Monica Capoor Solutions for Chapter: Linear Equations in One Variable, Exercise 4: EXERCISE

The numerator of a rational number is $3$ less than the denominator. If the numerator and denominator are increased by $2$, the new fraction becomes $\frac{6}{7}$. Find the original number.

In a bus $\left(2x+5\right)$ passengers bought $50$ paise tickets and $\left(3x-2\right)$ bought $75$ paise tickets. If the bus was $48$ seater and was just full, find the number of passengers for each category.

Mrs Bhavnani received a certain amount of money as bonus from her employer. She gave one-third of this money and additional sum of $₹3000$ to her son. She also gave half of the money received and additional sum of $₹10000$ to her daughter. If the son gets half as much as the daughter, find the money Mrs Bhavnani received as bonus.

The ages of Tanay and Vihaan are in ratio of $8:7$. Six years later, their ages will be in ratio $10:9$. Find their ages.

Five years ago, Amit was three times as old as Armaan. Ten years later Amit would be twice as old as Armaan. How old are they now?

A boy covers a distance of $20 \mathrm{km}$ in $2\frac{1}{2} \mathrm{hours}$, partly on foot at the rate of $5 \mathrm{km}/\mathrm{hr}$, partly on bicycle at the rate of $10 \mathrm{km}/\mathrm{hour}$. If the distance covered on foot is $k \mathrm{km}$, then find $k$.

The distance between two stations $\mathrm{A}$ and $\mathrm{B}$ is $540 \mathrm{km}$. Two trains start simultaneously from these stations on parallel tracks to cross each other. The speed of one of them is greater than the other by $5 \mathrm{km}/\mathrm{h}$. If the distance between these two trains after $3 \mathrm{hours}$ of their start is $165 \mathrm{km}$, find the speed of each train.

A boat travels $30 \mathrm{km}$ upstream in the same amount of time it takes to travel $60 \mathrm{km}$ downstream in the same river. If the speed of the river is $4 \mathrm{km}/\mathrm{h}$, the speed of the boat in still water is $k \mathrm{km}/\mathrm{h}$. Find $k$.