Maths question from Laboratory Attendant exam, 2026 by JKSSB
A man ordered 4 pairs of black socks and some pairs of brown socks. The price of a black socks is double that of a brown pair. While preparing the bill the clerk interchanged the number of black and brown Pairs by mistake which increased the bill by 50%. The ratio of the number of black and brown pairs of socks in the original order was:
Last updated Jun 13, 2026
Correct Answer:
Option B —
1:4
Step-by-Step Breakdown:
Set Up the Prices:
We are told that the price of a black pair of socks is double that of a brown pair.
Let's assume the price of a brown pair is 1 unit. This means the price of a black pair is 2 units.
Understand the Quantities:
The original order contains 4 pairs of black socks. Let the unknown number of brown socks be represented by the word "Brown".
Calculate the Original Bill:
4 pairs of black socks at 2 units each equals 8 units.
"Brown" pairs of brown socks at 1 unit each equals "Brown" units.
Total Original Bill = 8 plus "Brown".
Calculate the Mistaken Bill:
The clerk interchanged the quantities by mistake. Now, there are "Brown" pairs of black socks and 4 pairs of brown socks.
"Brown" pairs of black socks at 2 units each equals 2 times "Brown" units.
4 pairs of brown socks at 1 unit each equals 4 units.
Total Mistaken Bill = 4 plus 2 times "Brown".
Apply the 50% Increase Condition:
We are told that this mistake increased the bill by 50 percent. This means the mistaken bill is 1.5 times (or 3 divided by 2 times) the original bill.
Let's set up the relationship:
Mistaken Bill = 1.5 times the Original Bill
4 plus 2 times "Brown" = 1.5 times (8 plus "Brown")
4 plus 2 times "Brown" = 12 plus 1.5 times "Brown"
Solve for the Number of Brown Socks:
Subtract 1.5 times "Brown" from both sides: 0.5 times "Brown" plus 4 = 12.
Subtract 4 from both sides: 0.5 times "Brown" = 8.
If half of the brown pairs equals 8, then the total number of brown pairs must be 16.
Find the Original Ratio:
The original order had 4 pairs of black socks and 16 pairs of brown socks.
The ratio of black to brown is 4 to 16.
Simplifying this by dividing both numbers by 4 gives a ratio of 1 to 4.
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
