# PERCENTAGE

Percentage

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", or the abbreviations "pct.", "pct"; sometimes the abbreviation "pc" is also used. A percentage is a dimensionless number. Percent means per hundred or out of 100

To expressdecimal or fraction as percent multiply the given fraction or decimal by 100%

To express percent as decimal or fraction divide the given percent by 100 and remove the % sign

To find the value of the given percent of quantity multiply the given quantity by the given %.

Examples

1.What is the sum whose 35% is Rs 168?

Soln

Let the total number be x. Then,

Here, 35 % = ${\rm{Rs}}.\frac{{168}}{{\rm{x}}}$

Or, $\frac{{35}}{{100}}$ = $\frac{{168}}{{\rm{x}}}$

Or, x = $\frac{{168{\rm{*}}100}}{{35}}$

So, x = Rs. 480.

Alternate way,

35 % of x = Rs. 168

Or, $\frac{{35}}{{100}}$ * x = 168

Or, x = $\frac{{168{\rm{*}}100}}{{35}}$

So, x = Rs. 480.

2. A and B were two candidates in an election .If 2% of the people in the voters’ list did not cast the vote, 200 votes were invalid and A obtained 55% of valid votes and won the election by a majority of 1940 votes , find the total number of voters in the list .

Soln

Let the total voters be x. Then,

Total number of votes not given = 2% of x = 0.02x.

So, Valid vote = x – 0.02x – 200 = 0.98x [200 votes were invalid]

According to question,

Winner’s vote = 55%of(0.98x -200)

Losing candidate’s vote = 45%of (0.98x -200)

Also,

The election was won by 1940 votes. So,

55% of (0.98x -200) - 45%of (0.98x -200) = 1940

or, $\frac{{55}}{{100}}$ * (0.98x -200) – $\frac{{45}}{{100}}$ * (0.98x -200) = 1940

or,(0.98x -200)($\frac{{55}}{{100}} - \frac{{45}}{{100}}$) = 1940

or, (0.98x -200) * $\frac{{10}}{{100}}$ = 1940

or, 0.98x -200 = 19400

\x = 20000

Hence, there were 20,000 voters.

3. If the rate of the kerosene is increased by 40%, by what percent should a customer reduce his consumption to maintain his previous expenditure?

Soln

Let the price of the previous kerosene be x. Then when it is increased by 40% its new price is:

x + 40% of x = 1.4x

Now, the increment in price is 1.4x – x = 0.4x.

So, the customer should reduce his consumption by $\frac{{0.4{\rm{x}}}}{{1.4{\rm{x}}}}$ * 100% = 28.57%.

4. The population of a village is 15000.when the male population increases by 12% and the female population decreases by 8%, the total population remains the same .Find the male and female population of the village.

Soln

a.

The total population of village = 15,000

Let the male population be x and female population be y. Then,

Then for males, the population increase by 12% = $\frac{{12}}{{100}}$ of x + x = 1.12x

When the female population decreases by 8% = y –8 % of y = 0.92y.

So, 1.12x + 0.92 y = 15,000…(i)

Before the population was increased or decreased,

Or, x + y = 15,000

Or, x = 15,000 – y…(ii)

Putting x in (i) , we get,

Or, 1.12(15,000 – y) + 0.92y = 15,000

Or, 16,800 – 1.12y + 0.92 y = 15,000

Or, 16,800 – 15000 = 0.2y

Or, y = 9000.

So, Now, putting y = 9000 in (ii), we get,

X = 15000 – 9000

So, x = 6000.

So, the total male population is 6000 whereas total female population is 9000.

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