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## Answers

a : b = c : d

Let a/b = c/d = k ( a constant )

Now ,

LHS = xa + yb ÷ xc + yd

= b( xa/b + y ) ÷ d( xc/d + y )

= b(xk + y) ÷ d(xk + y)

= b/d = RHS

Given ,

a:b = c:d

a/b = c/d

ad = bc ------(1)

( 6a + 7b ) ( 3c - 4d )=( 6c + 7d ) ( 3a - 4b )

18ac - 24 ad + 21bc - 28bd = 18ac - 24bc + 21ad - 28bd

(- 24ad) + 21bc = (- 24bc) + 21ad

(- 24bc) + 21bc = (- 24bc) + 21bc { from (1) }

(- 3bc) = (- 3bc)

Hence proved