Question

A sum Rs. 500 is in the form of denomination of Rs. 5 and Rs.10. if the total number of notes is 90. Find the number of notes of each denomination.

Answer 1

Hint:
Total sum is given to be Rs.500
Two denominations are given i.e. Rs. 5 and Rs. 10.
Total numbers of notes are given to be 90.
Let the number of notes of Rs. 5 =x and hence the number of notes of Rs. 10 = (90- x)
So, the given problem would be getting connected into an algebraic problem.

Complete step by step solution:
Step 1
Consider the number of % rupee notes = x
Step 2
As the total number of notes are given to be 90.So, the number of 10 rupees notes = 90 –x
Step 3
As the total sum of these notes is given to be Rs 500. So, it means x times Rs. 5 and (90-x) times rs. 10 would get added.
i.e. $ (5 \times x) + \left[ {10 \times (90 - x)} \right] = 500 $
i.e. $ 5x + 900 - 10x = 500 $
On rearranging the terms and performing the required operations;
We get, 5x = 400
Which means x = 80 which implies 90-x = 90-80= 10

Hence, would be 80 notes of Rs. 5 and there would be 10 notes of Rs. 10.

Note:
The Indian currency is divided into so many denominations but these days, the lowest denomination of the Indian currency is 1 rupee whereas the highest denotations of the Indian currency is Rs. 2000 right now.
In the above problem, the total sum of rs. 500 was divided into two denominations Rs. 5 and Rs. 5 and Rs. 10.
The total number of notes were given to be 90. So, we supposed the number of notes of 5 rupees to be x
Hence, the number of notes of 10 rupees becomes (90-x ), and hence, the problem gets converted into an algebraic equation. In an algebraic equation, there are two types of terms i.e. variable term and a constant term. The variable term is usually any or a character whereas the constant term would be the mathematical digit. Variables can have different values for different problems but the constant will be having a fixed value.