**Dividing a quantity in a given ratio :**

To divide a quantity in the given ratio, we need to follow the steps given below.

(i) Write the given quantity

(ii) Write the ratio that we have to split.

(iii) By adding the ratio, we can find the total number of parts that we have to split.

(iv) Divide the given quantity by the total number of parts

(v) Multiply each the number in the ratio by the unit rate to get the answer.

Let us see some examples based on the above concept.

**Example 1 :**

Divide $280 in the ratio 3:5

**Solution :**

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

Hence we can split 280 as 105 and 175 in the ratio 3:5.

**Example 2 :**

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

**Solution :**

Breadth = 77 cm

The ratio of length to breadth is 4:7

Breadth = 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 3 :**

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

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 4 :**

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

Hence 2 kg 500 gm and 3 kg are the two parts.

**Example 5 :**

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 6 :**

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

After having gone through the stuff given above, we hope that the students would have understood "Dividing a quantity in a given ratio".

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