Two numbers are in the ratio 7 : 5. If the first number is increased by 14 and the second
number is decreased by 5, then the ratio becomes 4 : 2. What is the sum of the original
two numbers?
-
A.
96
-
B.
106
-
C.
111
-
D.
115
Correct Answer:
A. 96
Explanation:
Let the two original numbers be 7x and 5x. Based on the problem, (7x + 14) / (5x - 5) = 4 / 2. Simplifying the ratio to 2 / 1 and cross-multiplying gives 7x + 14 = 2(5x - 5), which simplifies to 7x + 14 = 10x - 10. Solving for x, we find 3x = 24, so x = 8. The sum of the original numbers is 7x + 5x = 12x. Substituting x = 8, the total sum is 12 * 8 = 96.
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