# DIVIDING A QUANTITY IN A GIVEN RATIO

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

So, we can divide \$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 77 cm, find the length.

Solution :

The ratio of length to breadth is 4 : 7.

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

So, 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. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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