 # Consecutive Increments The increase and decrease in prices of the product are very common phenomena. Every day you see various discounts and offers being given to lure the customers. This increase and decrease can also be calculated by percentage. Today we are going to discuss only the increase in this percentage and how to calculate the consecutive increments of the product. We will also discuss what type of articles are asked on this topic.

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### Suggested Videos        ## Consecutive Increments

Consecutive increments are defined as more than one increment in the value of the product. Source: Max Pixel

## Solved Example

Q. Ram’s salary increases every year by 10 %. Last year his salary was Rs. 12000 per month.

1. What will be the salary of Ram in next year?
2. How will much percentage of Ram’s salary increase in 2 years?

Here, the salary of Ram last year was Rs. 12000. The increase in salary of Ram per year = 10 %.
Based on the last year, this year the salary of Ram will be, 10 % of 12000 = Rs. 1200. So, the salary of present year will be, 12000 + 1200 = Rs. 13200.
Next year again there is an increase of 10 % in Ram’s salary. So, for next year Ram’s salary will be, 10 % of 13200 = 1320 + 13200 = Rs. 14520.
Instead of doing this much amount of calculation, you can also use this method. Ram’s salary last year was Rs. 12000. Annual percentage increase = 10 %. 10 % can also be written as 1.10 times the initial salary. So, for next year Ram’s salary will be 1.1 x 1.1 x 12000 = Rs. 14520.

For an overall increase in salary, Ram’s salary grew from 12000 to 14520. So, increase = Rs. 14520 – Rs. 12000 = Rs. 2520.
Therefore, % increase = 2520/12000 x 100 = 21%.

To generalize, if there are successive changes of a %, b %, and c % on the initial value, than the final value P will be,
P = (1 + a/100)(1 + b/100)(1 + c/100) x A.
Use a, b, c with an appropriate sign i.e. use + a for an increase in % and – a for the decrease in %.

## Practice Questions

Q. Anil’s salary was Rs. 18000. An increase of 20 % in consecutive terms is equal to a single increment of what percentage?

A. 44 %         B. 40 %         C. 22 %           D. 400 %

Ans: The correct answer is A.

Q. It was determined in the experiment that the bacteria multiply by three times of its original population per hour. What will be the percentage rate of growth in one hour?

A. 33.33 %         B. 200 %           C. 300 %           D. 100 %

Ans: The correct answer is B.

Q. Shailesh had Rs. 96000 deposited in his locker a couple of years ago. During the first year, he added 25 % to that amount and in the second year, he deposited an additional 12.5 % of the amount in the bank locker. What is the present amount in his locker?

A. Rs. 135000                 B. Rs. 120000
C. Rs. 108000                D. Rs. 132000

Ans: The correct answer is A.

Q. Hillary’s present salary was Rs. 25000 per month. She decided to switch jobs and the new company offered an increment of 10 % for two consecutive years. What was the total percent equal to the percentage offered in two consecutive years?

A. 22 %        B. 21 %          C. 25 %           D. 20 %

Ans: The correct answer is B.

Q. The population in a town was 1,00,000. It was noted that every year there was an increase of 10 % per year. Find the population of the town at the start of the third year.

A. 1,21,000               B. 1,33,100
C. 1,20,000              D. 1,18,800

Ans: The correct answer is A.

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