Question

two numbers are in the ratio 2 ratio 3 if 9 is added to each they will be in the ratio 3 ratio 4 the number are ​

Answer 1

Answer:

Two numbers are in ratio 2:3.

Let the rational between two numbers be x, thus the two numbers are 2x and 3x

If 9 is added to each number, they will be in the ratio 3:4. On addition of 9 the numbers become 2x + 9 and 3x + 9, and their ratio 3 : 4

2x + 9 /3x + 9 = 3/4

Cross multiplication

3 ( 3x + 9) = 4 (2x + 9)

9x + 27 = 8x + 36

9x - 8x = 36 - 27

x = 9

The rational is 9, therefore the numbers

First number 2x = 2 × 9 = 18

Second number 3x = 3 × 9 = 27

Now the product of two numbers

18 × 27 = 486

The product of two numbers is 486

Answer : The two numbers are 18 and 27, while the product of two numbers is 486

Now checking the correctness of two numbers by taking their ratio after addition of 9

After addition of 9 the two derived numbers will be

18 + 9 = 27

27 + 9 = 36

Their ratio = 27/36 = 3 : 4

Answer 2

$\huge \mathfrak{ \red}solution$

➡️Two numbers are in ratio 2:3.

➡️Let the rational between two numbers be x, thus the two numbers are 2x and 3x

➡️If 9 is added to each number, they will be in the ratio 3:4. On addition of 9 the numbers become 2x + 9 and 3x + 9, and their ratio 3 : 4

➡️2x + 9 /3x + 9 = 3/4

➡️Cross multiplication

➡️3 ( 3x + 9) = 4 (2x + 9)

➡️9x + 27 = 8x + 36

➡️9x - 8x = 36 - 27

➡️x = 9

➡️The rational is 9, therefore the numbers

➡️First number 2x = 2 × 9 = 18

➡️Second number 3x = 3 × 9 = 27

➡️Now the product of two numbers

➡️18 × 27 = 486

➡️The product of two numbers is

$\huge \colorbox{cyan}{486}$