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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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There are in total 20,60 and 80 coins of Rs. 5, Rs. 2 and Rs. 1 respectively

There are in total 40,60 and 70 coins of Rs. 5, Rs. 2 and Rs. 1 respectively

There are in total 10,10 and 90 coins of Rs. 5, Rs. 2 and Rs. 1 respectively

There are in total 30,25 and 80 coins of Rs. 5, Rs. 2 and Rs. 1 respectively

answer is A.

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Detailed Solution

It is given the number of Rs. 2coins is 3 times the number of Rs. 5 coins and the total number of coins is 160.
Let the number of Rs. 5 coins be x.

⇒

Number of Rs. 5 coins + Number of Rs. 2 coins + Number of Rs. 1 coin= 160
Substituting values in above equation,

⇒

x+3x+ Number of Rs. 1 coin= 160

⇒

4x+ Number of Rs. 1 coin= 160
Simplifying the above equation,

⇒

Number of Rs. 1 coin

= 160 − 4 x

Analyse the table for the number of coins and the amount
Question Image

It is given that the total amount is 300.
Adding the amount of each coin and equate it with the total amount.
160-4x+6x+5x=300
160-4x+11x=300
160+7x=300
Simplifying the equation,
7x=300-160
7x=140

x = 1407

x=20
Substitute the value of x in the total number of each coin.
The number of Rs. 5 coins is x i.e., 20.
The number of Rs. 2 coin is 3x i.e.,

= 3 x = 3 × 20 = 60

Number of Rs. 1 coin is 160-4x

= 160 − 4 × 20 = 160 − 80 = 80

Hence, there are in total 20,60 and 80 coins of Rs. 5, Rs. 2 and Rs. 1 respectively.
Correct option is 1.

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