Question

How many $\text{kg}$ of sugar costing $\text{Rs.}5.75$ per $\text{kg}$ should be mixed with $75\text{kg}$ of cheaper sugar costing $\text{Rs.}4.50$ per $\text{kg}$ so that the mixture is worth $\text{Rs.}5.50$ per $\text{kg}$ ?

• A. $350\text{kg}$
• B. $300\text{kg}$
• C. $250\text{kg}$
• D. $325\text{kg}$

Answer 1

The correct option is B $300\text{kg}$

Let say $x\text{kg}$ sugar costing $\text{Rs.}5.75$ per $\text{kg}$ is added.

Total cost $=\text{Rs.}(5.75x+75)\times 4.50$

$=\text{Rs.}(5.75x+337.5)$

Total sugar $=(x+75)\text{kg}$

Average cost of sugar mixture $=\frac{\text{Total cost of sugar}}{\text{Total sugar}}$

$5.5=\frac{(5.75x+337.5)}{(x+75)}$

$5.5x+412.5=5.75x+337.5$

$75=0.25x$

$x=\frac{75}{0.25}$

$\therefore x=300\text{kg}$