Componendo and Dividendo

Q.

If (3x + 5y)/(3x – 5y) = 7/3, find x:y.

1. 23:6

2. 25:6

3. 19:7

4. 6:25

Q.

If $\frac{5a+2b}{5a-2b}=\frac{5}{3}$, then a : b =

1. $\frac{8}{3}$

2. $\frac{8}{5}$

3. $\frac{5}{8}$

4. $\frac{3}{8}$

Q.

Given that a:b::c:d, then which of the following follows Componendo and Dividendo property?

1. $d(a-b)=b(c-d)$

2. $(a-b):b=(c-d):d$

3. $\frac{a-b}{a+b}=\frac{c-d}{c+d}$

4. Both a and b

Q.

$\frac{8a+2b}{8a-2b}=\frac{7}{1}$, then b : a =

1. 3 : 1

2. 4 : 9

3. 25 : 1

4. 9 : 18

Q.

If $x=\frac{4\sqrt{6}}{\sqrt{2}+\sqrt{3}}$. Find the value of $\frac{x+2\sqrt{2}}{x-2\sqrt{2}}+\frac{x+2\sqrt{3}}{x-2\sqrt{3}}$, using the properties of proportion.

1. 1

2. 0

3. 3

4. 2

Q.

If $\frac{x}{1}=\frac{\sqrt{a+3b}+\sqrt{a-3b}}{\sqrt{a+3b}-\sqrt{a-3b}}$ then, which one of the following statements is true?

1. $3b{x}^2+9b-2ax=0$

2. $3b{x}^2+3b-2ax=0$

3. $3b{x}^2+3b-6ax=0$

4. $5b{x}^2+3b-2ax=0$

Q.

If a: b = 5 : 3, find : $\frac{5a-3b}{5a+3b}$

Q.

If $\frac{a-2b-3c+4d}{a+2b-3c-4d}$ = $\frac{a-2b+3c-4d}{a+2b+3c+4d}$

Show that : 2ad = 3ab.

Q.

If $x=\frac{\sqrt{a+3b+\sqrt{a-3b}}}{\sqrt{a+3b}-\sqrt{a-3b}}$, prove that : $3b{x}^2-2ax+3b=0$

Q.

If $\frac{5x+6y}{5u+6y}=\frac{5x-6y}{5u-6y};$

then prove that x : y = u : v.