A grocer professes to sell rice at the cost price, but uses a fake weight of 870 g for 1 kg. Find his profit percentage (correct to two decimal places).

The grocer claims to sell rice at its cost price, meaning the selling price of the rice he claims to sell is equal to its cost price. However, he uses a fake weight of 870 g instead of 1 kg (1000 g). This means for every 1 kg the customer pays for, the grocer only gives them 870 g of rice.

Let the cost price of 1 g of rice be $x$.
Then, the cost price of 1000 g (1 kg) of rice is $1000x$.
Since the grocer claims to sell the rice at cost price, the selling price of the quantity he sells as "1 kg" is equal to the cost price of 1 kg:
$\text{Selling Price (SP)}=1000x$

However, the actual quantity of rice he gives to the customer is only 870 g. Therefore, the actual cost to the grocer for this transaction is the cost price of 870 g:
$\text{Cost Price (CP)}=870x$

Now, we calculate the profit made by the grocer:
$\text{Profit}=\text{SP}-\text{CP}$
$\text{Profit}=1000x-870x=130x$

To find the profit percentage, we use the formula:
$\text{Profit Percentage}=\left(\frac{\text{Profit}}{\text{CP}}\right)\times 100$
$\text{Profit Percentage}=\left(\frac{130x}{870x}\right)\times 100$
$\text{Profit Percentage}=\frac{130}{870}\times 100$
$\text{Profit Percentage}=\frac{13}{87}\times 100$
$\text{Profit Percentage}=\frac{1300}{87}\approx 14.9425\%$

Rounding to two decimal places, we get 14.94%.