Question

If two numbers are in the ratio 2 : 3, and the product of their HCF and LCM is 33750, then the sum of the numbers is

• A. 250
• B. 425
• C. 325
• D. 375

Answer 1

The correct option is D 375

Let the numbers be 2x and 3x Then
$2x\times 3x=33750\Rightarrow 6x^2=33750$
$\Rightarrow x^2=5625\Rightarrow x^2=5^4\times 3^2$
$\Rightarrow x=5^2\times 3=75$
$\therefore$ The two numbers are 2 x 75 and 3 x 75 i.e.
150 and 225
$\therefore$ Required sum $=150+225=375$