A's salary is half of B's salary. If A got a 50% rise in his salary and B got…
2023
A's salary is half of B's salary. If A got a 50% rise in his salary and B got a 25% rise in his salary, then the percentage increase in the combined salary of both is:
- A.
33.33%
- B.
30%
- C.
55%
- D.
58%
Attempted by 6 students.
Show answer & explanation
Correct answer: A
Concept
When two quantities in a fixed ratio each change by a different percentage, the percentage change of their sum is a weighted average of the two individual percentage changes, weighted by each quantity's share of the original total -- not a simple average of the two rates.
Application
A's salary is half of B's salary, so take A = 100 and B = 200 (a 1 : 2 ratio).
Original combined salary = 100 + 200 = 300.
A's new salary after a 50% rise = 100 + (50% of 100) = 150.
B's new salary after a 25% rise = 200 + (25% of 200) = 250.
New combined salary = 150 + 250 = 400.
Percentage increase in the combined salary = ((400 - 300) / 300) x 100 = (100 / 300) x 100 = 100/3 % ≈ 33.33%.
Cross-check
Weighted-average check: A holds one-third of the original combined salary and rises 50%, while B holds two-thirds and rises 25%. Weighted rise = (1/3 x 50%) + (2/3 x 25%) = 50/3 % + 50/3 % = 100/3 % ≈ 33.33%, matching the direct calculation above.
