The selling price of 25 books is equal to the cost price of 41 books. Find the loss or gain percentage.

Question

Examoogle · Accepted Answer

The correct answer is Option B: 64 % gain. Use the formula: $\left( \frac{	ext{CP count} - 	ext{SP count}}{	ext{SP count}} ight) 	imes 100$. Here: $\frac{41 - 25}{25} 	imes 100 = \frac{16}{25} 	imes 100 = 64\%$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Use the formula: $\left( \frac{	ext{CP count} - 	ext{SP count}}{	ext{SP count}} ight) 	imes 100$. Here: $\frac{41 - 25}{25} 	imes 100 = \frac{16}{25} 	imes 100 = 64\%$.

Formula Used: $$	ext{Gain percentage} = \left( \frac{	ext{Quantity sold for SP} - 	ext{Quantity bought for CP}}{	ext{Quantity sold for SP}} ight) 	imes 100$$

Given: Selling price (SP) of 25 books = Cost price (CP) of 41 books.

Steps: Set up the equation: Given that the Selling Price ($SP$) of 25 books equals the Cost Price ($CP$) of 41 books, we write: $25 	imes SP = 41 	imes CP$.. Find the ratio of CP to SP: Rearrange the equation to find the ratio of $SP$ to $CP$: $\frac{SP}{CP} = \frac{41}{25}$.. Calculate the gain percentage: Since $SP > CP$, it is a gain. The gain is $SP - CP = 41 - 25 = 16$ units. Gain percentage is $\frac{	ext{Gain}}{CP} 	imes 100 = \frac{16}{25} 	imes 100$.

Answer: B is correct because the calculated gain percentage is $64\%$.

Exam Tip: This type of 'item-based' profit/loss question is a standard in competitive exams; always identify which quantity corresponds to the denominator (the base value) to avoid the common inversion error.

Examoogle · Answer

Option A: $\frac{100}{16} \% 	ext{ gain}$

Examoogle · Answer

Option C: $\frac{100}{16} \% 	ext{ loss}$

Examoogle · Answer

Option D: 64 % loss

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)