We know that Per Cent means per hundred or out of a hundred. It is denoted by the symbol %. x% denotes the fraction x/100.

**Applications
of Percentage in Word Problems**

We know that
Per Cent means per hundred or out of a hundred. It is denoted by the symbol **%**_{.}
** x% **denotes
the fraction

** **

__Example 4.1__

If *x* % of 600 is 450, then find the value of
*x*.

*Solution:*

Given,* x *% of 600 = 450

(*x*/100) × 600 = 450

*x* = 450/6

*x* = 75

** **

__Example 4.2__

When a number
is decreased by 25 % , it becomes 120. Find the number.

*Solution:*

Let the number
be *x* .

⇒* x *= 160

**Aliter: **Using the above formula,

If we start with a quantity A and then decrease that quantity by
*x*% , we will get the decreased quantity
as,

D = (1 − *x*/100) A

** **

__Example 4.3__

Akila scored
80 % of marks in an examination. If her score was 576 marks, then find the maximum
marks of the examination.

*Solution:*

Let the maximum
marks be *x* .

Now, 80 %
of *x* = 576

80/100 × *x* =
576

⇒
*x *= 576 × (100/80) = 720 marks

Therefore,
the maximum marks of the examination = 720.

** **

__Example 4.4__

If the price
of Orid dhall after 20% increase is ₹96 per *kg*,
then find the original price of Orid dhall per *kg*.

*Solution:*

Let the original
price of Orid dhall be ₹ *x* .

New price
after 20% increase

**Aliter: **Using the above formula,

A=₹80

If we start with a quantity A and then increase that quantity by x% , we will get the increased quantity as,

D = (1 + *x*/100) A

** **

**Try these**

1. What percentage of a day is 10 hours?

**Solution:**

In a day, there are 24 hours

∴ 10 hrs out of 24 hrs is 10/24

As a percentage, we need to multiply by 100

∴ Percentage = [10/24]
× 100 = 41.67%

2. Divide ₹350 among P, Q and R such that P gets 50% of what Q gets
and Q gets 50% of what R gets.

**Solution:**

Let R get *x*, Q gets 50% of what R gets

∴ Q gets = (50/100) × *x*
= *x*/2

P gets 50% of what Q gets

∴ P gets = 50/100 × *x*/2 = *x*/4

Since 350 is divided among the three

∴ 350 = *x* + *x*/2
+ *x*/4

350 = [4*x* + 2*x* + *x* ] / 4 = 7*x* / 4 =
350

* x *= [350 × 4] / 7 = 200

Q gets = *x*/2 = 200/2 = 100, P gets = *x*/4 = 200/4 =
50

∴ P = 50, Q = 100, **R = 200**

** **

**Think**

With a lot of pride, the traffic police commissioner of a city reported
that the accidents had decreased by 200% in one year. He came up with this number
by stating that the increase in accidents from 200 to 600 is clearly a 200% rise
and now that it had gone down from 600 last year to 200 this year should be a 200%
fall. Is this decrease from 600 to 200, the same 200% as reported by him? Justify.

**Solution:**

Increase from original value 200 to 600

% increase = [ **Change in value / original value ]** × 100

= [(600 – 200) / 600] × 100 = [400 / 200] × 100 = 200 % increase

Decrease from original value 600 to 200

% decrease = [ **Change in value / original value ]** × 100

here original value is 600

% decrease = [ (600 – 200) / 600 ] × 100 = [ 400 / 600 ] × 100 =
66.67 % increase

Increase from 200 → 600 and % decrease from 600 → 200 are not
the same

** **

__Example 4.5__

The income
of a person is increased by 10% and then decreased by 10 % . Find the chang in his
income.

*Solution:*

Let his initial
income be ₹* x *.

Income after
10% increase is

That is,
income of the person is reduced by 1%.

**Aliter:**

Let his income
be ₹100

Income after
10% increase is

100 + 100
× (10/100) = ₹110.

Now, income
after 10% decrease is,

110 – 110
× (10/100) = 110–11= ₹99

∴
Net change in his income = 100 – 99 = 1

∴
Percentage change = 1/100 × 100% = 1% .

That is,
income of the person is reduced by 1%.

** **

**Note**

For any given number, when it is increased first by* x *% and then decreased by* y *%, then the value of the number is increased
or decreased by ( *x *+* y *+ [*xy*/100] )% . Use ‘negative’ sign for decrease and also assume ‘decrease’ if the sign is
negative. Use this note to check the answer for the Example 4.5.

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