Calculating Final Price After Successive Discounts

The problem asks for the final price of a Rs. 1000 item after applying two successive discounts: 20% and then 10%. We need to calculate the price step-by-step.

Step 1: Calculate Price After First Discount

The initial price of the item is Rs. 1000.

The first discount is 20%. The amount of the first discount is:

$Discount_1$ = 20% of Rs. 1000

$ \text{Discount\_1} = \frac{20}{100} \times 1000 = 0.20 \times 1000 = 200 $

The price after the first discount is:

$ \text{Price\_1} = \text{Original Price} - \text{Discount\_1} $

$ \text{Price\_1} = 1000 - 200 = 800 $

So, after the first 20% discount, the price becomes Rs. 800.

Step 2: Calculate Price After Second Discount

The second discount of 10% is applied to the price obtained after the first discount (Rs. 800).

The amount of the second discount is:

$Discount_2$ = 10% of Rs. 800

$ \text{Discount\_2} = \frac{10}{100} \times 800 = 0.10 \times 800 = 80 $

The final price paid by the buyer is:

$ \text{Final Price} = \text{Price\_1} - \text{Discount\_2} $

$ \text{Final Price} = 800 - 80 = 720 $

Alternative Method: Combined Discount Calculation

We can also calculate the final price directly:

$ \text{Final Price} = \text{Original Price} \times (1 - \text{Discount Rate 1}) \times (1 - \text{Discount Rate 2}) $

$ \text{Final Price} = 1000 \times (1 - 0.20) \times (1 - 0.10) $

$ \text{Final Price} = 1000 \times (0.80) \times (0.90) $

$ \text{Final Price} = 1000 \times 0.72 $

$ \text{Final Price} = 720 $

Conclusion

The final price paid for the item after successive discounts of 20% and 10% is Rs. 720.