A retail store placed an order for 8 dozen class-A notebooks and a certain number of dozen class-B notebooks. The price of one dozen class-A notebooks is 2.5 times that of one dozen class-B notebooks. Upon arrival of the order, it was discovered that the ordered quantities of the two types of notebooks had been interchanged, which resulted in a 50% increase in the total bill amount. What was the original ratio of the quantity of class-A notebooks to class-B notebooks ordered?

The correct option is 4:11.

Here is the step-by-step solution to find the original ratio of class-A to class-B notebooks ordered:

Step 1: Define the variables for price and quantity.

Let the price of one dozen class-B notebooks be $p$.

The price of one dozen class-A notebooks is 2.5 times that of one dozen class-B notebooks.

Price of 1 dozen class-A notebooks = $2.5p$

Quantity of class-A notebooks ordered = $8$ dozen.

Let the quantity of class-B notebooks ordered = $x$ dozen.

Step 2: Calculate the original bill amount.

The original bill amount ($B_1$) is calculated as:

$B_1=(8\times 2.5p)+(x\times p)$

$B_1=20p+xp=(20+x)p$

Step 3: Calculate the new bill amount after interchanging quantities.

Upon arrival, the ordered quantities of the two types of notebooks were interchanged:

Quantity of class-A notebooks received = $x$ dozen.

Quantity of class-B notebooks received = $8$ dozen.

The new bill amount ($B_2$) becomes:

$B_2=(x\times 2.5$

)+(8×p)

$B_2=2.5xp+8p=(2.5x+8)p$

Step 4: Set up the equation using the given percentage increase.

Interchanging the quantities resulted in a 50% increase in the total bill amount. Therefore:

$B_2=1.5B_1$

Substitute the expressions for $B_1$ and $B_2$:

$(2.5x+8)p=1.5\times (20+x)p$

Divide both sides of the equation by $p$:

$2.5x+8=1.5(20+x)$

Expand the right side:

$2.5x+8=30+1.5x$

Subtract $1.5x$ and $8$ from both sides:

$2.5x-1.5x=30-8$

$x=22$

So, $22$ dozen class-B notebooks were originally ordered.

Step 5: Calculate the original ratio of class-A to class-B notebooks ordered.

$\text{Original Ratio}=\text{Class-A}:\text{Class-B}=8:22$

Simplifying the ratio by dividing both numbers by 2:

$\text{Original Ratio}=4:11$

Thus, the original ratio of the quantity of class-A notebooks to class-B notebooks ordered was 4:11.