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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?

Q.15 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?

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Let the no. of Rs.1 coin be y.

And the no. of Rs.5 coin be x.

Thus according to question no. of Rs.2 coin will be 3x.

Also, the total no. of coins = 160

This implies : y + x + 3x = 160

or                     y + 4x = 160

Transposing 4x to the RHS 

                       y = 160 - 4x = No. of Rs.1 coin.

 

Now, it is given that total amount is Rs.300.

i.e.,        1(160-4x) + 2(3x) + 5(x) = 300

or             160 - 4x + 6x + 5x = 300

or               160 + 7x = 300

Transposing 160 to the RHS :

        7x = 300 - 160 = 140

  Dividing both sides by 7:

     x = \frac{140}{7} = 20

       x = 20

Thus number of Rs.1 coin = 160 - 4x = 160 - 80 = 80

         number of Rs.2 coin = 3x = 60

         number of Rs.5 coin = x = 20

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