Question

A total of 90 currency notes, consisting only of ₹ 5 and ₹ 10 denominations, amount to ₹ 500. Find the number of notes in each denomination.​

Answer 1

Let the number of Rs. 5 currencies be denoted as 'x' and Rs. 10 currencies be denoted as y.

According to the question,

.

$\Rightarrow x+y=90$

Also, it is given that total amount is Rs. 500. Therefore it is given as:

$\Rightarrow5x+10y=Rs 500$

$\bold \Rightarrow x+2y=100$

Solving both the equations we get,

$\Rightarrow x+2y=100;$

$\Rightarrow x=100-2y$

Substituting this in the first equation we get,

$\Rightarrow(100-2y)+y=90;$

$\Rightarrow100-y=90;$

$\Rightarrow y=100-90;$

$\Rightarrow y=10$

Therefore x can be found out as:

$\Rightarrow x=100-2y;$

$\Rightarrow x=100-2( 10)$

$\Rightarrow x=100-20;$

$\Rightarrow x=80$

Therefore number of notes of Rs. 5 denominations were 80 and that of Rs. 10 were 10.