Question & Answer
QUESTION

I have a total of Rs.300 in coins of denomination Re.1, Rs.2 and Rs.5. The number of Rs.2 coins is 3 times the number of Rs.5 coins. The total number of coins is 160. How many coins of each denomination are with me?

ANSWER Verified Verified
Hint: Here we go through by assuming the number of one coin as variable and by that variable we will find the number of other coins. After that we will apply the condition of the question to find out the variable term.

Complete step-by-step answer:
Here in the given questions the coins of denomination are Re.1, Rs.2 and Rs.5.
Now let the number of Rs.5 coins is x.
Then automatically the number of Rs.2 coins becomes 3x as in the question it is given that Rs.2 coins is 3 times the number of Rs.5 coins.
It is also given that the number of total coins is 160.
So by subtracting the Rs.5 and Rs.2 coin from the total no of coins we will get the number of Re.1 coins.
I.e. the number of Re.1 coins =160-3x-x.
And the total amount value of that coin is given as Rs.300
The value of total Rs.5 coins= 5x
The value of total Rs.2 coin= 2(3x)
And the value of total Re.1 coins=1(160-3x-x).
By adding the values and equating with total values we get
5x+6x+160-4x=300
7x=140
X=20
There the number of Rs.5 coin is 20
Rs.2 coin is $3 \times 20 = 60$
And Re.1 coins are 160-60-20=80.

Note: Whenever we face such type of question the key concept for solving the question is you have to assume one coin as variable instead of different variables because by the help of one variable you will be able to find the another variable and the find the total values of coin separately and add them total and equate it with the values given in the question to find out the number of coins.