I have a total of rupees 300 in coins of denomination rupees 1, 2, 5 the number of rupees 2 coins is 3 times the number of rupees 5 coins. The total number of coins is 160. Find the number of coins of each denomination.


Given: 

Total amount = Rs. 300

The number of rupees 2 coins is 3 times the number of rupees 5 coins.

To find: Here we have to find the number of coins of each denomination.

Solution:

Let the number of Rs 5 coins = $x$

So,

Number of Rs 2 coins = 3$x$

The number of Rs 1 coin = $y$



Total no. of coins = 160


$x\ +\ 3x\ +\ y\ =\ 160$


$4x\ +\ y = 160$ 



Given that, total amount is Rs. 300:


$5x\ +\ 2(3x)\ +\ y\ =\ 300$


$11x\ +\ y\ =\ 300$



By elimination method on subtracting both the equations


$4x\ +\ y\ -\ 11x\ -\ y\ =\ 160 -\ 300$


$-7x\ =\ -140$


$x\ =\ \frac{140}{7}$


$x\ =\ 20$



On putting the value of $x$ in $4x\ +\ y\ =\ 160$ 


$4(20)\ +\ y\ =\ 160$


$80\ +\ y\ =\ 160$


$y\ =\ 80$



Now,


Number of Rs 2 coins $=\ 3(x)\ =\ 3(20) =\ 60$


No. of Rs 5 coins $=\ x\ =\ 20$


No. of Rs 1 coins $=\ y\ =\ 80$

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Updated on: 10-Oct-2022

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