Question

two umbers are in the ratio 5:8 and their difference is 12 find the numbers​

Answer 1

Answer:

Let the two numbers are, smaller number x and larger number y.

As per statement the two numbers difference is 10

y - x = 10

y = 10 + x.. Eq…1

Two numbers ratio is 5 : 7

Ratio of x and y is

x / y = 5 / 7

5y = 7x

y = 7x / 5….Eq..2

Now putting the value of y from Eq..2 to Eq..1

y = 10 + x

7x/5 = 10 + x

Cross multiplication

7x = 5 (10 + x)

7x = 50 + 5x

7x - 5x = 50

2x = 50

x = 50/2

x = 25

The smaller number is 25

Now putting the value of x in Eq..2 to get the value of y

y = 7x/5

y = 7 × 25/5

y = 7 × 5

y = 35

The larger number is 35

Answer 2

Ratio of first number = 5x

Ratio of second number = 8x

A.T.Q.

8x - 5x = 12

3x = 12

x = 12/3 = 4

x = 4

First number = 5 × 4 = 20

Second number = 8 × 4 = 32