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.

Problem 6 :

The ratio of boys to girls is 3 to 2. If there are 12 boys, how many girls are there?

Solution :

Ratio between boys to girls = 3 : 2

Number of boys = 3x and number of girls = 2x

3x = 12 (Given)

x = 12/3

x = 4

Number of girls = 2(4) ==> 8

Problem 7 :

It takes one Super Giant Pizza to feed 3 people. If you invite 36 people, how many pizzas will you need?

Solution :

1 pizza will be served for 3 people.

3x = 36

x = 36/3

x = 12

Number of pizzas to be ordered = 12 pizzas

Problem 8 :

At a recent party, it cost $9.50 for refreshments for 10 guests. At this rate, how much would it cost to have refreshments for 80 guests?

Solution :

Cost spent for 10 guests = $9.50

Cost spent for 80 guests = 9.50 x 8

= $76

Amount spent for 80 guests is $76.

Problem 9 :

A car can travel 240 km in 15 litres of petrol. How much distance will it travel in 25 litres of petrol?

Solution :

15 liters of petrol will cover the distance 240 km

Let x be the distance covered using 25 liters of petrol.

15 : 240 = 25 : x

15x = 25(240)

x = 25(240) / 15

x = 400

So, the required distance covered is 400 km.

Problem 10 :

The yield of wheat from 8 hectares of land is 360 quintals. Find the number of hectares of land required for a yield of 540 quintals?

Solution :

8 hectares of land will yield 360 quintals

Let x be the land required in hectares.

8 : 360 = x : 540

8/360 = x/540

8(540) = 360x

x = 8(540)/360

x = 8(1.5)

x = 12

So, the required quantity of land is 12 hectares.

Problem 11 :

The earth rotates 360^o about its axis in about 24 hours. By how much degree will it rotate in 2 hours?

Solution :

Ratio between angle measure to number of hours.

360 : 24

Let x be the required degree in 2 hours.

360 : 24 = x : 2

360/24 = x/2

360(2) = 24x

x = 720/24

x = 30

So, the required degree in 2 hours is 30^o