Question

if (3a + 4b ) : (3a - 4b) = (3c +8d) : (3c - 8d) then which of the following is true a. ad = bc b. 2ad = bc c. 2ab = cd d. ab= cd​

Answer 1

GIVEN :–

$\\ \implies \bf (3a + 4b ) : (3a - 4b) = (3c +8d) : (3c - 8d)$

TO FIND :–

• Simplified form = ?

SOLUTION :–

$\\ \implies \bf (3a + 4b ) : (3a - 4b) = (3c +8d) : (3c - 8d)$

$\\ \implies \bf \dfrac{3a + 4b}{3a - 4b} = \dfrac{3c +8d}{3c - 8d}$

• C & D Rule –

$\\ \implies \bf \dfrac{(3a + 4b)+ (3a - 4b)}{(3a + 4b) - (3a - 4b)} = \dfrac{(3c +8d) +(3c - 8d)}{(3c +8d) - (3c - 8d)}$

$\\ \implies \bf \dfrac{3a + 4b+3a - 4b}{3a + 4b -3a + 4b} = \dfrac{3c +8d +3c - 8d}{3c +8d-3c + 8d}$

$\\ \implies \bf \dfrac{3a+3a}{ 4b + 4b} = \dfrac{3c+3c }{8d+8d}$

$\\ \implies \bf \dfrac{6a}{8b} = \dfrac{6c}{16d}$

$\\ \implies \bf \dfrac{a}{8b} = \dfrac{c}{16d}$

$\\ \implies \bf 16ad = 8bc$

$\\ \implies \bf 2ad = bc$

• Hence , Option (b) is correct.

$\\\rule{220}{2}$

✯ C & D Rule :–

→ If $\bf\dfrac{a}{b} = \dfrac{c}{d}$ then we should write this as $\bf\dfrac{a+b}{a-b} = \dfrac{c+d}{c-d}$.