Mr. Cook sold a book at a profit of 14%. If he had sold it for Rs. 5.40 more, then he would have made a profit of 20%. Find the cost price of the book.

Correct option is D

Given:
Mr. Cook sold the book at a 14% profit,
If he had sold it for 5.40 more, his profit would have been 20%
Formula Used:
​$$\text{Selling Price (SP)} = \text{Cost Price (CP)} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right)$$​​
Solution:

Let the cost price be x
First Selling Price at 14% profit:
Selling Price=$$x \times \left(1 + \frac{14}{100}\right) = x \times 1.14$$​​
If he had sold it for 25.40 more, his profit would have been 20%
Selling Price= $$x \times \left(1 + \frac{20}{100}\right) = x \times 1.20$$​​
Since selling it for 5.40 more results in the 20% profit:
1.20x-1.14x = 5.40
0.06x=5.40
x= 90
Cost Price of the book= Rs. 90
Alternate Solution:
Selling price at 14% profit = CP + 14% of CP = 1.14CP
If he had sold it for 25.40 more, the selling price would be 1.14CP + 5.40
Profit in this case = 20%
So, 1.14CP + 5.40 = CP + 20% of CP
1.14CP + 5.40 = 1.2CP
0.06CP = 5.40
CP = $$\frac{5.40}{0.06} = 90$$​​
CP = Rs. 90