Question

Two numbers are in the ratio of 15:11. If their H.C.F is 13, the numbers will be:

• A. 190 and 140
• B. 185 and 143
• C. 195 and 143
• D. 185 and 163

Answer 1

The correct option is C 195 and 143

Let the required numbers be 15x and 11x.

Now, $15x=3\times 5\times x$ ...(i)
$11x=11\times x$ ...(ii)

From (i) and (ii), we can say that x is the only common factor for both $15x$ and $11x.$
$\therefore x$ is the H.C.F. of $15x$ and $11x.$

It is given that the H.C.F of the numbers is 13.
$\therefore x=13$

$\therefore$ The numbers are $15\times 13$ and $11\times 13$ i.e. 195 and 143.