Two numbers are in the ratio of 5:8. If 12 is added to each number, the new ratio becomes 11:17. What is the sum of the original two numbers?
Show answer & explanation
Correct answer: D
Explanation
Given:
Ratio of numbers = 5 : 8
Add 12 to each, the new ratio = 11 : 17
Formula:
Numbers = 5x and 8x
(5x + 12) / (8x + 12) = 11 / 17
17(5x + 12) = 11(8x + 12)
85x + 204 = 88x + 132
204 − 132 = 88x − 85x
72 = 3x
x = 24
Numbers
= 5x = 120
= 8x = 192
Sum = 120 + 192 = 312
Sum of the original two numbers = 312