SOVLING WORD PROBLEMS ON RATIO

Problem 1 :

The ratio of boys and girls in the school is 7 : 9, when 22 new boys are joined in this school then the ratio becomes 9 : 10. How many girls in this school?

Solution :

The ratio = 7x : 9x

Number of boys are joined in this school = 22

The ratio = 9 : 10

 7x + 22/9x = 9/10

By using cross multiplication. We get

70x + 220 = 81x

By combining like terms

220 = 81x – 70x

220 = 11x

220/11 = x

20 = x

Number of girls = 9x

= 9(20)

= 180

So,180 girls in this school.

Problem 2 :

If two numbers are in the ratio 11 : 13 and their difference is 8, find the numbers.

Solution :

Let the numbers be 11x and 13x

Difference between the numbers = 8

3x – 11x = 8

2x = 8

x = 4

Value of 11x = 11(4) = 44

Value of 13x = 13(4) = 52

So, the numbers are 44, 52.

Problem 3 :

The length and breadth of the rectangle are in the ratio 9 : 7. Find the perimeter of the rectangles if its breadth is 378 cm.

Solution :

Length of the rectangle = 9x and breadth of the rectangle 7x.

Given, breadth of the rectangle = 378 cm

7x = 378

x = 378/7

x = 54 cm

Length of the rectangle = 9x = 9(54)= 486 cm

Perimeter of the rectangle = 2(l + b)

= 2(486 + 378)

= 2 × 864

= 1728

So, the perimeter of the rectangle is1728 cm.

Problem 4 :

Find the measures of the angles of a triangle if the ratio of their measures is 4 : 12 : 29.

Solution :

Let x be the measures of the angles of a triangle.

The ratio of their measures = 4 : 12 : 29.

x = 4

4x = 4 × 4 = 16

12x = 12 × 4 = 48

29x = 29 × 4 = 116

So, the measures of the angles of a triangle is 16, 48, 116.

Problem 5 :

The perimeter of a square is 26 cm while the area of another square is 121 cm². Find the ratio of their lengths.

Solution :

Given, the perimeter of a square = 26 cm

Area of a square = 121 cm²

Perimeter of a square = 4 x side

26 = 4 x side

26/4 = side

s = 6.5 cm

Area of a square = side x side

121 = side²

√121= side¹

side¹ = 11

So, the ratio of their lengths is 6.5, 11.