If $a : b : : c : d$ , show that $(2 a + 3 b) : (2 c + 3 d) : : (2 a - 3 b) : (2 c - 3 d)$ .

Open in App

Solution

Proof of the given relation:
If $\frac{a}{b} = \frac{c}{d}$ , then the property of componendo and dividendo implies that $\frac{a + b}{a - b} = \frac{c + d}{c - d}$ .
Given proportional is equivalent to $\frac{a}{b} = \frac{c}{d}$ .
$\Rightarrow \frac{2 a}{3 b} = \frac{2 c}{3 d} (M u l t i p l y i n g b o t h s i d e s b y \frac{2}{3}) \Rightarrow \frac{2 a + 3 b}{2 a - 3 b} = \frac{2 c + 3 d}{2 c - 3 d} (b y c o m p o n e n d o a n d d i v i d e n d o) \Rightarrow \frac{2 a + 3 b}{2 c + 3 d} = \frac{2 a - 3 b}{2 c - 3 d} (b y c r o s s m u l t i p l y i n g) \Rightarrow (2 a + 3 b) : (2 c + 3 d) : : (2 a - 3 b) : (2 c - 3 d)$
Hence proved.

Suggest Corrections

Similar questions

Please Use the Components of Proportion like Componendo and dividends etc

If (a+3b+2c+6d)(a-3b-2c+6d)=(a+3b-2c-6d)(a-3b-2c+2c-6d)

Prove that a:b::c:d

1176 = 2^{a} \times 3^{b} \times 7^{c}

2 a - [3 b - {a - (2 c - 3 b) + 4 c - 3 (a - b - 2 c)}]

Join BYJU'S Learning Program