Question

A grocer purchased 80 kg sugar at Rs. 13.50 per kg and mixed it with 120kg sugar at Rs .16 per kg. At what rate should he sell the mixture (per kg) to gain 16%?
A.Rs. 15.50
B.Rs. 19.18
C.Rs. 17.40
D.Rs. 18.06

Answer 1

Hint: The amount of sugar bought at Rs. 13.50 per kg is 80 kg (given in the question). Using this we calculate the cost price of sugar of weight 80 kg at Rs. 13.50. After that, the amount of sugar brought at 16 per kg is 120 kg (this is also given in the question). We calculate the cost of sugar again. Then, the total cost price of sugar and also the total weight of sugar is obtained. At last, using both values we calculate the profit of 16%.

Complete step by step answer:
The amount of sugar he bought at Rs. 13.50 per kg\[=\text{ }80\text{ }kg\].
The price of sugar which he brought is Rs. 13.50 per kg,
Cost price of sugar \[=80\times 13.5\].
The cost price of sugar at Rs. 13.50 per kg $=Rs.1080$.
Now, the amount of sugar he bought at Rs. 16 per kg $=120\text{ }kg$.
The price of sugar which he bought is Rs. 16 per kg,
Cost price of sugar$=120\times 16$.
The cost price of sugar at Rs. 16 per kg $Rs.\text{ 1920}$.
Now, calculate the total cost price of sugar:
Total cost price of sugar $=1920+1080=Rs.\text{ 3000}$.
Now, the total weight of sugar$=80+120=200\text{ kg}$.
To gain the profit of 16% in sugar, the selling price of sugar is:
Selling price$=\dfrac{116}{100}\times 3000$.
Selling price$=Rs.\text{ 3480}$.
$\therefore $The selling price of 200 kg sugar is Rs. 3480.
Now, the selling price of sugar per kg,
Selling price of sugar per kg$=\dfrac{3480}{200}$.
Selling price of sugar per kg$=Rs.\text{ 17}\text{.40}$.
Hence, the selling price of sugar per kg is $Rs.\text{ 17}\text{.40}$.
Therefore, option (c) is correct.

Note: The key step for this question is individual calculation of sugar at different rates. Then, addition of this individual event is performed to obtain the net amount of sugar and total cost price of sugar. Then, final evaluation for profit is performed. This stepwise approach will minimize the error probability.