A shopkeeper mixes three types of tea costing worth rs. 40/- kg and 48/- per kg and 60/- per kg. Thus the cost of mixture becomes 50/- per kg. if the quantity of third type of tea was 2 kg. Then find out quantity (exact value) of second type of tea?
My method
I assume first type of tea in quantity $a$ kg. I assume second type of tea in quantity $b$ kg.
so the equation becomes
$40a+48b+60\cdot2= 50(a+b+2)$
from above equation we can't find an exact value of $b$ because there will be many values of $a$ and $b$ which will satisfy the equation. so according to this quantity of second type of tea can't be found.
Now other type to solve this problem is to make two type of equation. In this equation we assume the third quantity 2 kg. as $c$
$40a+60c=50(a+c)$
$48b+60c= 50(b+c)$
from above equation we can find ratio of $a:b$ and $b:c$ and after that we can find $a:b:c$ and finally I can find the exact value of $B$
My question is which equation is right? Why these equations are giving two different solutions?
Thanks
If we assume that the amount of tea in the mix was a whole kg quantity for each type, and that all three types of tea were used, then the amount of 40/- tea is the point to start. We know that if we have $2$ kg of 40/- tea then the average is already 50/- before we even start adding any 48/- tea (which would take the average below 50/-).
So since we cannot have $0$ kg of 40/- tea, immediately we know that $a=1$ in your variables. Then you can solve to a definite value for $b$.