A shopkeeper ordered 12 kg of premium coffee and some kg of regular coffee. The price of premium coffee per kg was three times that of regular coffee. Due to a billing mistake, the quantities of the two types were interchanged, which reduced the total bill by 30%. What was the ratio of the quantity of premium coffee to regular coffee in the original order?

The correct option is 23:11.

Let us solve this step-by-step to find the original ratio of the quantity of premium coffee to regular coffee.

Step 1: Define the variables for price and quantity.

Let the price of 1 kg of regular coffee be $p$.
Since the price of premium coffee per kg is three times that of regular coffee, the price of 1 kg of premium coffee is $3p$.

Let the original ordered quantity of regular coffee be $x$ kg.
The original ordered quantity of premium coffee is given as $12$ kg.

Step 2: Calculate the original bill amount.

Original Bill = (Quantity of Premium × Price of Premium) + (Quantity of Regular × Price of Regular)
Original Bill = $(12\times 3p)+(x\times p)$
Original Bill = $36p+xp=p(36+x)$

Step 3: Calculate the interchanged (new) bill amount.

Due to the billing mistake, the quantities were interchanged. So, the billed quantity of premium coffee became $x$ kg, and regular coffee became $12$ kg.

New Bill = (Interchanged Quantity of Premium × Price of Premium) + (Interchanged Quantity of Regular × Price of Regular)
New Bill = $(x\times 3p)+(12\times p)$
New Bill = $3xp+12p=p(3x+12)$

Step 4: Use the percentage reduction condition.

The total bill was reduced by 30%, which means the New Bill is 70% (or $0.7$) of the Original Bill.

$\text{New Bill}=0.7\times \text{Original Bill}$

Substituting the expressions derived for both bills:

$p(3x+12)=0.7\times p(36+x)$

Since $p$ (price) is non-zero, we can cancel $p$ from both sides:

$3x+12=0.7(36+x)$

Multiply both sides by 10 to clear the decimal:

$10(3x+12)=7(36+x)$
$30x+120=252+7x$

Subtract $7x$ and $120$ from both sides:

$30x-7x=252-120$
$23x=132$
$x=\frac{132}{23}$ kg

Step 5: Find the ratio of premium coffee to regular coffee in the original order.

$\text{Ratio}=\frac{\text{Quantity of Premium Coffee}}{\text{Quantity of Regular Coffee}}$
$\text{Ratio}=\frac{12}{x}=\frac{12}{\left(\frac{132}{23}\right)}$
$\text{Ratio}=\frac{12\times 23}{132}$

Dividing both numerator and denominator by 12:

$\text{Ratio}=\frac{23}{11}$

Thus, the required ratio of the quantity of premium coffee to regular coffee in the original order is 23:11.