# Linear Equations in Two Variables Practice Set 1.5 ### Hi friends, welcome on Maths Master, here you will learn how to solve word problems based on simultaneous equations.

Click here for Practice Set 1.1 Elimination Method

#### While solving word problems, converting the given information into mathematical form is an important step in this process. In the following flow-chart, the procedure for finding solutions of word problems is given.

• Read the given word problem carefully and try to understand it.
• From given information, use proper variables for given quantities
• Form the mathematical statements from above variables
• Use suitable method to solve the equations
• Find the solution
• Substituting the values of the variables in both the equations, verify your result.
• Write the answer.

Click here for Practice Set 1.2 Graphical Method

## Word Problems

Now we will see various types of word problems.
(1) Problems regarding age.
(2) Problems regarding numbers.
(3) Problems based on fractions.
(4) Problems based on money transactions.
(5) Problems based on geometrical properties
(6) Problems based on speed, distance, time.

Let’s see some examples :

Q. Sum of two numbers is 103. If greater number is divided by smaller number then the
quotient is 2 and the remainder is 19. Then find the numbers.

Solution:

Let the greater number be x and the smaller number be y.

By first condition,

x + y = 103………………………..(I)

By second condition,

dividend = divisor X quotient + remainder

x = 2 X y + 19

x – 2y = 19………………. (II)

Substituting value of y in equation x + y = 103.
x + 28 = 103
x = 103 – 28
x = 75
Given numbers are 75 and 28.

## Practice Set 1.5

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

(3) 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.

(4) 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.

(5) 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 weighes 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.

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

Click Here For Video Solution English Medium

Click Here For Video Solution Hindi Medium

## Some more Questions for Practice

1. A two digit number is 3 more than 4 times the sum of its digits. If 18 is added to this
number, the sum is equal to the number obtained by interchanging the digits. Find the
number.

2. The total cost of 8 books and 5 pens is 420 rupees and the total cost of 5 books and 8
pens is 321 rupees. Find the cost of 1 book and 2 pens.

3. The ratio of incomes of two persons is 9 : 7. The ratio of their expenses is 4 : 3. Every person saves rupees 200, find the income of each.

4. If the length of a rectangle is reduced by 5 units and its breadth is increased by 3 units, then the area of the rectangle is reduced by 8 square units. If length is reduced by 3 units and breadth is increased by 2 units, then the area of rectangle will increase by 67 square units. Then find the length and breadth of the rectangle.

5. The distance between two places A and B on road is 70 kilometers. A car starts from A and the other from B. If they travel in the same direction, they will meet after 7 hours. If they travel towards each other they will meet after 1 hour, then find their speeds.

6.The sum of a two digit number and the number obtained by interchanging its digits
is 99. Find the number.

7. Sum of two numbers is 103. If greater number is divided by smaller number then the
quotient is 2 and the remainder is 19. Then find the numbers.

8. Salil’s age is 23 years more than half of the Sangram’s age. Five years ago, the sum of
their ages was 55 years. Find their present ages.

9. A two digit number is 4 times the sum of its digits. If we interchange the digits, the
number obtained is 9 less than 4 times the original number. Then find the number.

10. The population of a certain town was 50,000. In a year, male population was increased by 5% and female population was increased by 3%. Now the population became 52020 . Then what was the number of males and females in the previous year?

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