Two numbers are in the ratio of 7 : 8. If the difference between the numbers…
2022
Two numbers are in the ratio of 7 : 8. If the difference between the numbers is 30, then find the numbers.
Answer: D. 210, 240 — ConceptWhen two numbers are in the ratio a : b, they can be represented as ax and bx, where x is a common scale factor. Their difference is (b − a)x, so the…
- A.
215, 245
- B.
205, 235
- C.
220, 250
- D.
210, 240
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Show answer & explanation
Correct answer: D
Concept
When two numbers are in the ratio a : b, they can be represented as ax and bx, where x is a common scale factor.
Their difference is (b − a)x, so the given difference determines the scale factor.
Application
Represent the two numbers as 7x and 8x.
Use the difference: 8x − 7x = x = 30, so x = 30.
Substitute x = 30: 7x = 210 and 8x = 240.
Cross-check
The difference is 240 − 210 = 30, and 210 : 240 reduces to 7 : 8 after division by 30.
Result
Therefore, the numbers are 210 and 240.