Question

55.) Two numbers are in the ratio 2:3. If 9 is added
to each, they will be in the ratio 3:4, the
numbers are
(2) 18,27 (3) 8, 12 10, 15
(1) 12, 28​

Answer 1

Answer:

Part 2

18, 27

Step-by-step explanation:

9 * 2 = 18

9 * 3 = 27

18 : 27

2 : 3

18 + 9 = 27

27 + 9 = 36

27 : 36

3 : 4

Hence, the answer is 18, 27.

Answer 2

Answer:

(2) 18, 27

Step-by-step explanation:

Given -

Two numbers are in ratio = 2 : 3

After adding 9 to each = 3 : 4

To find -

The two numbers

Solution -

Let us think two numbers as 2x and 3x respectively.

So after adding 9 to each the ratio will be

2x + 9 : 3x + 9

Real ratio = 3 : 4

2x + 9 : 3x + 9 = 3 : 4

$= > \frac{2x + 9}{3x + 9} = \frac{3}{4} \\ (after \: cross \: multiplication) \\ = > 4 \times (2x + 9) = 3 \times (3x + 9) \\ = > 8x + 36 = 9x + 27 \\ = > 8x + 36 - 27 = 9x \\ = > 36 - 27 = 9x - 8x \\ = > 9 = x \\ = > x = 9$

Hence

First number = 2x = 2(9) = 18

Second number = 3x = 3(9) = 27

These two numbers are in ratio 2 : 3 and after adding 9 to each both will be in ratio 3 : 4.

Hence our answer is correct.

hope it helps.