# The sum of three numbers is 123. If the ratio between the first and second number is 2 : 5 and that of between the second and third is 3 : 4, then find the difference between the second and third number.

The question is based on equation solving and ratios.

## Answer: The required numbers are 18, 45, 60 which add up to 123, with the ratio between the first and second number as 2 : 5 and the ratio of second and third as 3 : 4.

Let us find the required numbers.

**Explanation:**

Let the numbers be a, b, and c.

Given that,

The ratio of the first number and the second number is 2:5

a : b = 2 : 5

a/b = 2/5

a = 2b/5

The ratio of the second number and the third number is 3:4

b : c = 3 : 4

b/c = 3/4

c/b = 4/3

c = 4b/3

The sum of the three numbers is 123 ⇒ a + b + c = 123

2b/5 + b + 4b/3 = 123

(6b + 15b + 20b) / 15 = 123 -------> By taking LCM of 3 and 5

41b / 15 = 123

b = (123 × 15) / 41

b = 3 × 15

b = 45

a = 2b/5 = (2 × 45) / 5 = 18

c = 4b/3 = (4 × 45) / 3 = 60