The price of an electronic machine decreased by 5%, 10% and 15% during the first three years. What will be the price of the machine after three years if the value at the beginning was ₹ 8,000?

Correct option is B

Given:
Initial price = ₹8000
Price decreases: 5% in the first year, 10% in the second year, 15% in the third year.
Formula Used:
Successive percentage decrease formula:
After each year:
New Price = Old Price $$\times \left(1 - \frac{\text{percentage decrease}}{100}\right)$$​​
Solution:
After 1st year:
​$$8000 \times \left(1 - \frac{5}{100}\right) = 8000 \times 0.95 = 7600$$​​
After 2nd year:
​$$7600 \times \left(1 - \frac{10}{100}\right) = 7600 \times 0.90 = 6840$$​​
After 3rd year:
​$$6840 \times \left(1 - \frac{15}{100}\right) = 6840 \times 0.85 = 5814$$​​
Thus, the correct option is (b) ₹5,814
Alternate Solution:

Let, final price is x.
Cumulative successive percentage formula:
Final price = Initial price × (successive percentage decrease)

5% = $$-\frac{1}{20}$$ ; 10% = - $$-\frac{1}{10}$$ ; 15 % = -$$\frac{3}{20}$$​​

$$x = 8000 \times \frac{19}{20} \times \frac{9}{10} \times \frac{17}{20} = ₹5,814$$​​