Understanding the Problem

We are given a relationship between the selling price (SP) of a certain number of items and the cost price (CP) of another number of items. The goal is to find the overall gain or loss percentage.

• Given: SP of 10 books = CP of 16 books.
• To Find: Gain or Loss Percentage.

Setting up the Equation

Let the cost price (CP) of one book be $C$ and the selling price (SP) of one book be $S$.

From the problem statement, we can write the equation:

$10 \times S = 16 \times C$

Calculating Selling Price relative to Cost Price

We can express the selling price ($S$) in terms of the cost price ($C$):

$S = \frac{16}{10} \times C$

$S = 1.6 \times C$

Since the selling price ($S = 1.6 \times C$) is greater than the cost price ($C$), there is a gain.

Calculating Gain Percentage

The gain amount for one book is:

$Gain = S - C$

$Gain = (1.6 \times C) - C$

$Gain = 0.6 \times C$

The gain percentage is calculated using the formula:

$Gain \ Percentage = \left( \frac{Gain}{C} \right) \times 100$

Substitute the value of Gain:

$Gain \ Percentage = \left( \frac{0.6 \times C}{C} \right) \times 100$

$Gain \ Percentage = 0.6 \times 100$

$Gain \ Percentage = 60\%$

Conclusion

Therefore, there is a gain of 60%.