Question

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

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

Answer 1

The correct option is A 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.