We will learn how to divide a quantity in a given ratio and its application in the word problems on ratio.

**1.** John weights 65.7 kg. If he reduces his weight in the
ratio 5 : 4, find his reduced weight.

**Solution:**

Let the previous weight be 5x.

5x = 65.7

x = \(\frac{65.7}{5}\)

x = 13.14

Therefore, the reduce weight = 4 × 13.14 = 52.56 kg.

**2.** Robin leaves $ 1245500 behind. According to his wish, the
money is to be divided between his son and daughter in the ratio 3 : 2. Find
the sum received by his son.

**Solution:**

We know if a quantity x is divided in the ratio a : b then the two parts are \(\frac{ax}{a + b}\) and \(\frac{bx}{a + b}\).

Therefore, the sum received by his son = \(\frac{3}{3 + 2}\) × $ 1245500

= \(\frac{3}{5}\) × $ 1245500

= 3 × $ 249100

= $ 747300

**3.** Two numbers are in the ratio 3 : 2. If 2 is added to the
first and 6 is added to the second number, they are in the ratio 4 : 5. Find
the numbers.

**Solution:**

Let the numbers be 3x and 2x.

According to the problem,

\(\frac{3x + 2}{2x + 6}\) = \(\frac{4}{5}\)

⟹ 5(3x + 2) = 4

⟹ 15x + 10 = 8x + 24

⟹ 15x – 8x = 24 - 10

⟹ 7x = 14

⟹ x = \(\frac{14}{7}\)

⟹ x = 2

Therefore, the original numbers are: 3x = 3 × 2 = 6 and 2x = 2 × 2 = 4.

Thus, the numbers are 6 and 4.

**4.** If a quantity is divided in the ratio 5 : 7, the larger
part is 84. Find the quantity.

**Solution:**

Let the quantity be x.

Then the two parts will be \(\frac{5x}{5 + 7}\) and \(\frac{7x}{5 + 7}\).

Hence, the larger part is 84, we get

\(\frac{7x}{5 + 7}\) = 84

⟹ \(\frac{7x}{12}\) = 84

⟹ 7x = 84 × 12

⟹ 7x = 1008

⟹ x = \(\frac{1008}{7}\)

⟹ x = 144

Therefore, the quantity is 144.

● **Ratio and proportion**

**Basic Concept of Ratios****Important Properties of Ratios****Ratio in Lowest Term****Types of Ratios****Comparing Ratios****Arranging Ratios****Dividing into a Given Ratio****Divide a Number into Three Parts in a Given Ratio****Dividing a Quantity into Three Parts in a Given Ratio****Problems on Ratio****Worksheet on Ratio in Lowest Term****Worksheet on Types of Ratios****Worksheet on Comparison on Ratios****Worksheet on Ratio of Two or More Quantities****Worksheet on Dividing a Quantity in a Given Ratio****Word Problems on Ratio****Proportion****Definition of Continued Proportion****Mean and Third Proportional****Word Problems on Proportion****Worksheet on Proportion and Continued Proportion****Worksheet on Mean Proportional****Properties of Ratio and Proportion**

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