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# Given Four Quantities A, B, C and D Are in Proportion. Show that (A - C)B^2 : (B - D)Cd = (A^2 - B^2 - Ab) : (C^2 - D^2 - Cd) - ICSE Class 10 - Mathematics

#### Question

Given four quantities a, b, c and d are in proportion. Show that (a - c)b^2 : (b - d)cd = (a^2 - b^2 - ab) : (c^2 - d^2 - cd)

#### Solution

Let a/b = c/d = k

=> a = bk and c = dk

L.H.S = ((a - c)b^2)/((b -d)cd)

= ((bk - dk)b^2)/((b - d)d^2k)

= b^2/d^2

R.H.S = (a^2 - b^2 - ab)/(c^2 - d^2 - cd)

= (b^2k^2 - b^2 - bkb)/(d^2k^2 - d^2 -  dkd)

= (b^2(k^2 - 1 - k))/(d^2(k^2 - 1 - k))

= b^2/d^2

=> L.H.S = R.H.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: 13

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Solution Given Four Quantities A, B, C and D Are in Proportion. Show that (A - C)B^2 : (B - D)Cd = (A^2 - B^2 - Ab) : (C^2 - D^2 - Cd) Concept: Proportions.
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