Question

A stationery shop ordered 6 dozen red pens and some additional dozen blue pens. The price of the red pens per dozen was three times that of the blue ones. When the order was delivered, it was found that the number of dozens of the two colours had been interchanged. This increased the bill by 40%. Find the ratio of the number of dozens of red pens to the number of dozens of blue pens in the original order.

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

Answer 1

Answer:

B. 1 : 2

Let the price of 1 dozen blue pens be ₹(x).

Then the price of 1 dozen red pens is ₹(3x).

Given:

• Red pens ordered = 6 dozen

• Blue pens ordered = (b) dozen

Original bill

$6(3x)+b(x)=18x+bx=(18+b)x$

Delivered order (quantities interchanged)

• Red pens delivered = (b) dozen

• Blue pens delivered = 6 dozen

New bill:

b(3x)+6(x)=3bx+6x=(3b+6)x

The bill increased by 40%, so:

(3b+6)x=1.4(18+b)x

Cancel (x):

3b+6=25.2+1.4b
1.6b=19.2
b=12

Therefore, the original order was:

• Red pens = 6 dozen

• Blue pens = 12 dozen

So the required ratio is

6:12 = 1:2

✅ Answer: (1:2).