Maharashtra Board Solutions for Chapter: Linear Equations in Two Variables, Exercise 2: Practice set

The denominator of a fraction is $1$ less than twice its numerator. If $1$ is added to numerator and denominator respectively, the ratio of numerator to denominator is $3:5$. Find the fraction.

The total number of lions and peacocks in a certain zoo is $50$. The total number of their legs is $140$. Find the number of peacocks in the zoo.

Sanjay gets fixed monthly income. Every year there is a certain increment in his salary. After $4$ years, his monthly salary was $₹4500$ and after $10$ years his monthly salary became $₹5400$. Find his original salary and yearly increment.

The price of $3$ chairs and $2$ tables is $₹4500$ and the price of $5$ chairs and $3$ tables is $₹7000$. The price of $2$ chairs and $2$ tables is $₹k$. Find the value of $k$.

The sum of the digits in a two-digits number is $9$. The number obtained by interchanging the digits exceeds the original number by $27$. Find the two-digit number.

In $△ABC$, the measure of $\angle A$ is equal to the sum of the measures of $\angle B$ and $\angle C$. Also the ratio of measures of $\angle B$ and $\angle C$ is $4:5$. Find the measures of angles of the triangle.

Divide a rope of length $560 \mathrm{cm}$ into $2$ parts such that twice the length of the smaller part is equal to $\frac{1}{3}$ of the larger part. If the length of the larger part is $k \mathrm{cm}$, the find the value of $k$.

In a competitive examination, there were $60$ questions. The correct answer would carry $2$ marks, and for incorrect answer, $1$ mark would be subtracted. Yashwant had attempted all the questions and he got total $90$ marks. How many questions did he got wrong?