Question

there are 12 pieces of five, ten and twenty rupee currencies whose total value is₹150 but when first 2 sorts are inter changed in their numbers its value will be increased by₹20.find the number of currencies in each sort

Answer 1

Answer:

Number of 5 rupees currency is 7

Number of 10 rupees currency is 3

Number of 20 rupees currency is 2

Step-by-step explanation:

Let x, y and z be the number of currecies in each category Rs.5, Rs.10 and Rs. 20.

As per given data

x + y + z=12...............(1)

5x + 10y + 20z = 105

x + 2y + 4z = 21............(2)

when first 2 sorts are interchanged,

5y + 10x +20z =125

2x + y + 4z = 25..........(3)

Adding (1) and (2)

3x + 3y + 8z = 46

3(x + y) + 8z = 46

3(12 - z) + 8z = 46

36 - 3z + 8z = 46

36 - 3z + 8z = 46

5z = 10

z=\frac{10}{5}z=

5

10

z = 2

using z = 2 in (1) and (2)

x + y = 10

x + 2y = 13

subtracting we get

- y = - 3

y = 3

Now (1) gives

x + 3 + 2 =12

x = 12 - 5

x = 7