Question

make a 1 rupee note change in a such way that there are exactly 50 coins but having no 2 paise coin
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Answer 1

Answer:

let x be number of 1 paisa coin

let y be number of 5 paisa coin

let z be number of 10 paisa coin

x+5y+10z=100

x+y+z=50

subtracting abov e two results in

4y+9z=50

z=(50-4y)/9

let us check for what value of y z will be positive integer bcoz number of coins is always an integer

if y=0

z =50/9 not an integer

if y=1

z=46/9 not an integer

if y=2

z=42/9 not an integer

if y=3

z=38/9 not an integer

if y=4

z=34/9 not an integer

if y=5

z=30/9 not an integer

if y=6

z=26/9 not an integer

if y=7

z=22/9 not an integer

if y=8

z=18/9=2 is an intger(=> x=40 , y =8 , z=2 is a solution)

if y=9

z=z=14/9 not an intger

if y=10

z=10/9 not an integer

if y=11

z=6/9 not an integer

if y=12

z=2/9 not an integer

rest all are not solutions as number of coins cant be negative

So there is one and only one solution

i.e x=40 , y=8 , z=2 is only solution possible for the above problem

Answer 2

Answer:

As we can't use 2 paise coins.

So we find Coins who average is 2.

Like 3 paise and 1 paise.

So equal number of 3 paise and 1 paise.

That is 25 Coins of 3 paise.

And 25 Coins of 1 paise.

So sum total equal to 50 Coins and cost= 75+25= 100 paise= 1 rupee