NCERT Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 1: Exercise

The population of a village is $7500$. $42\%$ of the population are females and the rest males. The total number of literate persons in the village is $2370$ while there are $90$ more male illiterates compared to female illiterates. What is the percentage of literate males out of the total number of males in the village?

Complete the following.

The break-even point for a new flavour ice cream is the number of units sold at which the total cost price of the ice cream is the same as the total selling price. The parlour launches another new flavour whose fixed cost is Rs$10000,$ variable cost is Rs $40$ and the selling price of each unit Rs $60.$

Find the number of units at the break-even point of the other new flavour. Show your work. 

Answer the question based on the given information.

The total cost of snowden ice cream parlour is divided into fixed cost $\left(x\right)$ and variable cost $\left(y\right).$ Fixed cost is the cost that the ice cream parlour has to incur even at zero level of production and variable cost is the cost that will be directly proportional to each unit of ice cream sold.

The parlour launched a new flavour of ice cream and wanted to find the fixed and variable cost associated with it. They found that their total cost for that flavour was Rs $27500$ after selling $150$ units and Rs $32500$ after selling $250$ units.

Find the variable cost per unit incurred by the ice cream parlour for the new flavour. Show your work.

Match the graphical representation in column $\mathrm{I}$ with their corresponding criteria in column $\mathrm{II}$ and consequences in column $\mathrm{III}.$

​​​​​​​

(Note: Match the alphabets $A), B), C)$ in column $\mathrm{I}$ with the corresponding numbers $1)$, $2)$,$3)$ in column $\mathrm{II}$ and $\mathrm{i})$, $\mathrm{ii}),\mathrm{iii})$ in column $\mathrm{iii})$ respectively.

Two linear equations in variables $x$ and $y$ are given below.

$a_{1}x+b_{1}y+c=0$

$a_{2}x+b_{2}y+c=0$

Which of the following pieces of information is independently sufficient to determine if a solution exists or not for this pair of linear equations?

I. $\frac{a_1}{b_1}=\frac{a_2}{b_2}=1$ II. $\frac{a_1}{a_2}=\frac{b_1}{b_2}$ III. $\frac{a_1}{a_2}=\frac{a_1}{b_1}\ne 1$ IV. $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$

Harsh correctly solved a pair of linear equations in two variables and found their only point of intersection as $\left(3, -2\right)$. One of the lines was $x-y=5$. Which of the following could have been the other line?

I: $3x-3y=15$

II: $2x-3y=12$

III: $2x-3y=14$

A small tank can be filled by two pipes $P$ and $Q$ individually in $60$minutes and $80$minutes respectively. If both the pipes are opened simultaneously, after how much time should pipe $P$ be closed so that the unfilled part of the tank is filled in $16$minutes by pipe $Q$?