Get ‘percent’ questions right to ace SI exam

Hyderabad: This article is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exam. Here are some previously asked questions and answers along with explanations on the percentage topic. 1. Percentage The word ‘per cent’ can be understood as follows: Per cent ⇒ for every 100 So, when percentage is […]

Hyderabad: This article is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exam. Here are some previously asked questions and answers along with explanations on the percentage topic.

1. Percentage

The word ‘per cent’ can be understood as follows:

Per cent ⇒ for every 100
So, when percentage is calculated for any value, it means that you calculate the value for every 100. When you see the word ‘per cent’ or the symbol %, remember it means 1/100
Example:

20 per cent = 20% = 20×1/100 = 1/5

2. Why Percentage?
Percentage is a concept evolved so that there can be a uniform platform for comparison of various things. (Since each value is taken to a common platform of 100)
Example:
To compare three different students depending on the marks they scored we cannot directly compare their marks until we know the maximum marks for which they took the test. But by calculating percentages they can directly be compared with one another.

Concept of Percentage

By a certain per cent, we mean that many hundredths. Thus x per cent means x hundredths, written as x%.

To express x% as a fraction: We have, x%= x/100.
Thus, 20%= 20/100= 1/5;

48%= 48/100= 12/25
To express a/b as a per cent: We have, a/b = a/b x 100%

Thus, 1/4= 1/4 X 100% = 25%;
3/5 = 3/(5 ) × 100% = 60%.

Note:
x % of y = y % of x
x is what % of y = x/y x 100 %
% change = change/(Initial value ) x 100%
Commodity Price Increase/Decrease

If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:
= R/(100 R)×100%

If the price of the commodity decreases by R%, then to maintain the same expenditure by increasing the consumption is:

= R/(100-R)×100%
Results on Population
Let the population of the town be P now and suppose it increases at the rate of R% per annum, then:
1. Population after n years = P {〖1 R/100 }〗^n

2. Population n years ago = P/({〖1 R/100 }〗^n )

Results on Depreciation
Let the present value of a machine be P. Suppose it depreciates at the rate R% per annum. Then, in the above formula we have to substitute –R instead of R.
If the present population of a city is P and there is an increment of R1%, R2%, and R3% in first, second and third year respectively, then Population of the city after 3 years = P(1 R1/100) (1 R2/100) (1 R3/100)
3. Percentages – Fractions Conversions

For faster calculations, we can convert the percentages into their respective fraction notations.

Example:

What is 62.5% of 320?
Solution:

Value = 5/8 x 320 = 200 (since 62.5%= 5/ 8)
4. Important Points to Note
When the actual value is x, find the value when it is 30% decreased.
Then, it becomes 70 % of x
Example:
A value after an increase of 20% became 600. What is the value?

Solution:

120% of x = 600 (since 20% increase)
6/(5 ) of x = 600  x= 500
Example:
If 600 is decrease by 20%, what is the new value?

Solution:

New value = 80% of 600 = 480 = 80/100 x 600 = 480. (Since 20% decrease)
PREVIOUS YEAR QUESTIONS:
1. A person gives 47.5% of his property to the elder son, 32.5% to the younger son, 5% to a temple and the balance of Rs 6 lakh to his daughter. The share of the younger son (in lakhs of rupees) is

(SI Mains 2018)

a) 2 b) 6 c) 13 d) 15

Ans: c

Explanation:

In percentages, total value is always equal to 100%
Total property = 100%

47.5% (elder son) 32.5% (younger son) 5% (temple) 6 lakhs = 100%
85% 6 lakhs = 100%

15% = 6 lakhs
Then, Total property = 100% = 6/15×100 = 40 lakhs

The share of the younger son = 32.5% of 40 = 13 lakhs
2. If 25% of a number is added to another number, then the second number is increased by 10%. The ratio of the first number to the second is (SI Mains 2018)

a) 1:2 b) 2:1 c) 2:5 d) 5:2

Ans: c
Explanation:
25% of x y = 110% of y

0.25 * x = 1.1 * y- y

0.25 * x = 0.1 * y

x/y = 0.1/0.25 = 0.1: 0.25 = 2: 5

To be continued…

Banda Ravipal Reddy

Director, SIGMA
Sai Institute of General Mental Ability
Hyderabad