R. D. Sharma Solutions for Chapter: Quadratic Equations, Exercise 2: EXERCISE 4.2

The product of two consecutive positive integers is $306.$ Form the quadratic equation to find the integers, if $x$ denotes the smaller integer.

John and Jivanti together have $45$ marbles. Both of them lost $5$ marbles each, and the product of the number of marbles they now have is $128 .$ Form the quadratic equation to find how many marbles they had to start with, if John had $x$ marbles.

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be $55$ minus the number of toys produced in a day. On a particular day, the total cost of production was $₹750$. If $x$ denotes the number of toys produced that day, form the quadratic equation fo find $x.$

(Note: The word article is replaced by toys)

The height of a right triangle is $7\mathrm{cm}$ less than its base. If the hypotenuse is $13 \mathrm{cm},$ form the quadratic equation to find the base of the triangle.

An express train takes $1$ $\mathrm{hour}$ less than a passenger train to travel $132 \mathrm{km}$ between Mysore and Bangalore. If the average speed of the express train is $11\mathrm{km}/\mathrm{hr}$ more than that of the passenger train, from the quadratic equation to find the average speed of express train.

A train travels $360 \mathrm{km}$ at a uniform speed. If the speed had been $5 \mathrm{km}/\mathrm{hr}$ more, it would have taken $1$ hour less for the same journey. Form the quadratic equation to find the speed of the train.