**Solving Word Problems with Cross Multiplication Method :**

In this section, we will learn, how to solve word problems using cross multiplication method.

**Example 1 :**

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the car travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other ,they meet in 1 hour. What are the speeds of the two cars?

**Solution :**

Let “x km/hr” be the speed of 1st car

Let “y km/hr” be the speed of the 2nd car

Time = Distance/Speed

Speed of both cars while they are traveling in the same direction = (x – y)

Speed of both cars while they are traveling in the opposite direction = (x + y)

5 = 100/(x -y)

x – y = 100/5

x - y = 20

x - y - 20 = 0 ---(1)

1 = 100/(x + y)

x + y = 100

x + y - 100 = 0------(2)

x/(100 + 20) = y/(-20 + 100) = 1/(1 + 1)

x/120 = y/80 = 1/2

x/120 = 1/2 y/80 = 1/2

x = 120/2 y = 80/2

x = 60 y = 40

So, the speed of first car = 60 km/hr

Speed of second car = 40 km/hr

**Example 2 :**

The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

**Solution :**

Area of any rectangle = Length x breadth

Let “x” be the length of rectangle

Let “y” be the breadth of rectangle

(x – 5) (y + 3) = xy – 9

x y + 3x - 5y – 15 = xy – 9

xy – xy + 3x – 5y – 15 + 9 = 0

3 x – 5 y – 6 = 0 -------(1)

(x + 3) (y + 2) = xy + 67

xy + 2x + 3y + 6 – xy – 67 = 0

2x + 3 y – 61 = 0 -------(2)

x/(305+18) = y/(-12 + 183) = 1/(9 + 10)

x/323 = y/171 = 1/19

x/323 = 1/19 y/171 = 1/19

x = 323/19 y = 171/19

x = 17 y = 9

So, the length of rectangle = 17 units

Breadth of rectangle = 9 units

After having gone through the stuff and examples, we hope that the students would have understood, solving word problems with cross multiplication method.

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