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# If M: N is the Duplicate Ratio of M + X: N + X; Show that X2 = Mn. - Mathematics

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#### Question

If m: n is the duplicate ratio of m + x: n + x; show that x2 = mn.

#### Solution

m/n = (m + x)^2/(n + x)^2

m/n = (m^2 + x^2 + 2mx)/(n^2 + x^2 + 2nx)

mn^2 + mx^2 + 2mnx = m^2n + nx^2 + 2mnx

x^2(m - n) = mn(m - n)

x^2 (m - n) = mn(m - n)

x^2 = mn

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#### APPEARS IN

Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Exercise 7(A) | Q: 27 | Page no. 88
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If M: N is the Duplicate Ratio of M + X: N + X; Show that X2 = Mn. Concept: Ratios.
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