Monica Capoor Solutions for Exercise 7: Exercise 9.3

The ages of Asha and Sushma are in the ratio of 7:2. Eight years hence, the ratio of their ages will be 5:2. Find their present ages.

$[$HINT: Let Asha's and Sushma's present ages be 7x years and 2x years. 

Then $\frac{7x+8}{2x+8}=\frac{5}{2}$. Cross multiply to solve the equation.$]$

The numerator of a fraction is $2$ less than its denominator. If $1$ is added to both its numerator and denominator, it becomes $\frac{2}{3}$. Find the fraction.

Two supplementary angles differ by $18°$. Find the measure of each angle.

Two equal sides of a triangle are $\left(x+6\right) \mathrm{cm}$ and $\left(5x-2\right) \mathrm{cm}$. If the third side is $\left(7x-4\right) \mathrm{cm}$, find $x$. Then find the perimeter of the triangle.

The angles of a triangle are $4x°, \left(2x+30\right)°$ and $\left(5x-15\right)°$. Find the angles and then show that the triangle is an equilateral triangle.

A man sold an article for$₹ 432$ and gained $8\%$ on it. Find the cost price of the article.

A man is engaged as a typist for $30$ days on the condition that he receives $₹ 175$ for each day he works and has to pay $₹ 50$ for each day he remains absent. If he receives $₹ 4125$ in all, for how many days does he remain absent?

Mrs Arora left one-fourth of her property for her son, two-thirds for her daughter and the remainder for her niece. If her niece's share is $₹ 7,00,000$, what was the worth of her total property ?

$[$HINT: Let the worth of her property be $₹ x$. Then $\left(1-\frac{1}{4}-\frac{2}{3}\right)x=700000$ $]$