I have a total of Rs. 300/-in coins of denomination Rs. 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
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Answers
Let the no. of coins of Rs 5/- be x
Rs 2/- be 3x
Rs 1/- be 160-4x
The value of coins of Rs 5/- be 5*x=5x
Rs 2/- be 2*3x = 6x
Rs 1/- be 1*(160-4x) = 160-4x
5x+6x+160-4x = 300
7x = 300-160
x = 140/7
x = 20
No. of coins of Rs 1/- = 160-4x = 160-4(20)
=160-80
=80
No. of coins of Rs 2/- = 3x = 3(20) = 60
No. of coins of Rs 5/- = x = 20
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Answer:
The number of Rs. 5/- coins = 20
The number of Rs. 2/- coins = 60
The number of Rs. 1/- coins = 80
Step-by-step explanation:
Let,
The number of Rs. 5/- coins = x
The number of Rs. 2/- coins is 3 times the number of Rs. 5/- coins
So,
The number of Rs. 2/- coins = 3x
The number of Rs. 1/- coins = 160 - (3x + x)
⇒ 160 - 4x
★ Value of coins :
Rs. 5/- coins = 5x
Rs. 2/- coins = 6x
Rs. 1/- coins = 160 - 4x
★ According to the question :
⇒ 5x + 6x + 160 - 4x = 300
⇒ 5x + 6x - 4x = 300 - 160
⇒ 11x - 4x = 300 - 160
⇒ 7x = 140
⇒ x = 140 / 7
⇒ x = 20
The number of Rs. 5/- coins = 20
____________________________
The number of Rs. 2/- coins = 3x
⇒ 3 (20)
⇒ 60
The number of Rs. 2/- coins = 60
__________________________
The number of Rs. 1/- coins = 160 - 4x
⇒ 160 - 4 (20)
⇒ 160 - 80
⇒ 80
The number of Rs. 1/- coins = 80
Therefore,
The number of Rs. 5/- coins = 20
The number of Rs. 2/- coins = 60
The number of Rs. 1/- coins = 80