Question

there are 12 pieces of 5 ,10 and 20 rupee currencies whose total value is rupees 105. when first two sorts are interchanged in their numbers its value will be increased by rupees 20. find the number of currencies in each sort​

Answer 1

The number of 5 rupee note  = 7, number of ten rupee note  =  3 and number of twenty rupee note = 2.

Step-by-step explanation:

Let "x", "y" and "z" be the number of pieces of five, ten, and twenty rupee currencies.

x + y + z  =  12  ----(1)

5x + 10y + 20z  =  105

Divide it by 5  ==>  x + 2y + 4z  =  21 ----(2)

10x + 5y + 20z  =  105 + 20

10x + 5y + 20z  =  125

Divide it by 5  ==>  2x + y + 4z  =  25 ----(3)

(1) - (2)

 x + y + z  =  12

x + 2y + 4z  =  21

(-)   (-)  (-)    (-)

-------------------

  - y - 3z  =  -9 ---(4)

 

2(1) - (3)

 2x + 2y + 2z  =  24

 2x + y + 4z  =  25

 (-)   (-)   (-)    (-)

--------------------

 y - 2z  =  -1  ----(5)

(4) + (5)

-y - 3z  =  -9

 y - 2z  =  -1

 -------------

    -5z  =  -10  ==>  z  =  2

By applying z = 2 in (5)

y - 2(2)  =  -1

 y = -1 + 4  ==> y = 3

By applying the value of y and z in (1)

x + 3 + 2  =  12

x  =  12 - 5

x  =  7

Hence the number of 5 rupee note  = 7, number of ten rupee note  =  3 and number of twenty rupee note = 2.