A shop owner offers the following discount options on an article to a customer:
1. Successive discounts of 10% and 20%, and then pay a service tax of 10%
2. Successive discounts of 20% and 10%, and then pay a service tax of 10%
3. Pay a service tax of 10% first, then successive discounts of 20% and 10%
Which one of the following is correct?

To determine which option is the best for the customer, let us calculate the final amount a customer pays under each of the three given schemes.

Let the marked price (or original price) of the article be P.

Analysis of Option 1:

Successive discounts of 10% and 20%, followed by a service tax of 10%.

• After a 10% discount, the price becomes $P\times (1-0.10)=P\times 0.90$

• After a second discount of 20%, the price becomes $P\times 0.90\times (1-0.20)=P\times 0.90\times 0.80$

• Adding a service tax of 10% increases the final price by a factor of $(1+0.10)=1.10$

So, the final amount paid in Option 1 is:

${\mathrm{Final\; Price}}_1=P\times 0.90\times 0.80\times 1.10=P\times 0.792$

Analysis of Option 2:

Successive discounts of 20% and 10%, followed by a service tax of 10%.

• After a 20% discount, the price becomes $P\times 0.80$

• After a second discount of 10%, the price becomes $P\times 0.80\times 0.90$

• Adding a service tax of 10%, the price becomes:

${\mathrm{Final\; Price}}_2=P\times 0.80\times 0.90\times 1.10=P\times 0.792$

Analysis of Option 3:

Paying a service tax of 10% first, then successive discounts of 20% and 10%.

• Adding a service tax of 10% first, the price becomes $P\times 1.10$

• Applying a discount of 20%, the price becomes $P\times 1.10\times 0.80$

• Applying a further discount of 10%, the price becomes:

${\mathrm{Final\; Price}}_3=P\times 1.10\times 0.80\times 0.90=P\times 0.792$

Conclusion:

Since multiplication is commutative ($a\times b\times c=b\times a\times c$), the order in which percentage increases and percentage decreases are applied does not affect the ultimate final price.

In all three options, the customer pays exactly $0.792\times P$ (or 79.2% of the original price).

Therefore, All the options are equally good for the customer.