Question

Two numbers are in the ratio of 2:5. If 4 is added to each, they would be in the ratio 4:9. Find the numbers

Answer 1

Answer:

The numbers are 20 and 50

Step-by-step explanation:

Let the numbers be x and y

Given that

x/y = 2/5

x= 2y/5 — (I)

Also,

x+4/y+4 = 4/9

9x +36 = 4y + 16

4y - 9x = 20

Substituting (I)

4y - 9*(2y/5) = 20

20y - 18y = 100

2y = 100

y = 50

x = 2y/5

x = 2*50/5

x = 20

Answer 2

Given - Ratio and addition

Find - Numbers

Solution - The numbers are 20 and 50.

Let the numbers be 2x and 5x. In addition to 4, the new expression will be 2x+4/5x+4.

The complete mathematical expression will be -

2x + 4/5x + 4 = 4/9

Solving the equation to find the value of x.

(2x + 4)*9 = (5x + 4)*4

Performing multiplication to find the value of x.

18x + 36 = 20x + 16

36 - 16 = 20x - 18x

Performance subtraction to find the value of x.

20 = 2x

Performing division to find the value of x.

x = 20/2

x = 10.

Thus, the numbers are -

Number = 2x

Number = 2*10

Number = 20

Number = 5x

Number = 5*10

Number = 50

Therefore, the numbers are 20 and 50.