Question

A trader purchases $70$kg of tea at $Rs.15.00$ per kg and $30$kg of tea at $Rs.18.00$ per kg and mixes the two. If the packing charges are $5$ percent and he would like to make a profit of $20$ percent, he should sell the tea at (approximately):

• A. $Rs.17.50$ per kg
• B. $Rs.18.20$ per kg
• C. $Rs.20$ per kg
• D. $Rs.19.50$ per kg

Answer 1

The correct option is C $Rs.20$ per kg

Let mean price $=x$
By rule of allegation
Cost of 1kg type of tea
$Rs.15$
$(18-x)$
Mean Price $Rs.x$
Cost of 1kg of other type of tea
$Rs.18$
$(x-15)$
$\frac{18-x}{x-15}=\frac{70}{30}$
$\frac{18-x}{x-15}=\frac{7}{3}$
$54-3x=7x-105$
$159=10x$
$\Rightarrow$ $x=15.9$
Packing charge $5$%
Profit $=20$%
Price above mean price $=20+5+\frac{20\times 5}{100}=26$%
$\therefore SP=CP\left(\frac{100+P}{100}\right)$
$=15.9\times 126100=Rs.20.03=Rs.20$ (approx.)