Question

Two numbers are in the ratio of 5:6 and if 4 is added to the first number and 4 is subtracted from the second number then the ratio becomes 3:2. Find the difference between two numbers.

Answer 1

given the numbers are in ratio 5:6

so let the numbers be 5x and 6x

so 5x/6x is the ratio now

now 4 is added to first number (5x) and 4 is subtracted from second number (6x)

so now ratio becomes

5x+4/6x-4

according to given the above given ratio is equal to ratio 3:2 or 3/2

hence

5x+4/6x-4=3/2

2(5x+4)=3(6x-4)

10x+8=18x-12

8x=20

x=20/8

x=5/2

so number 1 is 5x = 5(5/2)=25/2

second number is 6x= 6(5/2)=15

difference between these two numbers=15-25/2

30-25/2=5/2

hence difference is 5/2

hope this helps and u understand my answer well

:)

Answer 2

Answer:

Let the numbers be x and y.

x:y = 5:6, or

6x = 5y …(1)

(x+4):(y-4) = 3:2, or

2x+8 = 3y-12, or

2x = 3y-20, or

6x = 9y-60 …(2)

Equate (1) and (2)

6x = 5y = 9y-60, or

4y = 60, or

y = 15 and so x = 75/6 = 12.5

Check: 12.5+4 = 16.5 and 15–4 = 11, so ratio of 16.5:11 = 3:2. Correct.

The difference between the two numbers is 2.5.