Question:
I have Rs 1000 in ten and five rupee notes. If the number of ten rupee notes that I have is ten more than the number of five rupee notes, how many notes do I have in each denomination?
Solution:
Let the number of five $-$ rupee notes be $\mathrm{x} .$
Therefore, the number of ten $-$ rupee notes will be $(\mathrm{x}+10)$.
Now,
Value of five - rupee notes $=$ Rs. $5 \mathrm{x}$
Value of ten $-$ rupee notes $=$ Rs. $10(\mathrm{x}+10)$
According to the question,
$5 \mathrm{x}+10(\mathrm{x}+10)=1000$
or $15 \mathrm{x}=1000-100$
or $\mathrm{x}=\frac{900}{15}=60$
$\therefore$ Number of five - rupee notes $=60$.
Number of ten - rupee notes $=60+10=70$.