A man has an equal number of ₹2 and ₹5 coins. He has also some ₹1 coins. If the total number of coins is 40 and their value is ₹ 120,
How many ₹5 and ₹2 coins does he have ?
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Answers
Answer:
he has 20 coins of Rs.5 and 10 coins of Rs.2
Step-by-step explanation:
Answer :
The number of ₹5 coins = 16
The number of ₹2 coins = 16
Step-by-step explanation :
Given :
- A man has an equal number of ₹2 and ₹5 coins.
- He has also some ₹1 coins.
- the total number of coins is 40 and their value is ₹ 120.
To find :
- the number of ₹5 and ₹2 coins
Solution :
Let
- the number of ₹5 coins be x
- Since, the number of ₹5 and ₹2 coins are equal.
The number of ₹2 coins = x
- the number of ₹1 coins be y
the total number of coins = 40
x + x + y = 40
2x + y = 40 --[1]
The total amount = ₹120
x(₹5) + x(₹2) + y(₹1) = ₹120
5x + 2x + y = 120
7x + y = 120 --[2]
Subtract equation [1] from equation [2],
7x + y - (2x + y) = 120 - 40
7x + y - 2x - y = 80
5x = 80
x = 80/5
x = 16
Therefore,
The number of ₹5 coins = 16
The number of ₹2 coins = 16
Also, to find the number of ₹1 coins ; substitute x = 16 in equation [1]
2x + y = 40
2(16) + y = 40
32 + y = 40
y = 40 - 32
y = 8
∴ The number of ₹1 coins = 8
Verification :
- The number of ₹5 coins = 16
- The number of ₹2 coins = 16
- The number of ₹1 coins = 8
Condition - 1 : the total number of coins is 40
16 + 16 + 8 = 40
32 + 8 = 40
40 = 40
LHS = RHS
Condition - 2 : the total value of coins is ₹120
16(₹5) + 16(₹2) + 8(₹1) = ₹120
₹80 + ₹32 + ₹8 = ₹120
₹112 + ₹8 = ₹120
₹120 = ₹120
LHS = RHS
Hence verified!