Find the largest possible value of $ r $ less than 100 for which

\[

\frac{k}{9}+\frac{k}{10}=r

\]

where $ r, k $ are positive integers.

Given :

$\frac{k}{9}+\frac{k}{10}=r$

r and k are positive integers.

To find :

We have to find the largest possible value of r less than 100.

Solution :

$ \frac{k}{9} +\frac{k}{10} =r$

This implies,

$\frac{k\times 10+k\times 9}{9\times 10} =r$

$\frac{10k+9k}{90} =r$

$19k=90r$

$k=\frac{90}{19} r$

Given that r and k are positive integers.

Therefore, r should be a multiple of 19 for k to be a positive integer.

Multiples of 19 below 100 are 19,38,57,76 and 95.

This implies,

The largest possible value of r less than 100 is 95.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

36 Views

Kickstart Your Career

Get certified by completing the course

Get Started