Two numbers are in the ratio 21:10. If their HCF is 11, then the sum of the…
2023
Two numbers are in the ratio 21:10. If their HCF is 11, then the sum of the numbers is
Answer: A. 341 — ConceptWhen two numbers are in the ratio a:b and gcd(a,b) = 1, they can be written as ak and bk. Their HCF is k, so their sum is (a + b)k. ApplicationSince…
- A.
341
- B.
141
- C.
241
- D.
More than one of the above
- E.
None of the above
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Show answer & explanation
Correct answer: A
Concept
When two numbers are in the ratio a:b and gcd(a,b) = 1, they can be written as ak and bk.
Their HCF is k, so their sum is (a + b)k.
Application
Since gcd(21, 10) = 1, write the two numbers as 21k and 10k.
HCF(21k, 10k) = k. The given HCF is 11, so k = 11.
The numbers are 21 × 11 = 231 and 10 × 11 = 110.
Their sum is 231 + 110 = 341.
Cross-check
HCF(231, 110) = 11, and 231:110 simplifies to 21:10. Both given conditions are satisfied.
Result
Therefore, the sum of the numbers is 341.