When 20% of a number x is added to another number y, y increases by 50%. What…
2024
When 20% of a number x is added to another number y, y increases by 50%. What is the ratio x : y?
Answer: C. 5 : 2 — ConceptA percentage of a quantity can be written as a decimal multiplier. If adding a part of one number produces a stated increase in another number, those…
- A.
2 : 3
- B.
3 : 5
- C.
5 : 2
- D.
5 : 3
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Show answer & explanation
Correct answer: C
Concept
A percentage of a quantity can be written as a decimal multiplier. If adding a part of one number produces a stated increase in another number, those two quantities are equal.
After forming that equality, isolate x/y; the resulting fraction directly gives the ratio x : y.
Application
Twenty percent of x is 0.20x.
A 50% increase in y is 0.50y.
Therefore, 0.20x = 0.50y.
Dividing both sides by 0.20y gives x/y = 0.50/0.20 = 5/2.
Cross-check
Take x = 5 and y = 2. Then 20% of x is 1, while 50% of y is also 1; adding 1 to 2 increases y from 2 to 3, exactly by 50%. Hence x : y = 5 : 2.