A room is 15 ft long and 12 ft broad.\nA rectangular mat is to be placed on the floor, leaving a uniform space of 1.5 ft from all the walls (on every side).\nWhat will be the cost of the mat at the rate of ₹3.50 per sq ft?

Introduction:
This question tests area calculation after reducing dimensions due to margins. The mat does not cover the entire floor; it leaves a uniform gap from the walls. That means both length and breadth of the usable mat area reduce by twice the margin (once on each opposite side). After finding the mat’s area, multiplying by the cost per square foot gives the total cost. This is a direct, single-formula aptitude problem, but it checks attention to detail: many mistakes happen when people subtract the margin only once instead of twice.

Given Data / Assumptions:

• Room length = 15 ft
• Room breadth = 12 ft
• Space from walls on each side = 1.5 ft
• Cost rate = ₹3.50 per sq ft
• Mat dimensions reduce on both sides, so subtract 2 * 1.5 from each dimension

Concept / Approach:
Mat length = 15 - 2*1.5 and mat breadth = 12 - 2*1.5. Then mat area = length * breadth. Finally cost = area * rate. The key idea is “uniform border on all sides” means the reduction happens twice per dimension.

Step-by-Step Solution:
Mat length = 15 - 2*1.5 = 15 - 3 = 12 ftMat breadth = 12 - 2*1.5 = 12 - 3 = 9 ftMat area = 12 * 9 = 108 sq ftCost = 108 * 3.50 = 378

Verification / Alternative Check:
Check the border logic: leaving 1.5 ft on left and 1.5 ft on right consumes 3 ft of total length. Similarly, leaving 1.5 ft on top and bottom consumes 3 ft of total breadth. So 12 ft by 9 ft is consistent. Multiplying 108 by ₹3.50 is also straightforward: 108*3 = 324 and 108*0.5 = 54, total 378.

Why Other Options Are Wrong:
₹472.50 or ₹496: usually from using wrong mat dimensions or wrong multiplication.₹630: often from taking full room area 15*12 = 180 and multiplying by 3.5.₹405: comes from subtracting margin only once in one dimension.

Common Pitfalls:
Subtracting 1.5 only once instead of twice from length/breadth.Using room area instead of mat area.Mixing up “per sq ft” with “per ft”.Arithmetic error in 108 * 3.50.

Final Answer:
₹378