Question

A stationery supplier ordered 8 boxes of premium pens and some boxes of standard pens. The price of premium pens per box was twice that of standard pens. When the order was delivered. the number of boxes of premium and standard pens had been. accidentally interchanged. This increased the total bill by 25%. What was the ratio of the original number of boxes of premium pens to the original number of boxes of standard pens?

• A. 2 : 1
• B. 1 : 3
• C. 1 : 2
• D. 3 : 1

Answer 1

Answer:

C. 1 : 2

Let the price per box of standard pens be x.
Then premium pens cost 2x per box.

Step 1: Let original quantities be

• Premium boxes = 8

• Standard boxes = (y)

• Step 2: Original bill

$8 \cdot 2x + y \cdot x = 16x + yx = (16 + y)x$

Step 3: After interchange

Now premium and standard quantities are swapped:

• Premium = (y)

• Standard = 8

New bill:
$y \cdot 2x + 8 \cdot x = 2yx + 8x = (2y + 8)x$

Given condition (25% increase)

$(2y + 8)x = 1.25(16 + y)x$

Cancel (x):
$2y + 8 = 1.25(16 + y)$

Multiply:
$2y + 8 = 20 + 1.25y$

Step 5: Solve

$2y - 1.25y = 20 - 8$
$0.75y = 12$
$y = 16$

Step 6: Required ratio

Original premium : standard
8 : 16 = 1 : 2

Final Answer: 1 : 2