# 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.

5. Two numbers are in the ratio 3 : 5 and the smaller number is 18 less than the larger number. Find the numbers.

Solutions:

Let the required numbers be 3x and 5x.

Large number - smaller number = 18

5x - 3x = 18

⟹            2x = 18

⟹              x = $$\frac{18}{2}$$

⟹              x = 9

So, the numbers are (3 × 9) and (5 × 9) i.e., 27 and 45.

Hence, the required numbers are 27 and 45.

### Worksheet on Word Problems on Ratio:

1. A motorcycle covers 195 km in 3 hours while a bus covers 650 Km in 5 hours. Find the ratio of the speed of the motorcycle to the speed of the bus.

1. 1 : 3

2. A school starts at 8 a.m. and gets over at 1.30 p.m. During the school time, if there are two breaks of 15 minutes and 30 minutes, respectively, find the ratio of the break time to the total time the students spend in the school.

2. 3 : 22

3. Jennifer bought some pencils and pens. There were 35 more pencils than pens. If the ratio between the pencils and pens is 8 : 3, find the number of each of them purchased by Jennifer.

3. Pencils = 56 and Pens 21

4. In a fruit basket the ratio of mangoes to apples is 7 : 6. If there are 12 apples, how many mangoes are there?

4. Mangoes = 14

5. A box contains apples and lemon. If the ratio of the number of apples to lemon is 3 : 5 and the number of apples is 21, find the number of lemons.

5. Lemons = 35

● Ratio and proportion

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