Question

*12 Rs 80 paise : 14 Rs.40 Paise. Write the shortest form of a given ratio.*

1️⃣ 8:9
2️⃣ 9:8
3️⃣ 3:4
4️⃣ 4:3​

Answer 1

Given:

First value = 12 Rs. 80 paisa

Second value = 14 Rs. 40 paisa

To find:

Shortest form of the ratio of these numbers.

Solution:

We can write 12 Rs. and 80 paisa as  Rs 12.80

And 14 Rs. 40 paisa as Rs. 14.40

Because 1 rupee = 100 paisa, so 1 paisa = 1/100 Rs.

The ratio of the two values = 12.8 / 14.4

Multiplying by 10 in both nominator and denominator gives ratio = 128 / 144

When nominator and denominator are both divided by 16, we get:

128/144 = 8/9

Therefore the shortest form of ratio is 8:9, option A is correct.

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

12 Rs 80 paise : 14 Rs 40 Paise.

Write the shortest form of a given ratio.

1. 8 : 9

2. 9 : 8

3. 3 : 4

4. 4 : 3

EVALUATION

The simplification is done in the below way :

Step : 1

First write down the two terms of the given ratio

The two terms are

12 Rs 80 paise & 14 Rs 40 Paise.

Step : 2

Convert them into same unit

12 Rs 80 paise = 1280 paise

14 Rs 40 Paise = 1440 paise

Step : 3

Find out the common factors

$\sf{1280 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5}$

$\sf{1440 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5}$

So HCF

= 2 × 2 × 2 × 2 × 2 × 5

= 160

Step : 4

Divide both the terms by the HCF

So the ratio in the simplified form is

= 1280 : 1440

= 8 : 9

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