.
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 D) 10 nickels of Sanjay works.
Other offered options A), B), and C) do not work.
Answer. Of the four offered/asked options only option D) works.
Notice. 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.