R K Bansal Solutions for Exercise 1: EXERCISE

The speed of a boat in still water is $15 \mathrm{km}/\mathrm{hr}$. It can go $30 \mathrm{km}$upstream and return downstream to the original point in $4$ hours $30$ minutes. Find the speed of the stream.

Mr. Mehra sends his servant to the market to buy oranges worth $₹15$. The servant having eaten three oranges on the way, Mr. Mehra pays $25$ paise per orange more than the market price. Taking $\mathrm{x}$ to be the number of oranges which Mr. Mehra receives, form a quadratic equation in $\mathrm{x}$. Hence, find the value of $\mathrm{x}$.

$₹250$ is divided equally among a certain number of children. If there were $25$ children more, each would have received $50$ paise less. Find the number of children.

An employer finds that if he increases the weekly wages of each worker by $₹5$ and employs five workers less, he increases his weekly wage bill from $₹3,150$ to $₹3,250$. Taking the original weekly wage of each worker as $₹ \mathrm{x}$; obtain an equation in x and then solve it to find the weekly wages of each worker.

A trader bought a number of articles for $₹ 1,200$. Ten were damaged and he sold each of the remaining articles at $₹ 2$ more than what he paid for it, thus getting a profit of $₹ 60$ on the whole transaction?

Taking the number of articles he bought as $\mathrm{x}$, form an equation in $\mathrm{x}$ and solve it.

The total cost price of a certain number of identical articles is$₹ 4,800$. By selling the articles at $₹ 100$each, a profit equal to the cost price of $15$ articles is made. Find the number of articles bought.

The distance by road between two towns$\mathrm{A}$ and$\mathrm{B}$ is $216 \mathrm{km}$, and by rail it is $208 \mathrm{km}$. A car travels at a speed of$x \mathrm{km}/\mathrm{hr}$ and the train travels at a speed which is $16 \mathrm{km}/\mathrm{hr}$ faster than the car. Calculate the time taken by the car to reach town $\mathrm{B}$ from $\mathrm{A}$, in terms of $x$.

The distance by road between two towns $\mathrm{A}$ and $\mathrm{B}$ is $216 \mathrm{km},$ and by rail it is $208 \mathrm{km}.$ $\mathrm{A}$ car travels at a speed of $\mathrm{x} \mathrm{km}/\mathrm{hr}$ and the train travels at a speed which is $16 \mathrm{km}/\mathrm{hr}$ faster than the car. If the train takes $2$ hours less than the car to reach town $\mathrm{B}$. Hence, find the speed of the train.