Question

Two numbers are in the ratio 11:13, if 12 subtracted
from each, the reminders are in the ratio of 7:9.
Find out the number.​

Answer 1

Answer:

567

Step-by-step explanation:

So basically the actual ratio is 7:9.

Or it can also be written as 7 units:9 units

Now let a unit = x

Therefore ratio is 7x:9x

And the 2 numbers are also 7x and 9x, because ratio is basically division, si when you calculate ratio of these 2 numbers, it comes out as 7:9 which is the actual ratio.

Now when 12 is subtracted from each number ratio becomes 3:5

Which in a similar way to what I have explained above can be written as 3x:5x and the numbers will be 3x and 5x

Now we have

7x-12=3x

7x-3x=12

4x=12

x=12/4=3

Now we have the value of x, which can be verified by putting it in the other equation that is

9x-12=5x

9(3)-12=5(3)

27–12=15

15=15

Therefore the 2 numbers are

7(3)= 21

9(3)= 27

When we multiply then both together

21(27) = 567

Therefore the answer to your question is 567

Answer 2

Given:

• Two numbers are in the ratio 11:13

Let one number be 11x and

Another number be 13x

Now,

According to the question,

If 12 subtracted from each, the reminders are in the ratio of 7:9.

So,

$\implies \frac{11x - 12}{13x - 12} = \frac{7}{9}$

By cross multiplication, we will get,

$\implies 7(13x - 12) = 9(11x - 12)$

⇒ 91x - 84 = 99x - 108

⇒ 108 - 84 = 99x - 91x

⇒ 24 = 8x

⇒ 24 ÷ 8 = x

⇒ 3 = x

So, the value of x is 3.

So, one number is 11x = 11 × 3 = 33

And,

Another number is 13x = 13 × 3 = 39

Hence,

The numbers are 33 and 39.