3 accessories with 100 rupees

A man buy 3 accessories with 100 rupees. first one 5 rupees, second one 3 rupees, third one 0.5 rupees each. he bought total 100 pieces. How many pieces he bought for each accessory ?

Answer

First Accessory

Answer is 5

Second Accessory

Answer is 11

Third Accessory

Solution

lets say he bought x,y and z pieces.
Then we can make these two equations
Eq1: x + y + z = 100
Eq2: 5x + 3y + 0.5z = 100
2*Eq2 => 10x + 6y + z = 200
2*Eq2-Eq1 => 9x + 5y = 100
from this equation x should be a multiple of 5, for x = 5 => y = 11
for x = 10 => y = 2
for x = 15 or more y becomes -ve

So two possible answers
x = 5, y = 11, z = 84
x = 10, y = 2, z = 88

3 accessories with 100 rupees

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