Question:
The sum of two numbers is 240. If the numbers are in the ratio 3 : 5, then the sum of their LCM and HCF is:
The sum of two numbers is 240. If the numbers are in the ratio 3 : 5, then the sum of their LCM and HCF is:
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For numbers in a ratio, multiply the ratio by a variable, use sum condition to find the variable, then apply HCF and LCM formulas.
Updated On: Apr 21, 2025
- 450
- 460
- 490
- 496
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The Correct Option is C
Solution and Explanation
Let the numbers be \( 3x \) and \( 5x \).
\[
3x + 5x = 8x = 240 \Rightarrow x = 30
\Rightarrow \text{Numbers} = 90, 150
\]
Now,
- HCF(90,150) = 30
- LCM(90,150) = \( \frac{90 \times 150}{30} = 450 \)
Sum = \( 450 + 30 = 490 \)
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