I have a total of ₹ 300 in coins of denomination ₹ 1, ₹2 and ₹5. The number of ₹2 coins is 3 times the number of ₹ 5 coins. The total number of coins is 160. How many coins of each denomination are with me?
Answers
Step-by-step explanation:
Let the number of coins of ₹1 denomination be x
and the number of coins of ₹5 denomination be y
then number of coins of ₹2 denomination will be 3y
Now, according to question
total number of coins is 160
so, x+y+3y=160
x+4y=160
total cash of ₹1 denomination=x×1=x
total cash of ₹2denomination=3y×2=6y
total cash of ₹5 denomination=y×5=5y
Total amount he have is ₹300
So, x+6y+5y=300
x+11y=300
On solving the above two equation by elimination method
we get,
11y-4y=300-160
7y=140
y=20
and x=160-4×20
x=160-80
x=80
total coins of ₹1 denomination=x=80coins
total coins of ₹2 denomination=3y=3×20=60coins
total coins of ₹5 denomination=y=20coins
HOPE THIS WILL HELP YOU
जय महाकाल
Given :-
- I have a total of ₹ 300 in coins of denomination ₹ 1, ₹2 and ₹5.
- The number of ₹2 coins is 3 times the number of ₹ 5 coins.
- The total number of coins is 160.
To Find :-
- How many coins of each denomination are with me?
Solution :-
~Here, we’re given that we have total 160 coins of denomination ₹ 1 , ₹ 2 and ₹ 5 and their total amount makes ₹ 300. No. of ₹ 1 coins and amount will be same and no. of ₹ 2 coins are 3 times of ₹ 5 coins. We need to find the no. of coins of each denomination we have.
_____________
- Now, let the no. of ₹ 5 coins be ‘x’
- Then , no. of ₹ 2 coins will be ‘3x’
_____________
We can write it as,
→ No. of ₹ 5 coins = x
→ No. of ₹ 2 coins = 3x
→ No. of ₹ 1 coins = 160 – ( x + 3x )
= 160 – 4x
_____________
Amount made by each denomination of coin :-
Amount made by ₹ 5 coins = 5( x ) = ₹ 5x
Amount made by ₹ 2 coins = 2( 3x ) = ₹ 6x
Amount made by ₹ 1 coins = 1( 160 -4x ) = ₹ 160 -4x
ATQ ::
=> ₹ 5x + ₹ 6x + ₹ 160 -4x = ₹ 300
=> ₹ 7x + ₹ 160 = ₹ 300
=> ₹ 7x = ₹ 300 – ₹ 160
=> ₹ 7x = ₹ 140
=> x = 140/7
=> x = 20
Therefore,
- No. of ₹ 5 coins = 20
- No. of ₹ 2 coins = 60
- No. of ₹ 1 coins = 80
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