# Aptitude::Percentage

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Example 1 / 28

It can be solved as,

= 0.1 * 0.2 * 0.25 * 100

= 0.5%

So, the answer is a. 0.5

= 0.1 * 0.2 * 0.25 * 100

= 0.5%

So, the answer is a. 0.5

**Ans.****Formula Used:**

x% of y

= \(\frac{x}{100}\times y\)

NA

We can write directly as,

(i) 10% of 100 = 10

(ii) 1% of 100 = 1

e.g;

25% of 100 = (20+5)% of 100

= 2*10% of 100 + 5* 1% of 100

= 20+ 5 = 25

(i) 10% of 100 = 10

(ii) 1% of 100 = 1

e.g;

25% of 100 = (20+5)% of 100

= 2*10% of 100 + 5* 1% of 100

= 20+ 5 = 25

Example 2 / 28

Let the number be 'x'.

So, 0.3*x = 300

=> x = 1000

Thus, 50% of 1000 = 5*(100) = 500

So, 0.3*x = 300

=> x = 1000

Thus, 50% of 1000 = 5*(100) = 500

**Ans.****Formula Used:**

x% of y

= \(\frac{x}{100}\times y\)

NA

We can directly have a formula like:

Let the no. to be obtained be x

x = \(\frac{(The Obtained Percentage)}{\%Age Given}\)

e.g;

=> 30% of x = 300

=> x = \(\frac{300}{30%}\)

Let the no. to be obtained be x

x = \(\frac{(The Obtained Percentage)}{\%Age Given}\)

e.g;

=> 30% of x = 300

=> x = \(\frac{300}{30%}\)

Example 3 / 28

Given,

0.3* \(\frac{ab}{100}\) = 0.25*\(\frac{bc}{100}\)

0.3a = 0.25c

So, c = \(\frac {0.3}{0.25}\)

c = 1.20 a

0.3* \(\frac{ab}{100}\) = 0.25*\(\frac{bc}{100}\)

0.3a = 0.25c

So, c = \(\frac {0.3}{0.25}\)

c = 1.20 a

**Ans.****Formula Used:**

x% of y% of z

\(\frac{xyz}{10000}\)

NA

When 'n' number of % is given of some number is given then,

\(\frac{'n' numbers}{10^{(n-1)}}\)

\(\frac{'n' numbers}{10^{(n-1)}}\)

Example 4 / 28

0.4A + B = 1.25B

0.4 A = 0.25 B

A = 0.625 B

Since we don't know the values of A and B,

so, it can be depending upon the values of A and B.

0.4 A = 0.25 B

A = 0.625 B

Since we don't know the values of A and B,

so, it can be depending upon the values of A and B.

**Formula Used:**

X% of y

= \(\frac{x}{100} \times y\)

NA

To calculate p% of y, it is, (p% of y) = (y% of p)

Example 5 / 28

0.05A + 0.1B = \(\frac{1}{2}\)*( 0.2A + 0.1B)

0.05A + 0.1B = 0.5*(0.2A + 0.1B)

0.05A + 0.1B = 0.1A + 0.05B

0.05A = 0.05B

So, A:B = 1:1

0.05A + 0.1B = 0.5*(0.2A + 0.1B)

0.05A + 0.1B = 0.1A + 0.05B

0.05A = 0.05B

So, A:B = 1:1

**Ans.****Formula Used:**

X% of y

= \(\frac{x}{100} \times y\)

NA

We can directly have a formula like:

To calculate p% of y, it is, (p% of y) = (y% of p)

To calculate p% of y, it is, (p% of y) = (y% of p)

Example 6 / 28

Total votes = 12000

Invalid votes = 15% of 12000 = 0.15* 12000 = 1800

So, valid votes = 12000-1800 = 10200

No. of votes Chaman gets = 80% of 10200 = 0.80 * 10200 = 8160

No. of valid votes other candidates get = (10200 - 8160) = 2040

Invalid votes = 15% of 12000 = 0.15* 12000 = 1800

So, valid votes = 12000-1800 = 10200

No. of votes Chaman gets = 80% of 10200 = 0.80 * 10200 = 8160

No. of valid votes other candidates get = (10200 - 8160) = 2040

**Ans.****Formula Used:**

X% of y

= \(\frac{x}{100}\times y\)

NA

First take out total invalid vote and subtract it from the total votes, then find the no. of votes by taking out the percentage of the votes.

Example 7 / 28

Let the actual length of the coat be 'x'.

So, x + 15% of x = 345

=> x + 0.15 x = 345

=> 1.15 x= 345

=> x = 300cm

So, x + 15% of x = 345

=> x + 0.15 x = 345

=> 1.15 x= 345

=> x = 300cm

**Ans.**
y+ X% of y

=> \(y + \frac{x}{100} \times y\)

=> \(y + \frac{x}{100} \times y\)

NA

To calculate x, we can directly do as

X = \(\frac{Given Length}{1 + Given%}\)

X = \(\frac{Given Length}{1 + Given%}\)

Example 8 / 28

% change = \(\frac{(10+10)}{10}\) * 100 = 200%

**Formula Used:**

= \(\frac{Initial - Final}{Initial}\times 100\)

NA

To calculate the percent change = \(\frac{Initial - Final}{Initial}\)

Example 9 / 28

Let the length, breadth, and height be L, B, H respectively.

So, initial volume = L*B*H = LBH

So, now,

Increased length = L + 10% of L = 1.1 L

Increased breadth = B + 20% of B = 1.2 B

Increased height = H + 50% of H = 1.5 H

New volume = 1.1L * 1.2B * 1.5H = 1.98 LBH

% change in volume = \(\frac{new volume – initial volume}{initial volume}\)

= \(\frac{1.98 LBH - LBH}{LBH}\) = 98%

So, initial volume = L*B*H = LBH

So, now,

Increased length = L + 10% of L = 1.1 L

Increased breadth = B + 20% of B = 1.2 B

Increased height = H + 50% of H = 1.5 H

New volume = 1.1L * 1.2B * 1.5H = 1.98 LBH

% change in volume = \(\frac{new volume – initial volume}{initial volume}\)

= \(\frac{1.98 LBH - LBH}{LBH}\) = 98%

**Ans.****Formula Used:**

= \(\frac{New Volume – Initial Volume}{Initial Volume}\)

NA

To increase X by Y%, we have formula,

\(X \left(1 + \frac{Y}{100}\right)\)

\(X \left(1 + \frac{Y}{100}\right)\)

Example 10 / 28

Let the number be x.

Then, ideally, he should have multiplied by x by 5/3.

Hence Correct result was x * \(\frac{5x}{3}\) = \(\frac{5x}{3}\)

By mistake he multiplied x by \(\frac{3}{4}\).

Hence the result with error = \(\frac{3x}{5}\)

Then, error = \(\left(\frac{5x}{3} - \frac{3x}{5}\right)\) = \(\frac{16}{15}\)

Error % = (error/True value) * 100 = [(16/15) * x/(5/3) * x] * 100 = 64%

Then, ideally, he should have multiplied by x by 5/3.

Hence Correct result was x * \(\frac{5x}{3}\) = \(\frac{5x}{3}\)

By mistake he multiplied x by \(\frac{3}{4}\).

Hence the result with error = \(\frac{3x}{5}\)

Then, error = \(\left(\frac{5x}{3} - \frac{3x}{5}\right)\) = \(\frac{16}{15}\)

Error % = (error/True value) * 100 = [(16/15) * x/(5/3) * x] * 100 = 64%

**Ans.****Formula Used:**

Error% = \(\frac{error}{True Value} \times 100\)

NA

To calculate error%:

\(\frac{\left( true - incorrect \right)}{true}\)*100

\(\frac{\left( true - incorrect \right)}{true}\)*100

Example 11 / 28

Let the initial price of salt be Rs. 100 per kg.

Let the total consumption be 100 kg.

So, total expenditure= 100*100= Rs. 10,000.

Now, new price= Rs. 50.

Also, let new consumption be x kg.

So, new expenditure= Rs. 50x

Total expenditure increased by 50%.

So, 10,000* \(\frac{150}{100}\)= 50x

X = 300

His consumption increased by (300 - 100)kg = 200 kg.

So, 200% increase on monthly consumption.

Let the total consumption be 100 kg.

So, total expenditure= 100*100= Rs. 10,000.

Now, new price= Rs. 50.

Also, let new consumption be x kg.

So, new expenditure= Rs. 50x

Total expenditure increased by 50%.

So, 10,000* \(\frac{150}{100}\)= 50x

X = 300

His consumption increased by (300 - 100)kg = 200 kg.

So, 200% increase on monthly consumption.

**Ans.****Formula Used:**

= \(\frac{New Volume – Initial Volume}{Initial Volume}\)

NA

To increase X by Y%, we have formula,

\(X \left(1 + \frac{Y}{100}\right)\)

\(X \left(1 + \frac{Y}{100}\right)\)

Example 12 / 28

At an election, the candidate who got 60% of the votes cast won by 200 votes. Find the total number of voters on the voting list if 66.67% people cast their vote and there were no invalid votes.

Let the total votes be 3V

People who casted Votes = \(\frac{66.67}{100}\)*3V = 2V

Candidate who won got = \(\frac{60}{100}\)*2V = 1.2V

Other Candidate got = 2V - 1.2V = 0.8V

Difference = 1.2V - 0.8V = 0.4V

0.4V = 200

=> V = 500

3V = 1500

Total Number of Voters on Voting List = 1500

Let the total votes be 3V

People who casted Votes = \(\frac{66.67}{100}\)*3V = 2V

Candidate who won got = \(\frac{60}{100}\)*2V = 1.2V

Other Candidate got = 2V - 1.2V = 0.8V

Difference = 1.2V - 0.8V = 0.4V

0.4V = 200

=> V = 500

3V = 1500

Total Number of Voters on Voting List = 1500

**Ans.****Formula Used:**

= \(\frac{New Volume – Initial Volume}{Initial Volume}\)

NA

To increase X by Y%, we have formula,

\(X\left(1 + \frac{Y}{100}\right)\)

\(X\left(1 + \frac{Y}{100}\right)\)

Example 13 / 28

Population = 50,000

In first year = (50000 + 2% of 50000) = 60,000

In second year = (60,000 - 10% of 60000) = 54000

In the third year = (54000 + 30% of 54000) = 70200

In first year = (50000 + 2% of 50000) = 60,000

In second year = (60,000 - 10% of 60000) = 54000

In the third year = (54000 + 30% of 54000) = 70200

**Formula Used:**

To calculate increase of x by y%

New x = (x + y% of x)

To calculate decrease of x by y%

New x = (x - y% of x)

NA

If the current population is P and it increases at the rate of R% per annum, then,

=>population after n years = \(P \left(1 + \frac{R}{100}\right)^{n}\)

=> population n years ago = \(\frac{P}{\left(1 + \frac{R}{100}\right)^{n}}\)

=>population after n years = \(P \left(1 + \frac{R}{100}\right)^{n}\)

=> population n years ago = \(\frac{P}{\left(1 + \frac{R}{100}\right)^{n}}\)

Example 14 / 28

Let the monthly income be Rs. X.

Now, for household expenditure = 20%

For food = 30%

For clothes = 10%

So, remaining = 100% -(20% + 30% + 10%) = 40%

\(\frac{40x}{100}\) = 10080

=> X = 25200

Now, for household expenditure = 20%

For food = 30%

For clothes = 10%

So, remaining = 100% -(20% + 30% + 10%) = 40%

\(\frac{40x}{100}\) = 10080

=> X = 25200

**Formula Used:**

= x% of y

NA

If amounts spent are given, then, remaining will be Total - (sum of all the amount spent).

Example 15 / 28

Total population is 6000

Let no. of males = x and females = y

so (x + y) = 6000 ------(1)

x increases by 10% the new x = \(\frac{110x}{100}\)

y increases by 20% then new y = \(\frac{120y}{100}\)

Now, \(\frac{110x}{100}\) + \(\frac{120y}{100}\) = 6800 -------(2)

By solving (1) and (2)

y = 2000.

Let no. of males = x and females = y

so (x + y) = 6000 ------(1)

x increases by 10% the new x = \(\frac{110x}{100}\)

y increases by 20% then new y = \(\frac{120y}{100}\)

Now, \(\frac{110x}{100}\) + \(\frac{120y}{100}\) = 6800 -------(2)

By solving (1) and (2)

y = 2000.

**Ans.****Formula Used:**

=> if x increases by y%, then % increase= x+(y% of x)

NA

To increase X by Y%, we have shortcut formula,

\(X \left(1 + \frac{Y}{100}\right) \)

\(X \left(1 + \frac{Y}{100}\right) \)

Example 16 / 28

Let Assume total votes = 100V

Party SJP got = 12V + 132000

Party SJD Got = 132000

132000 + 12V + 132000 = 100V

88 V = 264000

V = 3000

Party SJD lost by 12V

12*3000 = 36000

Party SJP got = 12V + 132000

Party SJD Got = 132000

132000 + 12V + 132000 = 100V

88 V = 264000

V = 3000

Party SJD lost by 12V

12*3000 = 36000

**Ans.****Formula Used:**

= votes of SJP + votes of SJD + 0 invalid votes = Total Votes

NA

To find total votes, there is no need of taking out %. Directly we can add all the given votes and equate by total votes.

Example 17 / 28

If the salary of Ashok is Rs. 100 then, Vinay’s salary is Rs. 175

again,

If Ashok's salary is Rs. 125 then, Vinay's salary is 245

now,

Ashok's salary is less than Vicky by 120

less% = \(\frac{120}{125}\times 100\) = 96%

again,

If Ashok's salary is Rs. 125 then, Vinay's salary is 245

now,

Ashok's salary is less than Vicky by 120

less% = \(\frac{120}{125}\times 100\) = 96%

**Formula Used:**

if there is y% increase in x, then, new x = (x + y)% of x

NA

To increase X by Y%, we have formula,

\(X\left(1 + \frac{Y}{100}\right)\)

Also, we must remember, suppose we have considered a number 1000

Then,10% of 1000 = 100

1% of 1000 = 10

5% of 1000 = 5*(1% of 1000) = 50

75% of 1000 = 7*(10% of 1000) + 5*(1% of 1000) = 750

\(X\left(1 + \frac{Y}{100}\right)\)

Also, we must remember, suppose we have considered a number 1000

Then,10% of 1000 = 100

1% of 1000 = 10

5% of 1000 = 5*(1% of 1000) = 50

75% of 1000 = 7*(10% of 1000) + 5*(1% of 1000) = 750

Example 18 / 28

Let there is x kg of ore.

So, \(\frac{20x}{100}\)= alloy

So, 50% of \(\frac{20x}{100}\) = copper

For, 10kg of copper \(\frac{10x}{100}\) copper

So, 80% of ore has no copper, so, \(\frac{80x}{100}\)

So, we can say that,

\(\frac{10x}{100}\) = 10kg

=> X = 100 kg.

So, \(\frac{20x}{100}\)= alloy

So, 50% of \(\frac{20x}{100}\) = copper

For, 10kg of copper \(\frac{10x}{100}\) copper

So, 80% of ore has no copper, so, \(\frac{80x}{100}\)

So, we can say that,

\(\frac{10x}{100}\) = 10kg

=> X = 100 kg.

**Ans.****Formula Used:**

to take x% of y, we use

= x%*y

NA

x% of y% of z = xy% of z

Example 19 / 28

P = 4,00,000, t = 3 years, r = 20%

So, population at starting of 4th year = \(P\left(1 + \frac{r}{100}\right)^{3}\)

= \(4,00,000\left(1 + \frac{20}{100}\right)^{3}\) = 691200

So, population at starting of 4th year = \(P\left(1 + \frac{r}{100}\right)^{3}\)

= \(4,00,000\left(1 + \frac{20}{100}\right)^{3}\) = 691200

**Formula Used:**

To calculate increase of x by y%

New x = (x + y% of x)

To calculate decrease of x by y%

New x = (x - y% of x)

NA

If the current population is P and it increases at the rate of R% per annum, then,

=>population after n years = \(P\left(1 + \frac{R}{100}\right)^{n}\)

=> population n years ago = \(\frac{P}{\left(1 + \frac{R}{100}\right)^{n}}\)

=>population after n years = \(P\left(1 + \frac{R}{100}\right)^{n}\)

=> population n years ago = \(\frac{P}{\left(1 + \frac{R}{100}\right)^{n}}\)

Example 20 / 28

Let T be the price of tables and C be the price of the chairs.

So, New price of table = (3000 + 300) = 3300

New price of chair = (1000 + 200) = 1200

So, the price of 10 tables and 20 chairs = (10 * 3300 + 20 * 1200)

= 33000 + 24000 = 57,000

So, New price of table = (3000 + 300) = 3300

New price of chair = (1000 + 200) = 1200

So, the price of 10 tables and 20 chairs = (10 * 3300 + 20 * 1200)

= 33000 + 24000 = 57,000

**Ans.****Formula Used:**= increase of x by y%= new x= x+y%of x

NA

To increase X by Y%, we have formula,

\(X\left(1 + \frac{Y}{100}\right)\)

\(X\left(1 + \frac{Y}{100}\right)\)

Example 21 / 28

CP of house = Rs. 2,00,000

Repair cost = 6% of 2,00,000 = 12000

Annual tax = 12000

So, total = Rs. 2,24,000

Now, to get 20% on his net investment = 20% of 224000 = 44800

So, monthly amount = \(\frac{44800}{12}\) = Rs.3733.33

Repair cost = 6% of 2,00,000 = 12000

Annual tax = 12000

So, total = Rs. 2,24,000

Now, to get 20% on his net investment = 20% of 224000 = 44800

So, monthly amount = \(\frac{44800}{12}\) = Rs.3733.33

**Ans.****Formula Used:**monthly rent = \(\frac{Total Expense * given%}{12}\)

NA

For monthly rent = \(\frac{return\% \times Total Expense}{12}\)

Example 22 / 28

Given that \(\frac{4}{5}\) of the voters in Kanpur promised to vote for Modi and the rest promised to vote for Advani

Now, let the voters in Kanpur promised 4x votes for Modi and x votes for Advani.

The voters who actully voted to Modi = (4x - 10% of 4x) = (4x - 0.4x) = 3.6x

The number of votes Modi got = 216000

So,3.6x = 216000

=> x = 216000/3.6 = 60000

And

The voters who actully voted to Advani = (x - 20% of x) = (x- 0.2x) = 0.8x

Now,

Total polled votes = (3.6x + 0.8x) = 4.4x

So, Total polled votes = 4.4*60000 = 264000

Now, let the voters in Kanpur promised 4x votes for Modi and x votes for Advani.

The voters who actully voted to Modi = (4x - 10% of 4x) = (4x - 0.4x) = 3.6x

The number of votes Modi got = 216000

So,3.6x = 216000

=> x = 216000/3.6 = 60000

And

The voters who actully voted to Advani = (x - 20% of x) = (x- 0.2x) = 0.8x

Now,

Total polled votes = (3.6x + 0.8x) = 4.4x

So, Total polled votes = 4.4*60000 = 264000

**Formula Used:**

Decrease in x by y% = (x - y% of x)

NA

Tips: first, take our respective vots by given formula, then add and equate by total votes, and multiply by total polled

Example 23 / 28

Let the salary be x.

So, house rent = 25% of x.

Remaining= 75% of x.

So, for children's education = 20% of 75% of x = 15% of x

For clothes = 10% of x.

Money left with him = Rs.20,000

So, x - (25% of x) + (15% of x) + (10% of x) = 20000

so, x = 40,000

So, house rent = 25% of x.

Remaining= 75% of x.

So, for children's education = 20% of 75% of x = 15% of x

For clothes = 10% of x.

Money left with him = Rs.20,000

So, x - (25% of x) + (15% of x) + (10% of x) = 20000

so, x = 40,000

**Ans.****Formula Used:**

Remaining salary = Total - (sum of all expenses)

NA

To find the total salary, first find the total expense, add all and subtract from the salary and equate it to the remaining salary given.

Example 24 / 28

Monthly salary = A

Expenditure = X.

So, Remaining = (A-X).

Now, for next month, increase of C%

So, (A) + C% of (A) = \(A\left[1 + \frac{C}{100}\right]\)

New Expenditure = x + D% of x

= \(X\left(1 + \frac{D}{100}\right)\)

Remaining = (New Salary - New Expenditure)

= \(A\left[1+ \frac{C}{100}\right] - X\left[1+\frac{D}{100}\right]\)

Expenditure = X.

So, Remaining = (A-X).

Now, for next month, increase of C%

So, (A) + C% of (A) = \(A\left[1 + \frac{C}{100}\right]\)

New Expenditure = x + D% of x

= \(X\left(1 + \frac{D}{100}\right)\)

Remaining = (New Salary - New Expenditure)

= \(A\left[1+ \frac{C}{100}\right] - X\left[1+\frac{D}{100}\right]\)

**Ans.****Formula Used:**

Savings = (Salary - Expenditure)

Increase in salary by x% = salary + x% of salary

Increase in expenditure by y% = expenditure + y% of expenditure

New savings = (increased salary - increased expenditure)

NA

To increase X by Y%, we have formula,

X(1+\(\frac{Y}{100}\)

Also, Savings = (salary - expenditure)

X(1+\(\frac{Y}{100}\)

Also, Savings = (salary - expenditure)

Example 25 / 28

Rebate = 20% of 10000

i.e price after rebate is 80% of 10000 = 8000.

sales tax is 10% of 8000 = 800

Therefore,Final amount paid = 8000 + 800 = Rs. 8800

i.e price after rebate is 80% of 10000 = 8000.

sales tax is 10% of 8000 = 800

Therefore,Final amount paid = 8000 + 800 = Rs. 8800

**Ans.****Formula Used:**

Sale price(SP) = (P - R*P)

Where, P = original price, R = rebate(discount %)

Then Sales = S * SP, where S = sales%, SP = sales price

So, final amount paid = Sales + SP.

NA

Rebate is nothing but simple discount on the given original price.

Example 26 / 28

Let Bhuwan's salary be Rs.100.

So, Anuj's salary = Rs.80.

Salary of Chauhan = Rs.80 + 56.25% of 80 = Rs.125

So, Bhuwan's salary is less than Chahuhan's salary by Rs.(125 - 100) = Rs.25

% Decrease = \(\frac{25}{125} \times 100\) = 20%

So, Anuj's salary = Rs.80.

Salary of Chauhan = Rs.80 + 56.25% of 80 = Rs.125

So, Bhuwan's salary is less than Chahuhan's salary by Rs.(125 - 100) = Rs.25

% Decrease = \(\frac{25}{125} \times 100\) = 20%

**Ans.****Formula Used:**% Increase in x by y% = x + y% of x

NA

To increase X by Y%, we have formula,

\(X\left(1 + \frac{Y}{100}\right)\)

\(X\left(1 + \frac{Y}{100}\right)\)

Example 27 / 28

Total Runs = 100

Total boundaries = 4, Total sixes = 6

So, Total score made by running = 100-(4*4+6*6) = 100-52 = 48 runs

So, % Score = \(\frac{48}{100} \times 100\) = 48%

Total boundaries = 4, Total sixes = 6

So, Total score made by running = 100-(4*4+6*6) = 100-52 = 48 runs

So, % Score = \(\frac{48}{100} \times 100\) = 48%

**Ans.****Formula Used:**

Total score by running = (Total Score - (sixes + boundaries)

% score = \(\frac{Total Score By Running}{Total Runs}\times 100\)

NA

NA

Example 28 / 28

Let the length of the plot 'x' m and breadth be 'y' m respectively.

So, initial area= 'xy' sqm.

Now,

Increased length= x + 20% of x = \(\frac{120x}{100}\)

Increased breadth= y + 30%of y = \(\frac{130y}{100}\)

So, New Area = \(\frac{120x}{100}\)*\(\frac{130y}{100}\)

So, % change = \(\frac{ (New Area - Initial Area)}{Initial Area}\)*100

= \(\frac{\left(\frac{120x}{100} \times \frac{130y}{100}-xy \right)}{xy} \times 100\)

= 56%

So, initial area= 'xy' sqm.

Now,

Increased length= x + 20% of x = \(\frac{120x}{100}\)

Increased breadth= y + 30%of y = \(\frac{130y}{100}\)

So, New Area = \(\frac{120x}{100}\)*\(\frac{130y}{100}\)

So, % change = \(\frac{ (New Area - Initial Area)}{Initial Area}\)*100

= \(\frac{\left(\frac{120x}{100} \times \frac{130y}{100}-xy \right)}{xy} \times 100\)

= 56%

**Ans.****Formula Used:**

Increase in x by y% = x+y% of x.

= \(\frac{\left(New Area - Initial Area\right)}{Initial Area} \times 100\)

NA

Take out the new length and new breadth by the formula of % increase, i.e;

To increase X by Y%, we have formula,

\(X\left(1 + \frac{Y}{100}\right)\)

So, New Area = (New length * New breadth).

So, % change = \(\frac{\left(New Area - Initial Area\right)}{Initial Area} \times 100\)

To increase X by Y%, we have formula,

\(X\left(1 + \frac{Y}{100}\right)\)

So, New Area = (New length * New breadth).

So, % change = \(\frac{\left(New Area - Initial Area\right)}{Initial Area} \times 100\)