Percentage topic is one of the most common topics asked in competitive exams. You can be sure that there will be 3 – 4 questions always asked in any competitive exams. But the percentage is a very vast topic. There are almost 7 – 8 topics that you need to cover in percentage before being able to solve any question in the competitive exam. And that is why we have decided to go step by step and explain to you each topic in detail. And today our topic will be consecutive decrease.

### Suggested Videos

## Consecutive Decrease

The phenomena of a decrease in prices occurring more than once are called consecutive decrements. In reality, the prices of a commodity decrease when the items are on the sale or through discounts or any promotional offers, etc. We will also look at the types of questions that can come in section and will also have different types of questions for practice at the end.

## Solved Examples

Q. A shopkeeper gives a successive discount of 10 %, 20 %, and 10 % respectively. What is the total percentage of discount does the shopkeeper avail to the customer?

A. 36 %

B. 40 %

C. 35.5 %

D. 35.2 %

This type of question is very common in the consecutive decrease. Usually, you will be asked the discount or the selling price of the product after the discount.

Now, in this question, three successive discounts are given. For the first discount, let’s suppose that the base cost price was Rs. 100. So after 10 % of discount, the price will be Rs. 90. Again there is a 20 % discount so the price will be 20 % of 90 = 18 => 90 – 18 = Rs. 72. There is a third discount of 10 % as well. So, the final price will be 72 – 10 % of 72 = 72 – 7.2 = 64.8. For the total discount, 100 – 64.8 = 35.2. 35.2 % is the total discount availed by the shopkeeper to the customer. Thus, the correct answer is D.

## Decrease After Increase

This is another type of question asked in the consecutive decrease. If the price is increased by a %, and the price of the product is again decreased by the same a %, then in there-there will be a decrease of a^2 %.

Q. Suppose Ram’s salary was increased by 40 % and then again his salary was decreased by 40 %. What will be the net change in Ram’s salary?

A. 80 %

B. 8 %

C. 16 %

D. 1.6 %

Here, you can see that the increase and decrease in salary are done by 40 %. So, the net change will decrease in Ram’s salary. This will be calculated by (40 x 40)/100 = 16 %. Thus there is a net decrease of 16 % in Ram’s salary. The correct answer is C.

One must be wondering why is there decrease in salary even though there are an increase and decrease by the same percentage. Because the base amount on which we increase Ram’s salary is low as compared to the base amount on which we decrease Ram’s salary. And thus percentage on lower base amount < percentage on the higher base amount.

## Example Based on Wealth

Q. Anil receives a fortune from his father. He decides to invest it in the real estate and loses 32.5 %. Out of the balance left the thief stole Rs. 1,00,000. From the rest that is left with Anil, he decides to donate 20 % to the blind welfare fund. Further, he purchases a brand new car of Rs. 7.5 lakh. After all this, Anil makes a total and realizes that he is left with a cash of Rs. 2.5 lakh only. What was the total fortune that Anil inherited from his father?

A. 20 lakh

B. 25 lakh

C. 18 lakh

D. 22.5 lakh

This type of question is better solved using the options. If the options are given then you start solving options one by one. When there are no options given then you should start from the bottom.

Suppose, in this question the amount that is left is Rs. 2.5 lakh. This was left after purchasing the car of Rs. 7.5 lakhs. So he had Rs. 10 lakh before the purchase of a car. Before car, Anil donated 20 % amount. So, a decrease of 20 % is 25 % of the increase. So the total amount was Rs. 12.5 lakh before the donation. Before donation Rs. 1 lakh were stolen. So he Rs. 13.5 lakh. Now, he was left with 13.5 after a loss of 32.5%. Without the options, you need to try the trial and error and take different values to see the reduction on which value will Rs. 13.5. So, the answer is Rs. 20 lakh. When you have enough practice you will get this value very quickly.

The other way to go around this is using options. In option 1, the value given to us is Rs. 20 lakh. So, decrease from 20 lakh by 32.5 % will give 13.5 lakh. Further 1 lakh were stolen. So the value reduces to 12.5 lakh. Now, we give away 20 % in a donation. So, the value left with Anil is Rs. 10 lakh. Out of this, he purchases a car of 7.5 lakh. And so he is left with Rs. 2.5 lakh. Thus A is the correct answer.

## Practice Questions

Q. The prices of sugar were stumbling. Initially, there was an increase of 15 % and then there was a decrease of 15 % again. What was the net change in the prices of sugar?

A. 30 %

B. 22.5 %

C. 2.25 %

D. There was a change in the price

The correct answer is C.

Q. The entrance ticket of a cricket match in Pune was Rs. 250. When the price of the ticket was lowered, the sale of the tickets was increased by 50 %. But the collections noticed a reduction of 17.5 %. What was the reduction in the price of tickets?

A. Rs. 150

B. Rs. 120

C. Rs. 112.5

D. Rs. 105

The correct answer is C.

Q. A cow and a goat cost Rs. 1400 and Rs. 2000 respectively. If the price of the cow and goat is decreased by 20 % and 30 % respectively, then what will be the price of 5 cows and 8 goats?

A. Rs. 16800

B. Rs. 16000

C. Rs. 16400

D. Rs. 16600

The correct answer is A.