DIVIDING A QUANTITY IN A GIVEN RATIO

Example 1 :

Divide $280 in the ratio 3 : 5.

Solution :

Divide $280 in the ratio 3 : 5.

3 : 5 means the first quantity is 3 parts and the second quantity in 5 parts.

Total number of parts : 

= 3 + 5

= 8

8 parts = $280

1 part = 280/8 = $35

3 parts = 3 x 35 = $105

5 parts = 5 x 35 = $175

So, we can divide $280 as $105 and $175 in the ratio 3:5.

Example 2 :

The ratio of the number of boys to the number of girls in a school of 720 students is 3 : 5. Find the number of boys and number girls in the school.

Solution :

The ratio of the number of boys to the number of girls in a school of 720 students is 3 : 5.

Number of students in the school = 720.

Ratio of boys to girls = 3 : 5.

Number of boys = 3 parts.

Number of girls = 5 parts

Total number of parts :

= 3 + 5

= 8

8 parts = 720

1 part = 720/8 = 90

Number of boys in the school = 3 x 90 = 270.

Number of girls in the school = 5 x 90 = 450.

Example 3 :

The length and width of a rectangle are in the ratio 4 : 7. If the width is 77 cm, find the length.

Solution :

Width of the rectangle = 77 cm.

The ratio of length to breadth is 4 : 7.

Length = 4 parts.

Width = 7 parts.

7 parts = 77 cm

1 part = 77/7 = 11 cm

length = 4 parts

4 parts = 4 x 11 cm = 44 cm

Length of the rectangle = 44 cm.

Example 4 :

In a village of 1,21,000 people, the ratio of men to women is 6 : 5. Find the number of men and women.

Solution :

Number of people in the village = 1,21,000.

Ratio of men to women = 6 : 5.

Number of men = 6 parts.

Number of women = 5 parts

Total number of parts :

= 6 + 5

= 11

11 parts = 1,21,000

1 part = 121000/11 = 11000

Number of men in the village = 6 x 11,000 = 66,000.

Number of women in the village = 5 x 11,000 = 55,000.

Example 5 :

Divide 5 kg 500 gm in the ratio 5 : 6.

Solution :

Given quantity = 5 kg 500 gm.

First we have to convert the given measurement as one unit.

1 kg = 1000 gm

5 kg = 5 x 1000 = 5000 gm

5 kg 500 gm = 5000 + 500 = 5500 gm

Given ratio = 5 : 6.

Total number of parts = 5 + 6 = 11.

11 parts = 5500

1 part = 5500/11 = 500

Quantity of 1st part = 5 x 500 = 2500 grams.

Quantity of 2nd part = 6 x 500 = 3000 grams.

So, 2 kg 500 gm and 3 kg are the two parts.

Example 6 :

Divide 2 m 25 cm in the ratio 5 : 4.

Solution :

Given quantity = 2 m 25 cm.

First we have to convert the given measurement as one unit.

1 m = 100 cm

2 m = 2 x 100 = 200 cm

2 m 25 cm = 200 + 25 = 225 cm

Given ratio = 5 : 4.

Total number of parts = 5 + 4 = 9.

9 parts = 225

1 part = 225/9 = 25

Quantity of 1st part = 5 x 25 = 125 cm.

Quantity of 2nd part = 4 x 25 = 100 cm.

Example 7 :

Divide 5 hours in the ratio 1 : 5.

Solution :

Given quantity = 5 hours.

1 hour = 60 minutes

5 hours = 5 x 60 = 300 minutes

Given ratio = 1 : 5.

Total number of parts :

= 1 + 5

= 6

6 parts = 300

1 part = 300/6 = 50

Quantity of 1st part = 1 x 50 = 50 minutes.

Quantity of 2nd part = 5 x 50 = 250 minutes.

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