Let the two numbers be 5x and 7x. Increasing the first by 20% gives 5x × 1.2 = 6x. Decreasing the second by 20% gives 7x × 0.8 = 5.6x, which is 28x/5. The new ratio is 6x : (28x/5) = (6 × 5)x : 28x = 30x : 28x = 15:14. Therefore, 15:14 is the required new ratio.
Option A:
Option A, 4:5, would correspond to a situation where the first number becomes relatively smaller than 5x and the second number remains close to 7x. This contradicts the specified percentage changes, where the first number actually grows and the second shrinks. So 4:5 cannot arise from the given operations.
Option B:
Option B, 6:5, incorrectly suggests that the new ratio reflects only the increased numerator without accounting for the reduction in the denominator. If we take 6:5, the implied percentage change for the second number does not line up with a 20% decrease from 7x. Thus, 6:5 is not consistent with the given data.
Option C:
Option C is correct because it incorporates both the 20% increase of the first number and the 20% decrease of the second number. The algebraic simplification of the resulting expressions leads cleanly to 15:14. This ratio reflects the combined effect of both changes accurately.
Option D:
Option D, 7:6, might be guessed from the original ratio 5:7 by swapping roles and adjusting slightly, but no such transformation is described in the question. When we compute the actual new values, they do not simplify to 7:6, so this option fails the mathematical check.
Comment Your Answer
Please login to comment your answer.
Sign In
Sign Up
Answers commented by others
No answers commented yet. Be the first to comment!