Given : We have rs 100 we should buy 100 THINGS at 5rs and 1rs and .25 PAISE

To find : Different ways to buy

Solution:

Lets Thing buy A rs 5  = x

& thing buy at Rs 0.25 ( 25 Paise) = y

then thing bought at Rs 1 = 100 - (x + y)

AMOUNT for 5 Rs x thing  = 5x

Amount for Rs 0.25 y things = 0.25y

Amount for Rs  1  (100 - (x + y)) things = 100 -(x + y)

5x + 0.25y + 100 - (x + y)  = 100

=> 4x  - 0.75y  = 0

=>4x = 0.75y

=> 16x = 3y

Possible Values

x = 0  & y = 0

x = 3   & y  = 16  

x = 6  &  y =  32  

x  = 9 &  y = 48  

x = 12  & y = 64

x = 15  &  y = 80

x = 18  & y = 96  ( not possible as x + y ≤ 100)

Different ways to buy things

Rs 5                 Rs 1               Rs 0.25

0                       100               0

3                        81                16

6                       62                 32

9                       43                48        

12                      24               64

15                       5                 80

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