The price of an item is successively increased by 20% and 30%. and then decreased successively by 15% and 25%. If
the difference between the final price and the original price of the item is ₹17.60. then the original price of the item is:

Correct option is A

Given:

Successive increases: 20% and 30%

Successive decreases: 15% and 25%

Difference between final price and original price = ₹17.60

Formula Used:  

Successive first decrease and increase ; 

Effective Price = Original Price × $$\left(1 - \frac{d1}{100}\right) × \left(1 + \frac{d2}{100}\right)$$

Solution: 

Let the original price be P 

Final Price = P × $$\frac{120}{100}\times \frac{130}{100}\times \frac{85}{100}\times\frac{75}{100}$$​

= P × $$\frac{1989}{2000}$$​​

Now,

Final Price - Original Price  = ₹17.60

P × $$\frac{1989}{2000}$$ - P = 17.60 

​$$\frac{2000P - 1989P }{2000} = 17.60 \\ \ \\ \frac{11P}{2000} = 17.60 \\ \ \\ P = \frac{17.60 \times 2000}{11} = ₹3200$$​​

The original price of the item is ₹3,200