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:

• A. 450
• B. 460
• C. 490
• D. 496

Hint:

For numbers in a ratio, multiply the ratio by a variable, use sum condition to find the variable, then apply HCF and LCM formulas.

Answer 1

The Correct Option is C

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 = \( 450 + 30 = 490 \)