Question

Two numbers are in the ratio 5 : 9. on subtracting 3 form each, the ratio becomes 1 : 2. Find the numbers​

Answer 1

Step-by-step explanation:

Ratio before subtraction Number 1 : Number 2 = 5:9

Let x be the constant ratio.

Ratio before subtraction + Number 1: Number 2 = 5x: 9x

Ratio after subtraction Number 1 : Number 2 = 1:2

Let y be the constant ratio

Ratio after subtraction Number 1 : Number 2 = 1y : 2y

Form the equations:

5x - 3 = y ................[1]

9x - 3 = 2y ............... [2]

Substitute [1] into [2]:

9x - 3 = 2(5x - 3)

9x - 3 = 10x - 6

x = 3

Find the number:

5x = 5(3) = 15

9x = 9(3) = 27

The two numbers 15 and 27.

Answer 2

Answer:

The two numbers are 3/5 and 1/3.

Step-by-step explanation:

Let the one number be x and other be y.

Since, the given ratio is 5:9

thus, 5x = 9y

5x - 9y = 0 ....(I)

now on subtracting 3 we get 1:2 as new ratio....

thus, 5x - 3 = 1

9y - 3. 2

thus, 10x - 6 = 9y - 3 ... (by cross multiplying)

thus, 10x - 9y = 3 ..... (II)

on subtracting (I) from (II),

we get, 5x = 3

thus, x = 3

x = 3 5

on substituting the value of x in equation (I)

we get 3 - 9y = 0

thus, y = 1

y = 1 3

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