7B | Q: 17

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