Question

A man has certain notes of denominator Rs 20 and Rs 5 which amount to Rs 380. If the number of notes of each kinds are interchanged they amount to Rs 60 less than before. Find the number of notes of each denomination.

Answer 1

Let x no of Rs 20 Notes and y no of Rs 5 notes from the question first statement 

20 x + 5y = 380 .......................eq(1)

for interchnaged the notes

5 x + 20 y = 380-60 = 320.............eq(2)

after solving two linier equation you will get,

x = 16 and y =12

so there will be 16 notes of Rs 20  and 12 notes of Rs 5.

Answer 2

Suppose there are x notes of RS 20 and y notes of Rs 5

So total money the He is having = 20x + 5y

According to question 20x + 5y = 380-----------Equation (1)

If the number of notes are interchanged .

He is having x notes of RS 5 and y notes of Rs 20

Total money now he is having = 5x+20 y

Acording to question he is now having 380-60= 320 Rs

so 5x+ 20y = 320------------------Equation (2)

Now we have two linear equations in x and y

we can solve them to find x and y

WE would use substitution method

let us make equation (1) for y

we subtract 20x from both sides of equation (1)

it becomes : 5y = 380- 20x

Let us now divide each side by 5 it gives : y= 76-4x

Let us plug this value of y in equation (2)

equation (2) becomes : 5x + 20 (76-4x)= 320

5x + 1520 - 80x = 320

1520 - 75x = 320

let us add 75x both sides 1520 = 320 + 75x

let us subtract 320 both sides 1200 = 75x

divide each side by 75 16 = x

let us now find value of y . we have y= 76-4x

we plug x= 16 y= 76- 4*16

y= 76-64

y = 12

Answer he had 16 notes of RS 20 and 12 notes of Rs 5