Question

a sum of rs 500 is in the form of the denominations of rs 5 and 10 .if the total number of notes is 90 .find the number of notes ofeach type

Answer 1

Hey there !

Solution:

Let the number of notes in Rs. 5 denomination be x and Rs. 10 denomination be y.

Also it is given that the sum of x and y is 90.

So, x + y = 90  => Equation 1

5x + 10y = 500  => Equation 2

Simplifying Equation 1, we get,

x = 90 - y

Substituting this in Equation 2 we get,

=> 5 ( 90 - y ) + 10y = 500

=> 450 - 5y + 10y = 500

=> 5y = 500 - 450

=> 5y = 50

=> y = 50 / 5 = 10

Hence number of number of notes of Rs. 10 denomination is 10.

x = 90 - y

=> x = 90 - 10 = 80.

Hence number of notes of Rs. 5 denomination is 80.

Verification:

=> 5 ( 80 ) + 10 ( 10 )

=> 400 + 100 = 500

Hence Proved !

Hence x = 80, y = 10

Answer 2

Lets assume you have x notes of rs 5 and y notes of rs 10. So you have

x+y =90

And 5x+10y=500.

Puting x=10-y in 2nd equation you have

5(90-y)+10y=500.

450–5y+10y=500

5y=500–450

y=50/5=10.

Hence x=90–10=80.

So ans is 80 notes of rs 5 and 10 notes of 10.