Question

Suppose Mr. Ramesh have rupee $2,3$ and $5$ notes. In howmany ways he can get a sum of rupees $83$ such that atleast one note of each type is present and the number of $2$ rupee note(s) is less than number of $3$ rupee note(s) which is again less than the number of $5$ rupees note (s).

• A. $8$
• B. $9$
• C. $10$
• D. $12$

Answer 1

The correct option is C $10$

Let number of $2$ rupee notes $=x$,
number of $3$ rupee notes $=y$
and number of $5$ rupee notes $=z$
$2x+3y+5z=83$
$x\ge 1y\ge 1z\ge 1$
$x<y<z_{\propto }$
Total ways
$\begin{array}{ccc}1& 2& 15\\ 1& 7& 12\end{array}|\begin{array}{ccc}2& 3& 14\\ 2& 8& 11\end{array}|\begin{array}{ccc}3& 4& 13\\ 3& 9& 10\\ & & \\ & & \\ & & \end{array}|\begin{array}{ccc}4& 5& 12\\ 5& 6& 11\\ 6& 7& 10\\ 7& 8& 9\\ & & \end{array}$
Total ways $=10$