Question

Two numbers are in the ratio of 15:11. If their H.C.F. is 12, find the Numbers.

• A. 180,132
• B. 186,165
• C. 184,139
• D. 133,169
• E.

Hint:

To find actual numbers from a ratio given their HCF, multiply each part of the ratio by the HCF.

Answer 1

The Correct Option is A

Step 1: Let the numbers be \( 15x \) and \( 11x \), where \( x \) is the common multiplier.
Step 2: Since the HCF of the numbers is 12, we have:
\[ \text{HCF}(15x, 11x) = 12 \] Step 3: The HCF of 15 and 11 is 1, so:
\[ x = 12 \] Step 4: The numbers are:
\[ 15x = 15 \times 12 = 180 \] \[ 11x = 11 \times 12 = 132 \] Thus, the numbers are 180 and 132.