Question

There are a total of 12 notes of five,ten and twenty rupee whose total value adds upto ₹ 105. If the number of five and ten rupee notes are interchanged, then their value is increased by ₹ 20. What are the three equations using which we can find the number of currencies in each type?

• A. x +y+z =12
  
• B. x + y + z =14
• C. x + 2y +4z =21
• D. 2x +y +4z =25

Answer 1

Answer: (A), (C), (D)

The correct options are
A x +y+z =12

C x + 2y +4z =21
D 2x +y +4z =25

Let x,y and z be the number of 5,10 and 20 rupee currencies respectively.

As given in the question,

x+y+z =12.…...........(1)

Given: "Total value of currencies before interchanging is ₹ 105 "

$\Rightarrow$ 5x+10y+20z=105

$\Rightarrow$ x+2y+4z=21….........(2)

Given:"If the number of five and ten rupee notes are interchanged, then their value is increased by ₹ 20.

$\Rightarrow$ 10x+5y+20z =125

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

By solving equations (1),(2) and (3), we get the number of currencies in each type.