The selling price of 30 books is equal to the cost price of 45... | Mathematics MCQ | Examoogle

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MathematicsPrevious Year Paper 2024

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The selling price of 30 books is equal to the cost price of 45 books. Find the loss or gain percentage.

50 % gain

$\frac{100}{15}\% \text{ gain}$

50 % loss

$\frac{100}{15}\% \text{ loss}$

Correct Answer

📐 MA • Math Direct FormulaMathematicsPrevious Year Paper 2024

Option A

50 % gain

Quick Summary:

When $SP \times N_1 = CP \times N_2$ , if $N_2 > N_1$ , there is a gain. The gain % is $\frac{N_2 - N_1}{N_1} \times 100$ . Here, $\frac{45-30}{30} \times 100 = \frac{15}{30} \times 100 = 50\%$ .

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📐MAMath SolutionDirect Formula

📋 Given

Selling price of 30 books = Cost price of 45 books.

🔢 Formula Used

Gain percentage=(Cost quantity−Selling quantitySelling quantity)×100\text{Gain percentage} = \left( \frac{\text{Cost quantity} - \text{Selling quantity}}{\text{Selling quantity}} \right) \times 100Gain percentage=(Selling quantityCost quantity−Selling quantity​)×100

⚡ Exam Hall Shortcut / Speed Trick

When $SP \times N_1 = CP \times N_2$ , if $N_2 > N_1$ , there is a gain. The gain % is $\frac{N_2 - N_1}{N_1} \times 100$ . Here, $\frac{45-30}{30} \times 100 = \frac{15}{30} \times 100 = 50\%$ .

⚠️ Common Student Trap / Pitfall

Many students calculate loss or gain based on the count of 45 instead of the selling quantity (30), leading to incorrect denominators like 45.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Set up the equation

Let the cost price of one book be $C$ and the selling price be $S$ . We are given $30 \times S = 45 \times C$ .

30S=45C30S = 45C30S=45C

Determine Ratio

Rearrange the equation to find the ratio of $S$ to $C$ . $$S/C = 45/30 = 3/2$. This means for every 2 units of cost, the selling price is 3 units.

SC=32\frac{S}{C} = \frac{3}{2}CS​=23​

Calculate Gain Percentage

Since $S > C$ , it is a gain. The gain is $3 - 2 = 1$ . The percentage is calculated relative to the cost price: $(1/2) \times 100 = 50\%$ .

Gain %=(3−22)×100=50%\text{Gain \%} = \left( \frac{3-2}{2} \right) \times 100 = 50\%Gain %=(23−2​)×100=50%

✅

A is correct because the ratio of selling price to cost price is 3:2, resulting in a profit of 50%.

Core Concepts Used

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Profit and Loss Ratio and Proportion Cost Price vs Selling Price

💡 EXAM TIP

This type of inverse relationship problem frequently appears in Ratio/Proportion and Time-Work (where number of workers inversely relates to time) chapters.

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