Maharashtra Board Solutions for Chapter: Linear Equations in Two Variables, Exercise 5: Practice Set

Two numbers differ by $3$. The sum of twice the smaller number and thrice the greater number is $19 .$ Find the numbers.

Complete the following.

The sum of father's age and twice the age of his son is $70 .$ If we double the age of the father and add it to the age of his son the sum is $95 .$ Find their present ages.

The denominator of a fraction is $4$ more than twice its numerator. Denominator becomes $12$ times the numerator, if both the numerator and the denominator are reduced by $6$. Find the fraction.

Two types of boxes $A, B$ are to be placed in a truck having capacity of $10$ tons. When $150$ boxes of type $A$ and $100$ boxes of type$B$ are loaded in the truck, it weighs $10$ tons. But when $260$ boxes of type $A$ are loaded in the truck, it can still accommodate $40$ boxes of type $B$, so that it is fully loaded. Find the weight of each type of box.

Out of $1900 \mathrm{km}$, Vishal travelled some distance by bus and some by aeroplane. Bus travels with average speed $60 \mathrm{km}/\mathrm{hr}$ and the average speed of aeroplane is $700 \mathrm{km}/\mathrm{hr}$. It takes $5$ hours to complete the journey. Find the distance, Vishal travelled by bus.