Question

three numbers are in the ratio 2:3:4. if sum of the largest and smallest equals the sum of the third and 33 . find the number

Answer 1

Let the common factor be x

4x + 2x = 3x + 33

6x = 3x + 33

6x - 3x = 33

3x = 33

x = 33/3

x = 11

The number is 11.

Answer 2

let ,
the three numbers in the ratio 2:3:4  be 2x, 3x and x respectively
obviously the largest and smallest numbers will be 4x and 2x respectively.
according to the question,
4x + 2x = 3x + 33
⇒6x = 3x +33
⇒6x - 3x = 33
⇒ 3x = 33
⇒x = 33/3
⇒x = 11
the three numbers are,
2x = 2× 11 = 22
3x = 3 ×11 = 33
4x = 4×11 =44