# Word Problems on Ratio

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