An order was placed for the supply of a carpet whose breadth w... | Mathematics MCQ

MathematicsPrevious Year Paper 2024

An order was placed for the supply of a carpet whose breadth was 6 m and whose length were 1.44 times the breadth. What is the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. [The cost of a carpet is Rs. 45 per sq m.]

Rs. $3642.60$

Rs. $4216.20$

Rs. $4082.40$

Rs. $3868.80$

Correct Answer

📐 MA • Math Ratio & MultiplierMathematicsPrevious Year Paper 2024

Option C

Rs. $4082.40$

Quick Summary:

Area multiplies by $1.40 \times 1.25 = 1.75$ . Original Area $= (1.44 \times 6) \times 6 = 51.84\text{ m}^2$ . New Area $= 51.84 \times 1.75 = 90.72\text{ m}^2$ . Total Cost $= 90.72 \times 45 = \text{Rs. } 4082.40$ .

🎯

Crack Previous Year Paper 2024 with Examoogle SuperTeachers

Get Free Demo Classes & Live Mocks →

📐MAMath SolutionRatio & Multiplier

📋 Given

Carpet 1: Breadth $b_1 = 6\text{ m}$ , Length $l_1 = 1.44 \times 6\text{ m}$ . Carpet 2: Length $l_2 = 1.40 \times l_1$ , Breadth $b_2 = 1.25 \times b_1$ . Rate = $\text{Rs. } 45/\text{m}^2$ .

🔢 Formula Used

Total Cost=Area2×Rate=(l1×1.40)×(b1×1.25)×45\text{Total Cost} = \text{Area}_2 \times \text{Rate} = (l_1 \times 1.40) \times (b_1 \times 1.25) \times 45Total Cost=Area2​×Rate=(l1​×1.40)×(b1​×1.25)×45

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Calculating individual lengths and breadths first and rounding intermediate values leads to decimal errors. Use direct multiplier $1.40 \times 1.25 = 1.75$ .

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate Dimensions of Carpet 1

Breadth $b_1 = 6\text{ m}$ . Length $l_1 = 1.44 \times b_1 = 1.44 \times 6 = 8.64\text{ m}$ .

l1=8.64 m,b1=6 ml_1 = 8.64\text{ m}, \quad b_1 = 6\text{ m}l1​=8.64 m,b1​=6 m

Determine Dimensions of Carpet 2

Length is increased by $40\%$ and breadth by $25\%$ . Thus, $l_2 = 1.40 \times l_1 = 1.40 \times 8.64 = 12.096\text{ m}$ and $b_2 = 1.25 \times b_1 = 1.25 \times 6 = 7.5\text{ m}$ .

l2=12.096 m,b2=7.5 ml_2 = 12.096\text{ m}, \quad b_2 = 7.5\text{ m}l2​=12.096 m,b2​=7.5 m

Calculate Area of Carpet 2

Multiplying new length and breadth gives the new area: $A_2 = 12.096 \times 7.5 = 90.72\text{ m}^2$ .

Area2=90.72 sq m\text{Area}_2 = 90.72\text{ sq m}Area2​=90.72 sq m

Calculate Total Cost

Multiply the total area of Carpet 2 by the given rate per sq m: $\text{Cost} = 90.72 \times 45 = 4082.40$ .

Total Cost=Rs. 4082.40\text{Total Cost} = \text{Rs. } 4082.40Total Cost=Rs. 4082.40

✅

Option C is correct because multiplying the new carpet area of $90.72\text{ sq m}$ by the rate of $\text{Rs. } 45/\text{sq m}$ gives $\text{Rs. } 4082.40$ .

Core Concepts Used

Click any tag to open in AI Tutor

Mensuration - Area of Rectangle Percentage Increase Multipliers Cost Calculation

💡 EXAM TIP

Whenever dimensions scale by factors $k_1$ and $k_2$ , the new area scales directly by $k_1 \times k_2$ . This technique is frequently used in profit-loss and successive percentage questions.

Was this solution helpful?

⚡ Practice on Android App · 4.8 ★

Solve 10,000+ More Questions with AI Tutor

Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.

Free Download • 100K+ Aspirants

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)