Maharashtra Board Solutions for Chapter: Ratio and Proportion, Exercise 6: Problem set

If $\frac{\mathrm{a}}{\mathrm{b}}=\frac{2}{3}$ then find the value of the following expression. Write your answer in fraction form.

$\frac{4\mathrm{a}+3\mathrm{b}}{3\mathrm{b}}$

If $\frac{\mathrm{a}}{\mathrm{b}}=\frac{2}{3}$ then find the values of the following expression.

$\frac{5{\mathrm{a}}^2+2{\mathrm{b}}^2}{5{\mathrm{a}}^2-2{\mathrm{b}}^2}$

If $\frac{\mathrm{a}}{\mathrm{b}}=\frac{2}{3}$ then find the value of the following expression.

$\frac{{\mathrm{a}}^3+{\mathrm{b}}^3}{{\mathrm{b}}^3}$

If $\frac{\mathrm{a}}{\mathrm{b}}=\frac{2}{3}$ then find the value of the following expression.

$\frac{7\mathrm{b}-4\mathrm{a}}{7\mathrm{b}+4\mathrm{a}}$

If a, b, c, d are in proportion, then prove that,

$\sqrt{\frac{a^2+5c^2}{b^2+5d^2}}=\frac{a}{b}$

If a, b, c, d are in proportion, then prove that

$\frac{a^2+ab+b^2}{a^2-ab+b^2}=\frac{c^2+cd+d^2}{c^2-cd+d^2}$

If a, b, c are in continued proportion, then prove that

$\frac{b}{b+c}=\frac{a-b}{a-c}$

Solve:

$\frac{12x^2+18x+42}{18x^2+12x+58}=\frac{2x+3}{3x+2}$