ratio and proportion (Question:144597.0)

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NEERAJA P M

· started a discussion

· 1 Months ago

ratio and proportion (Question:144597.0)

There is an error in answer.

Question:

If p, q and r are in continued proportion, then find the value of \(\cfrac{1+\left ( \cfrac {p}{q} \right )^2}{\left (1+ \cfrac {r}{p} \right )^2}+\cfrac{1+\left ( \cfrac {q}{r} \right )^2}{\left (1+ \cfrac {p}{r} \right )^2}\)

Options:

A) 2

B) 1

C) 3

D) 4

Solution:

Ans (b) q² = pr (given)

Given expression

= \(\cfrac{(p^2+q^2)}{(p+r)^2}+\cfrac{(r^2+q^2)}{(r+p)^2}\) = \(\cfrac{(p^2+2q^2+r^2)}{(p+r)^2}\)

= (p²+2.pr+r²)/(p+r)² = (p+r)²/(p+r)² = 1

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