Question

A grocer purchased $200$ kg of rice at Rs. $25$ per kg. He sold $80$ kg of it at a gain of $10\%$ and $40$ kg at a loss of $4\%$. At what rate per kg should he sell the remainder to gain $8\%$ on his total investment ?

• A. Rs. $25$ per kg
• B. Rs. $28$ per kg
• C. Rs. $30$ per kg
• D. Rs. $32$ per kg

Answer 1

The correct option is B Rs. $28$ per kg

Purchase cost $=200\times 25=Rs5,000$

Selling price of 80 kg rice - at 10% gain $\Rightarrow$ 110% of price

$\Rightarrow$ $\frac{110}{100}\times Rs25$.

So money earned by selling 80 kg rice $=80\times \frac{110}{100}\times$ $25=Rs2,200$

Selling price of 40 kg rice at a loss of 4% $\Rightarrow$ 96% of price

$\Rightarrow \frac{96}{100}\times Rs25$

Money earned by selling 40 kg $=40\times \frac{96}{100}\times 25=$Rs $960$

Remaining quantity $=200-40-80=80kg$

Total gain required = 8% $\Rightarrow$

Overall money to be earned thru sales $=\frac{108}{100}\times$ cost =

$\frac{108}{100}\times 5,000=Rs5,400$

Money to be earned through sale of remaining 80 kg

$=Rs5,400-Rs2,200-Rs960=Rs2,240$

Selling price of the remainder rice $=\frac{Rs2,240}{80kg}=Rs28/kg$