Embibe Experts Solutions for Chapter: Linear Equations in Two Variables, Exercise 1: Exercise

Age of a person $P$ is $2$ times the age of the sibling, $Q$ at present. Which of the following graphs gives the relationship of their future ages?

A stone was thrown vertically with an upward velocity $30 \mathrm{m}/\mathrm{s}$. The stone's velocity was reducing at a constant rate then stopped momentarily at the end of $3 \mathrm{seconds}$. While falling back, the velocity of the stone was increasing and became $30 \mathrm{m}/\mathrm{s}$ again, just before it hit the ground at the end of$6 \mathrm{seconds}$ .  A stopwatch was used to record the time of travel from the start till the end when the stone touched the ground. 

What were the points of time at which the velocity of the stone was $15 \mathrm{m}/\mathrm{s}$?

Below is a minimal data points between time spent for practice and performance of students in a grade. A linear regression analysis was done to find the correlation between the two variables and based on the best fit, the equation $2x-3y+7=0$ was synthesised. 

What are data points that fit exactly in the equation?

Below is the graph showing the relationship between income of a person and the income tax the person has to pay to the government. The graph has three segments of straight lines. The equations of the lines operates only within the respective intervals $A \mathrm{to} B, B \mathrm{to} C$ and beyond $C$.

Person $P$ is earning $₹ 14 \mathrm{lakhs}$ per annum and person $Q$ is earning $₹ 9 \mathrm{lakhs}$ per annum. How much more tax does person $P$ pay than person $Q$?

A retailer seeks exchange notes for $₹20,000$ in either $₹20$ or $₹50$ denominations or a mix of both, from a service provider. The service provider deducts $1\%$ of the exchange amount as the fee. What is the minimum and maximum number of notes can the merchant get on this exchange? 

A farmer took a loan $₹9,00,000$ for agricultural purpose for annual interest of $6\%$. The loan is to be repaid in monthly instalments with fixed principal amount of $₹10,000$ along with interest for the outstanding principal amount.

Form an equation between two variables $x, y$ where $x$ is the number of months elapsed and $y$ is the monthly instalment. Use the equation to find the minimum number of months post which, his monthly instalment will be equal or fall below $₹12,000$.

A water tank contains $2000 \mathrm{L}$ of water. The tank is being filled $3 \mathrm{L}/\mathrm{s}$ through an incoming pipe and simultaneously water is let out at the rate of $5 \mathrm{L}/\mathrm{s}$.  Form an equation connecting the volume of water in the tank with the passage of time. Also find the time required to get the water in the tank reduced to half of its initial volume.

Two trains $100 \mathrm{km}$ apart, are approaching each other along a straight path at speed of $90 \mathrm{km}/\mathrm{h}$ and $70 \mathrm{km}/\mathrm{h}$. Form a linear equation to find the distance between the two trains and the time. Use the equation to find the distance between the trains at the end of $30 \mathrm{minutes}$, $37.5 \mathrm{minutes}$ and $1 \mathrm{hour}$.