CBSE Class 6 Ratio and Proportion Worksheet | PDF - Free Printable

Let's solve each question from the Class VI Worksheet - 13 (Ratio and Proportion) step by step.

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1. Fill in the blanks:

#### i) Ratio of 20 minutes to 2 hrs.

- First, convert both quantities to the same unit.
- 2 hours = 2 × 60 = 120 minutes
- So, ratio = $ \frac{20}{120} = \frac{1}{6} $
- Answer: $ \boxed{1 : 6} $

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#### ii) $ \frac{24}{18} = \frac{\square}{3} = \frac{8}{\square} $

We simplify $ \frac{24}{18} $:
- $ \frac{24 ÷ 6}{18 ÷ 6} = \frac{4}{3} $

So,
- $ \frac{24}{18} = \frac{4}{3} $ → So first blank is 4
- Now $ \frac{4}{3} = \frac{8}{x} $ → Cross-multiply: $ 4x = 24 $ → $ x = 6 $
- So second blank is 6

Answer: $ \frac{24}{18} = \frac{4}{3} = \frac{8}{6} $

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#### iii) Are 13, 39, 7, 21 in proportion?

Check if $ \frac{13}{39} = \frac{7}{21} $

- $ \frac{13}{39} = \frac{1}{3} $
- $ \frac{7}{21} = \frac{1}{3} $

Since both ratios are equal, they are in proportion.

Answer: Yes

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2. Match the following:

Given: a, b, c, d are first, second, third, and fourth terms of a proportion:
i.e., $ a : b = c : d $ or $ \frac{a}{b} = \frac{c}{d} $

Now match:

| Question | Answer |
|--------|--------|
| i) First and fourth terms are | extreme values → (b) |
| ii) Second and third terms are | middle values → (c) |
| iii) Product of extremes (a×d) | Product of middle values (b×c) → (a) |

> Note: In proportion $ a:b = c:d $, we have $ a \times d = b \times c $

So:

- i) → b
- ii) → c
- iii) → a

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3. MCQs

#### i) The ratio of 60 cm to 1.5 meter is

Convert 1.5 meters to cm:
1.5 m = 150 cm

So, ratio = $ \frac{60}{150} = \frac{2}{5} $

Answer: (b) $ \frac{2}{5} $

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#### ii) If cost of one book is ₹15, cost of 9 books will be

$ 15 × 9 = ₹135 $

Answer: (c) ₹135

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#### iii) If $ x : 32 :: 4 : 16 $, then value of $ x $ is

This means: $ \frac{x}{32} = \frac{4}{16} $

Simplify RHS: $ \frac{4}{16} = \frac{1}{4} $

So: $ \frac{x}{32} = \frac{1}{4} $ → $ x = \frac{32}{4} = 8 $

Answer: (b) 8

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4. Solve:

#### i) Divide 50 pens in the ratio 2 : 3

Total parts = 2 + 3 = 5

- First part: $ \frac{2}{5} × 50 = 20 $
- Second part: $ \frac{3}{5} × 50 = 30 $

Answer: 20 and 30 pens

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#### ii) The length and breadth of a rectangular field are in the ratio 4 : 5. If length is 20m, find breadth.

Let length = 4x, breadth = 5x
But length = 20m → $ 4x = 20 $ → $ x = 5 $

So, breadth = $ 5x = 5 × 5 = 25 $ m

Answer: 25 meters

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#### iii) If the cost of 12m of cloth is ₹300, find the cost of 8m cloth.

First, find cost per meter:
- Cost per meter = $ \frac{300}{12} = ₹25 $

Cost of 8m = $ 25 × 8 = ₹200 $

Answer: ₹200

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✔ Final Answers Summary:

#### 1. Fill in the blanks:
i) $ \boxed{1 : 6} $
ii) $ \frac{24}{18} = \frac{4}{3} = \frac{8}{6} $ → Blanks: 4, 6
iii) Yes

#### 2. Match:
i) → b (extreme values)
ii) → c (middle values)
iii) → a (product of middle values)

#### 3. MCQs:
i) (b) $ \frac{2}{5} $
ii) (c) ₹135
iii) (b) 8

#### 4. Solve:
i) 20 and 30 pens
ii) 25 meters
iii) ₹200

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