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If R2 = Pq , Show that P : Q is the Duplicate Ratio of (P+R) : ( Q+R) - ICSE Class 10 - Mathematics

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Question

If r2 = pq , show that p : q is the duplicate ratio of (p+r) : ( q+r) 

Solution

`"p"/"q" = ("p + q")^2/("q + r")^2`

`=> "p"/"q" = ("p"^2 + "r"^2 + 2"pr")/("q"^2 + "r"^2 + 2"qr")`

`=> "p"/"q" = ("p"^2 + "pq" + 2"pr")/("q"^2 + "pq" + 2"qr")`

⇒ pq2 +p2q+ 2pqr -p2q+pq2 + 2pqr 

Since LHS = RHS, therefore p:q 1s the duplicate ratio of  (p + r) :  (q + r) .  

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APPEARS IN

 Frank Solution for Frank Class 10 Mathematics Part 2 (2016 to Current)
Chapter 9: Ratio and Proportion
Exercise 9.1 | Q: 23

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Solution If R2 = Pq , Show that P : Q is the Duplicate Ratio of (P+R) : ( Q+R) Concept: Ratios.
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