Question 1117403
.
<pre>
Let x = #of Doug's    dimes,   and

    y = #of Sanjay's  dimes.


Then, according to the condition,  

   x = #of Sanjay's nickels and  2y = #of Doug's nickels


From there, you have this equation for the total in cents

   10x + 5x + 10y + 5*(2y) = 250   cents,   or

   15x + 20y = 250.


It is a Diophantine equation (the solutions must be positive integers).

And there are no any other conditions/equations.


All possible solutions to eq(1) are in this Table


    x     y
-------------

   14     2
  
   10     5

    6     8

    2     11


Of all possible given options only option  <U>D) 10 nickels of Sanjay</U>  works.


Other offered options  A), B), and C)  do not work.
</pre>

<U>Answer</U>. &nbsp;&nbsp;Of the four offered/asked options only option  &nbsp;D) &nbsp;works.


<pre>
<U>Notice</U>.   Other solutions are possible, listed in the Table.

          But since they do not match to offered options, I do not consider them as the answers to the problem's question.
</pre>