Question

In a purse there are $20$ rupee notes,$10$ rupee notes and $50$ rupee notes. The number of $50$ rupee notes exceeds $2$ times the number of $10$ rupee notes by $1$ and the number of $20$ rupee are $5$ less than the number of $10$ rupee notes. If the total value of money in the purse is $860$ find the number of each variety of notes.

Answer 1

Step-1 Form equations by using the given data

Given that,

• The number of $50$ rupee notes exceeds $2$ times the number of $10$ rupee notes by $1$
• The number of $20$ rupee are $5$ less than the number of $10$ rupee notes
• The total value of money in the purse is $860$ rupees

Let the number of $10$ rupee notes be $x$. $...\left(i\right)$

It is given that number of $20$ rupee notes are $5$ less than $10$ rupee notes.

$\Rightarrow$ Number of $20$ rupee notes$=x-5$ $...\left(ii\right)$

It is given that number of $50$ rupee notes exceeds $2$ times the number of $10$ rupee notes by $1$

$\Rightarrow$Number of $50$ rupee notes$=2x+1$ $...\left(iii\right)$

Step 2: Solve for the number of each variety of notes

From $\left(i\right),\left(ii\right),\left(iii\right)$ we can write the following equation

$\left(10\times x\right)+\left(\left(x-5\right)\times 20\right)+\left(\left(2x+1\right)\times 50\right)=860$

$\Rightarrow$ $10x+20x-100+100x+50=860$

$\Rightarrow$ $130x=910$

$\Rightarrow$ $x=7$

$\therefore$ $x-5=7-5=2$

$2x+1=14+1=15$

Hence,

The number of $10$ rupee notes is $7$.

The number of $20$ rupee notes is $2$.

The number of $50$ rupee notes is $15$.