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Ratio Applications

    Introduction

    Ratio

    Proportion

    Rate

    Unitary Method

    Direct Proportion

    Some situations in which we use percentages

    Exercise 6.1

    Exercise 6.2

    Exercise 6.3

    Exercise 6.4

    Exercise 6.5

    Exercise 6.6

    Looking Back

    Easy Level Worksheet Questions

    Moderate Level Worksheet Questions

    Hard Level Worksheet Questions

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Ratio Applications > Exercise 6.3

Exercise 6.3

1. A length of a bacteria enlarged 50,000 times attains a length of 5 cm. What is the actual length of the bacteria? If the length is enlarged 20,000 times only, what would be its enlarged length?

img(src="/content/scert/7/ratio/images/chapter3/bacteria.png" width=320 height=200)

Solution:

Given that:

A length of bacteria enlarged times attains a length of cm

We have to find:

The actual length of the bacteria

The actual length of the bacteria =

We divide

= cm

Now, if the length is enlarged 20,000 times:

Let's set up the proportion:

50,000 : 5 :: 20,000 : x

By cross multiplication:

50,000x = 20,000 ×

x = (20,000 × 5) ÷ 50,000

x =

Therefore, when enlarged 20,000 times, the length will be 2 cm

2. Observe the following tables and find if x is directly proportional to y.

(i)

x20171411852
y4034282216104

Solution:

Let's check if y/x is constant:

For first pair: 40/20 =

For second pair: 34/17 =

For third pair: 28/14 =

Since y/x = 2 for all pairs

Therefore, x and y are

(ii)

x6101418222630
y481216202428

Solution:

Let's check if y/x is constant:

For first pair: 4/6 =

For second pair: 8/10 =

Since y/x is not constant

Therefore, x and y are

(iii)

x581215182025
y1524366072100125

Solution:

Let's check if y/x is constant:

For first pair: 15/5 =

For second pair: 24/8 =

For third pair: 36/12 =

Since y/x = 3 for all pairs

Therefore, x and y are

3. Sushma has a road map with a scale of 1 cm representing 18 km. She drives on a road for 72 km. What would be her distance covered in the map?

Solution:

Given:

Scale: cm = km

Actual distance covered = km

Let's set up the proportion:

1 cm : 18 km :: x cm : 72 km

Using cross multiplication:

18x = 1 ×

x = 72 ÷ 18

x =

Therefore, the distance covered in the map would be 4 cm

4. On a Grid paper, draw five squares of different sizes. Write the following information in a tabular form.

Square 1Square 2Square 3Square 4Square 5
Length of a side (L)
Perimeter (P)
Area (A)

Solution:

(i) Length vs Perimeter

Let's check if length of a side is in direct proportion to perimeter:

For Square 1: P/L = 8/2 =

For Square 2: P/L = 12/3 =

For Square 3: P/L = 16/4 =

For Square 4: P/L = 20/5 =

For Square 5: P/L = 24/6 =

Since P/L = 4 for all squares

Therefore, length of a side is to perimeter

(ii) Length vs Area

Let's check if length of a side is in direct proportion to area:

For Square 1: A/L = 4/2 =

For Square 2: A/L = 9/3 =

For Square 3: A/L = 16/4 =

For Square 4: A/L = 25/5 =

For Square 5: A/L = 36/6 =

Since A/L is not constant (it keeps increasing)

Therefore, length of a side is to area

Note:

  • The perimeter is directly proportional to the length because P = 4L
  • The area is not directly proportional to the length because A = L2