Maths question from Laboratory Attendant exam, 2026 by JKSSB
The length breadth and height of a rectangular box are in the ratio 3: 2:4, respectively, and the cost of covering it with a sheet of paper at the rate of Rs. 1.50 per square metre is Rs. 1,950. Find 50% of the volume of the box (in m³).
Last updated Jun 13, 2026
Correct Answer:
Option A —
1500
Step-by-Step Breakdown:
Find the Total Surface Area:
The total cost to cover the box with paper is Rs. 1,950, and the rate is Rs. 1.50 per square meter.
To find the total surface area, we divide the total cost by the rate per square meter:
1,950 divided by 1.50 equals 1,300 square meters.
Set up the Dimensions using the Ratio:
The length, breadth, and height are in the ratio 3 to 2 to 4.
Let's define a common multiplier, which we will call "x".
Length = 3 times x
Breadth = 2 times x
Height = 4 times x
Use the Surface Area Formula:
The total surface area of a rectangular box is calculated by finding the area of all six faces: 2 times the sum of (length times breadth plus breadth times height plus length times height).
Length times Breadth = (3 times x) multiplied by (2 times x) = 6 times x-squared
Breadth times Height = (2 times x) multiplied by (4 times x) = 8 times x-squared
Length times Height = (3 times x) multiplied by (4 times x) = 12 times x-squared
Summing these up: 6 plus 8 plus 12 equals 26 times x-squared.
Multiplying by 2 for all six faces: 2 multiplied by 26 times x-squared equals 52 times x-squared.
Solve for the Multiplier (x):
We know the total surface area is 1,300 square meters:
52 times x-squared equals 1,300
x-squared equals 1,300 divided by 52, which equals 25
Since 5 multiplied by 5 is 25, our multiplier "x" is 5.
Calculate the Actual Dimensions:
Length = 3 multiplied by 5 = 15 meters
Breadth = 2 multiplied by 5 = 10 meters
Height = 4 multiplied by 5 = 20 meters
Find 50% of the Volume:
The total volume is length multiplied by breadth multiplied by height: 15 multiplied by 10 multiplied by 20 = 3,000 cubic meters.
We need to find 50 percent of this volume: 50 percent of 3,000 is 1,500 cubic meters.
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
