M L Aggarwal Solutions for Chapter: Quadratic Equations, Exercise 8: Chapter Test

A girl is twice as old as her sister. Four years hence, the product of their ages (in years) will be $160$. Find their present ages.

The length of the hypotenuse of a right-angled triangle exceeds the length of one side by $2 \mathrm{cm}$ and exceeds twice the length of the other side by $1 \mathrm{cm}$. Find the length of each side. Also find the area of the triangle.

The distance between Mumbai and Pune is $192 \mathrm{km}$. Travelling by Deccan Queen, it takes $48$ minutes less than another train. Calculate the speed of Deccan Queen if the speeds of the two trains differ by $20 \raisebox{1ex}{$\mathrm{km}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{h}$}\right.$.

A person on tour has $₹4200$ for his expenses. If he extends his tour for $3$ days, he has to cut down his daily expenses by $₹70$. Find the original duration of the tour.

By increasing the list price of a book by $₹10$, a person can buy $10$ books less for $₹1200$. Find the original list price of the book.

A trader bought a number of articles for $₹900$, five were damaged and he sold each of the rest at $₹2$ more than what he paid for it, thus getting a profit of $₹80$ on the whole transaction. Find the number of articles he bought.

Sum of the areas of the two squares is $468 {\mathrm{cm}}^2$. If the difference of their perimeters is $24 \mathrm{cm}$, find the sides of two squares.

Two taps running together can fill a tank in $3\frac{1}{13}$ hours. If one tap takes $3$ hours more than the other to fill the tank, find the time in which each tap would fill the tank.