What is a single discount equivalent to two successive discounts of 20% and 10%?a)28%b)38%c)22%d)32%Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Let be assumed the m.p( marked price) of an object is
100Rs.
As per the question , After applying two successive discounts i.e.,
20% of 100= 100 - 20 = 80 Rs.
then 10% of 80 = 80 - 8 = 72 Rs.
Here, Total discount = 100 - 72
= 28 Rs
Now the discount% = 28/100 × 100
= 28% ___
___

Answer

Let the marked price = ` 100
and Discount = 20%
then 100 – 20 = 80
Discount = 10% of 80
=

80 – 8 = 72
Successive discount = 100 – 72 = 28%

Answer

Calculation of single discount equivalent to two successive discounts of 20% and 10%:

To find the single discount equivalent to two successive discounts of 20% and 10%, we can use the concept of successive percentage changes.

Step 1: Finding the first discount equivalent:
When a discount of 20% is applied, it means the price is reduced by 20% of the original price. This can be calculated as follows:
Discount = 20% of original price = (20/100) * original price

After the first discount, the remaining price is 80% of the original price:
Remaining price = 100% - 20% = 80% of original price = 0.8 * original price

Step 2: Finding the second discount equivalent:
When a discount of 10% is applied to the remaining price, it means the price is reduced by 10% of the remaining price. This can be calculated as follows:
Discount = 10% of remaining price = (10/100) * remaining price

After the second discount, the final price is 90% of the remaining price:
Final price = 100% - 10% = 90% of remaining price = 0.9 * remaining price

Step 3: Finding the single discount equivalent:
Now, we need to find the single discount that is equivalent to the two successive discounts mentioned above. We want to find the discount that will reduce the original price directly to the final price.

Let the single discount be x% of the original price:
Final price = Original price - x% of original price

From Step 2, we know that the final price is 0.9 times the remaining price:
0.9 * remaining price = Original price - x% of original price

From Step 1, we know that the remaining price is 0.8 times the original price:
0.9 * 0.8 * original price = Original price - x% of original price

Simplifying the equation:
0.72 * original price = Original price - x% of original price

0.28 * original price = x% of original price

Therefore, the single discount equivalent is 28%.

Hence, the correct answer is option A) 28%.

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