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There are 12 pieces of five, ten and twenty rupee currencies whose total value is Rs 105. When first 2 sorts are interchanged in their numbers its value will be increased by Rs 20. Find the number of currencies in each sort.

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Let x, y and z be number of currency pieces of 5,10,20 rupees 

x + y + z = 12 … (1) 

5x + 10y + 20z = 105 … (2) 

10x + 5y + 20z = 125 … (3)

Sub, z = 2 in (5), we get 

15y + 20 x 2 = 85 

15y = 45 

y = 3

Sub; y = 3, z = 2 in (1) 

x + y + z = 12 

x = 7 

∴ The solutions are 

The number of Rs 5 are 7

The number of Rs 10 are 3 

The number of Rs 20 are 2

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