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Given:

salary reduced = 40%

salary increased = 40%

Calculation:

Let initial salary be 100%

After reduction = 100 - (40/100) ×100 = 60% 

Taking the reduced salary for increament

After increment = 60 + (40/100) × 60 = 84%

Loss % in salary = Initial salary - Final salary = 100 - 84 = 16%

∴ The final loss% in his salary is 16%

Given:

Cost of gold = Rs. 50,000

Calculation:

The cost increases by 10%

So, Total cost = (110/100) × 50000

Total cost after first growth = 55000

Now, the cost again increases by 10%

Total cost after second growth = (110/100) × 55000

Total cost after second growth = Rs. 60500

∴ Total growth at last = Rs. 60500

Given:

Arun gross annual salary is 80,000 Rupees

His wife contributes 10% of her salary before taxes to a retirement account

Then he pays 25% of his remaining salary in state and federal taxes

Finally, he pays 60 Rupees per month for health insurance

Calculation:

Arun receives 80,000.

First he contributes 10% of his salary to a retirement account.

⇒ 80,000 × (10/100) 

⇒ 8,000

⇒ 80,000 – 8,000 = 72,000 Rupees

After, contributing to his retirement account, Arun has 72,000 Rupees.

Then she pays 25% in taxes.

⇒ 72,000 × (25/100)

⇒ 18,000

⇒ 72,000 – 18,000 = 54,000

After, paying taxes, Arun has 27,000 Rupees left. 

Finally, he pays 30 Rupees per month for health insurance.

⇒ 60 × 12

⇒ 720 Rupees

Remaining salary,

⇒ 54,000-720

⇒ 53,280 Rupees

∴ Arun's annual take-home pay is 53,280 Rupees.

Given:

Initial salary = Rs. 20,000

Increase% = 14%

Calculation:

New salary = Rs. 20,000 × (114/100)

⇒ Rs. 22,800

∴ The new salary is Rs. 22,800

Given:

Total number of voters = 7200

Number of invalid votes = 10%

Percentage of valid votes that A got = 60%

Concept used:

Number of votes B get = Total number of voters – (Invalid votes + Number of votes secured by A)

Calculation:

Number of valid votes = 7200 × {(100 – 10)/100}

⇒ 7200 × {90/100}

⇒ 648000/100

⇒ 6480

Number of votes that A got = 6480 × (60/100)

⇒ 388800/100

⇒ 3888

Number of votes that B got = 6480 – 3888

⇒ 2592

∴ The number of votes B got is 2592.

Given:

Total valid votes = 60%

Invalid votes = 30%

Total numbers of vote = 8000.

Concept used:

Total valid vote = total votes - invalid votes

Calculation:

Total number of votes = 8000 

Given that 30% of Percentage votes were invalid

⇒ Valid votes = 70%

Total valid votes = 8000 × (70/100) 

⇒ Valid vote = 5600

1st candidate got 60% of the total valid votes. 

Hence the 2nd candidate should have got 40% of the total valid votes 

⇒ Valid votes that 2nd candidate got = total valid votes x (40/100) 

⇒ 5600 × (40/100)

⇒ 2240

∴ The valid votes of 2nd candidate is 2240

GIVEN:

% of people who didn't cast their votes = 20%

votes in favor of winner = 61% of votes polled

the margin of win = 1760 votes

EXPLANATION:

let the total number of votes be 100 ratio

\(votes \space polled = 80 ratio\\winner's\space share = 61\% \space of\space votes\space polled \\loser's \space share=39\%\space of \space votes\space polled \\margin = 61 - 39 = 22\%\space of \space votes\space polled \\22\%= 1760\Rightarrow 100\%=8000 \\80\%\space of \space list\space(20\%\space didn't\space cast)= 8000\\\therefore100\% \space of \space list=10000\)

Given:

Percentage of invalid votes = 10%

Percentage of valid votes winner got = 60%

Extra votes that the winning candidate got than losing candidate = 900

Concept used:

Total number of voters = Invalid votes + Number of votes secured by A + Number of votes secured by B

Calculation:

Let the total number of voters be x.

Number of valid votes = x × {(100 – 10)/100}

⇒ x × {90/100}

⇒ 0.90x

Number of votes that the winning candidates got = 0.90x × (60/100)

⇒ 0.54x

Number of votes that the losing candidates got = 0.54x – 900

Then, Total number of votes = 0.10x + 0.54x + 0.54x – 900 = x

⇒ 1.18x – 900 = x

⇒ 0.18x = 900

⇒ x = 5000

∴ The total number of voters is 5000.

Given:

20% of voters did not vote.

3500 votes were declared invalid.

The winner gets 60% of valid votes and wins by 5000 votes.

Formula used:

Percentage = (Value ⁄ Total Value) × 100

Calculation:

Let the total vote be ‘x’.

20% did not vote on the total voting list.

Number of voters appeared for voting = x × 80/100

⇒ Invalid votes = 3500

⇒ Valid votes = x × 80/100 – 3500

Difference between wining and losing candidate = 60 – 40 = 20% of valid votes

⇒ (x × 80/100 – 3500) × 20/100 = 5000

⇒ 4x/5 – 3500 = 25000

⇒ 4x/5 = 25000 + 3500

⇒ x = (28500 × 5)/4

⇒ x = 35625

Number of voters appeared for voting = x × 80/100

⇒ Number of voters appeared for voting = 35625 × 80/100

⇒ 28500

Given:

2 candidates participated,

10% votes did not cast, 80 votes are invalid

Winner gets 60% votes of the valid votes and wins by 2000 votes

Calculation:

Let the total number of valid votes be 100

Winner gets 60% of the votes,

⇒ 60/100 × 100

⇒ Winner gets 60 votes

Losing candidate gets,

⇒ 100 – 60

⇒ 40

Losing candidate gets 40 votes

Difference between them = 60 – 40

⇒ Difference between them = 20

According to the question,

20 = 2000

⇒ 1 = 100

⇒ Total number of valid votes = 100 × 100

⇒ Total number of valid votes = 10,000

Invalid votes = 80

⇒ Total casted votes = 10,000 + 80

⇒ Total casted votes = 10,080

10% of voters did not cast their votes.

⇒ 100% – 10% = 90% cast their votes

⇒ 90% = 10,080

⇒ 1% = 10,080/90

⇒ 100% = 100 × 10,080/90

⇒ 100% = 100 × 112

⇒ 100% = 11,200

∴ Total number of voters is 11,200.

Given:

Total Voters = 100%

Voters not voted = 10%

Voters voted = 90%

Invalid votes = 300

Valid votes = 90% - 300

Votes secured by winner candidate = 60%  (the winner gets 60% of the total voters)

Winner candidate won by 900 votes.

Calculation:

Votes secured by losing candidate =  valid votes - winner votes

⇒ (90% - 300) - 60%

= 30% - 300

As we know,

Winner candidate won by 900 votes.

⇒ 60% - (30% - 300) = 900

⇒ 30% + 300 = 900

⇒ 30% = 600

⇒ 90% = 1800

∴ Total valid votes = 1800 - 300= 1500

Given:

Percentage of voters cast their vote = 75%

Invalid vote percentage = 2%

Candidate got votes 75% of valid votes = 9261

Calculation:

Let us take the total number of voters be x

casted vote % = 75% of x 

valid casted vote = 98% of 75% of x

⇒ 75% of total valid vote = 75% of 98% of 75% of x

⇒ 9261 = 3/4 × 3/4 × 98/100 × x  

⇒ x = (1029 × 16 × 100)/98

⇒ x = 16800 

∴ The total number of voters will 16800

Given:

Number of votes declared invalid = 68 

Percentage of votes of winning candidate = 52%

Number of votes by which winning candidate wins by = 98 votes

Calculation:

Let the number of valid votes be x

Then, 52% of x – 48% of x = 98

⇒ 4% of x = 98

⇒ (4/100) × x =98

⇒ x = 98 × 25

⇒ x = 2450

Total number of votes polled = (2450 + 68)

⇒ 2518Unexpected text node: 'kkhh'Unexpected text node: 'kkhh' kkhh

\there∴ The total number of votes polled is 2518

Given:

In a village, 30% of the population cast vote in favor of losing candidate C.

Winner candidate D got 15,169 votes.

Concepts used:

Total votes cast = Vote gained by winner + votes gained by losing candidate

Calculation:

Let the total number of votes be x.

Votes gained by losing canidate C = 30% of x = 0.30x

Total votes cast = Vote gained by winner + votes gained by losing candidate

⇒ x = Vote gained by winner + 0.30x

⇒ Vote gained by winner  = x - 0.30x = 0.70x

Winner candidate D got 15,169 votes.

⇒ 0.70x = 15,169

⇒ x = 15,169/0.70

⇒ x = 21,670 votes

Votes gained by losing canidate C = 30% of x = 0.30x

⇒ 0.30 × 21,670

⇒ 6,501 votes

∴ Candidate C got 6,501 votes.

Given:

In a competitive exam, 25% of the students were ineligible to give that exam.

52% of eligible candidates were male and number of eligible female candidates were equal to 11,250.

Concepts used:

Total applicants = Ineligible applicants + Eligible applicants

Eligible applicants = Male eligible applicants + female eligible applicants 

Calculation:

Let the total number of applicants be x.

Ineligible applicants = 25% of x = 0.25x

Total applicants = Ineligible applicants + Eligible applicants

⇒ x = 0.25x + Eligible applicants

⇒  Eligible applicants = x - 0.25x = 0.75x

Eligible male applicants = 52% of 0.75x = 0.39x

⇒ Eligible female applicants = 0.75x - 0.39x = 0.36x 

Number of eligible female candidates were equal to 11,250.

⇒ 0.36x = 11,250

⇒ x = 11,250/0.36

⇒ x = 31250

∴ Total number of applicants in the exam were equal to 31250. 

Given:

In an exam, there were 5 questions. 10% of students solved all questions, 10% did not solve any question and 15% of the remaining students solved 1 question and 16% of total students solved 4 questions

24% of students solved 2 questions and 140 students solved 3 questions.

Calculation:

Let the total number of students be x.

10% of students solved all questions, 10% did not solve any question.

Number of students who solved all questions = 10% of x = 0.10x

Number of students who solved 0 question = 10% of x = 0.10x

15% of the remaining solved single question.

Remaining students = x – 0.10x – 0.10x = 0.80x = 4x/5

Number of students who solved 1 question = 15% of 4x/5 = 3x/25

Number of students who solved 4 questions = 16% of x = 0.16x = 4x/25

Number of students who solved 2 questions = 24% of x = 0.24x = 6x/25

Number of students who solved 3 questions = 140

Total number of students = Number of students who solved 0 question + Number of students who solved 1 question + Number of students who solved 2 questions + Number of students who solved 3 questions + Number of students who solved 4 questions + Number of students who solved all questions

⇒ x = x/10 + 3x/25 + 6x/25 + 150 + 4x/25 + x/10

⇒ x = 18x/25 + 140

⇒ x – 18x/25 = 140

⇒ 7x/25 = 140

⇒ x = 500 students

∴ Total students are equal to 500.

Given:

Total marks = 720.5

A got 10% less than B, B got 30% more than C and C got 25% less than D.

A got marks = 175.5

Calculation:

Marks obtained by given person in terms of another person = Marks obtained by another person +/- markspercentage by which another person obtains more/less marks than the given person

Calculation:

Let the marks obtained by D be x.

C got 25% less than D.

C = x – 25% of x

⇒ 75% of x = 0.75x

B got 30% more than C.

B = 0.75x + 30%of 0.75x

⇒ 0.75x + 0.225x

⇒ 0.975x

A got 10% less than B.

A = 0.975x – 10% of 0.975x

⇒ 0.975x – 0.10 × 0.975x

⇒ 0.8775x

A got marks = 175.5

⇒ 0.8775x = 175.5

⇒ x = 175.5/0.8775

⇒ x = 200 marks

∴ D obtained 200 marks. 

Given:

Percentage of students who were preparing for IIT-JEE = 60% 

Total number of students who were not preparing for IIT-JEE = 64 

Calculations:

Let the total number of student in the classroom be 100x 

Total number of students who were preparing for IIT-JEE = 100x × 60/100 = 60x 

Total number of students who were not preparing for II-JEE = 100x – 60x = 40x 

⇒ 40x = 64 

⇒ x = 64/40 = 8/5 

The total number of students = 100x = 100 × 8/5 = 160 

∴ The total number of students in the classroom is 160 

GIVEN:

Qualifying Marks = 72% of total marks and Total Marks = 650

CALCULATION:

Qualifying Marks = 72% of total marks and Total Marks = 650

Qualifying Marks = 72% × 650

= 36 × 13

= 468

∴ Required  qualifying cut-off in terms of marks obtained is 468

Given:

60% of employees are female

40% of employees are male

45% of employee earn more than 50000

Formula used:

Percentage = (Obtained value/Maximum value) × 100

Calculation:

Let the total employee of the company be 100

Number of Female in the company = 100 × (60/100) = 60

Number of Male in the company = 100 × (40/100) = 40

The total employees are earning more than 50000 = (45/100) × 100 = 45

25% of total female earning more than 50000 = 60 × (25/100)

Total Female who earn more than 50000 = 15

Total male who earn more than 50000 is = 45 - 15 = 30

Men who earn equal or less than 50000 is = 40 - 30

= 10

Required percentage = (10/40) × 100 = 25%

∴ The required result will be 25%.

Given:

Total number of students in a college = 2800

Calculation:

Total girls in a college = 2800 × 35/100 = 980

Total boys in a college = 2800 - 980 = 1820

Total number of girls and boys passed in exam = 980 × 85/100 + 1820 × 75/100 = 833 + 1365 = 2198

∴ The percentage of total students who passed the final examination is = 2198/2800 × 100 = 78.5%

Given:

40% girls and 92.5% girls pay fees

60% boys and 85% of boys pay fees

Calculation:

Let the total number of the students be 100

Number of girls = 40 

Number of girls paid fees = 92.5% of 40 = 37

Number of boys = 60 

Number of boys paid fees = 85% of 60 = 51

Number of student that didn't paid the fees = 100 - (37 + 51) = 12

And according to question,

12 = 180 

⇒ 1 = 15

So the number of students = 15 × 100 = 1500

Number of students pay fees = 15 × 88 = 1320

∴ The number of students that gets scholarship = (1/2) × 1320 = 660

Given:

Percentage of marks obtained by Janak = [100% – (100/3)%] × Pass marks

Percentage of marks obtained by Ram = 75% × Janak’s marks

Pass marks = 40% × total marks

Calculation:

Pass marks = 40% × 300 = 120

Marks obtained by Janak = [100% – (100/3)%] × 120 = 80

Mark obtained by Ram = 75% × 80 = 60

Marks required by Ram to pass the exam = 120 – 60 = 60

∴ The required solution is 60 marks.

Calculation:

Let total no. of students be 100%

The percentage of those who passed in both subjects = 100% – (35% +15% – 25%)

⇒ 100% – (50% – 25%)

⇒ 100% – (25%)

⇒ 75%

∴ The percentage of those who passed in both English and Reasoning will be 75%

Given

Number of boys = 1100

Number of girls = 900

Percentage of boys passed in examination = 50%

Percentage of girls passed in examination  = 40%

Calculation

Number of boys passed = 50% of 1100

⇒ 550

Number of boys failed = 1100 - 550 = 550

Number of girls passed = 40% of 900

⇒ 360

Number of girls failed = 900 - 360 = 540

Total number of students = 1100 + 900 = 2000

Total number of students failed = 550 + 540 = 1090

Percentage of students failed = (1090/2000) × 100 = 54.5%

Given:

Boys = 1200, Girls = 800

Passing percentage of boys = 45%

Passing percentage of girls = 35%

Formula used:

Failure Percentage = [(Total student – Passing student)/Total student × 100

Calculation:

Total number of student = 1200 + 800 = 2000

Total number of students pass = 45% of 1200 + 35% of 800

⇒ (45/100) × 1200 + (35/100) × 800

⇒ 540 + 280

⇒ 820

Numbers of student fails = 2000 – 820 = 1180

Percentage failure = (1180/2000) × 100

⇒ 118/2

⇒ 59

∴ The percentage of failure students is 59%.

(a) Total marks in the test = (280 + 80) x 100 /45 = 800

Passing marks for girls = 800 x 30/100 = 240

Required marks
= 240 – 108 = 132

Given:

Average pass percentage of girls in class XII examination = 80%

Average pass percentage of boys in class XII examination = 75%

Average pass percentage in class XII of that school = 76.5%

Calculation:

Let the number of girls and boys be x and y respectively

According to the question,

80x + 75y = 76.5 × (x + y)

⇒ 80x + 75y = 76.5x + 76.5y

⇒ 3.5x = 1.5y

⇒ 7x = 3y

⇒ x : y = 3 : 7

Percentage of number of boys in school = (7/10) × 100%

⇒ 70%

∴ The percentage of the number of boys in class XII of the school is 70%

Given :

A scored mark = 30%

A Failed by = 15 marks

B scored = 40% 

Obtained marks = 35

Calculation : 

Let x be maximum marks

⇒ 30% x + 15 = 40% x - 35

⇒ 30% x - 40% x = - 35 - 15

⇒ -10% x = -50

⇒ x = (50×100)/10

⇒ x = 500 

Therefore, The maximum marks is 500.

The pass marks is expressed as shown below,

Pass marks  

⇒ [(30 × 500)/100] + 15

Pass marks = 165 

Therefore, the pass percentage is calculated as shown below,

Pass% = (165/500) × 100

∴ The pass percentage is 33%.

Given:

Percentage of marks scored by Vinod = 25%

marks by which Vinod failed = 10

Percentage of marks scored by Sachin = 30%

marks obtained by Sachin above pas mark = 20

Calculation:

Let total marks in the exam be x.

Pass marks = Marks obtained by Vinod + 10 = 25% × x + 10

Pass marks = marks obtained by Sachin - 20 = 30% × x - 20

Equating the pass marks in both cases,

25% × x + 10 = 30% × x - 20

30 = 5% ×  x 

Or, x = 600

∴ The total marks of the exam is 600.

Given:

Salary increased by 22%

Salary decreased by 22%

Formula used:

If any value first increased by x% and later decreased by x%, then the net effect is always decrease and this loss is calculated by using the formula as follows:

(x²/100)%

Calculation:

[(22 × 22)/100]%

⇒ 4.84%

Alternative method:

Let the original salary is Rs. 100

Salary increased by 22%

New salary = 100 + 22% of 100 = Rs. 122

Salary decreased by 22%

Salary after decrease = 122 – 22% of 122 = Rs. 95.16

Salary decrease = 100 – 95.16 = Rs. 4.84

Decrease percentage = (4.84/100) × 100 = 4.84%

Given:

10% of a = b

Calculation:

(10/100) × a = b

⇒ a = 10b

Now, b% of 200 = 2b

From options,

20% of a = (20/100) × 10b = 2b

∴ The same value is 20% of a

Concept used:

1 km = 10000 dm

Calculation:

34% of 14 km

⇒ (34/100) × 14 km

⇒ (34/100) × 140000 dm

⇒ 47600 dm

∴ The required value is 47600 dm

Given:

Difference between the 30% of a number and 22% of the same number = 4800

Calculation:

Let the number be P

According to the question,

30% of P – 22% of P = 4800

⇒ 8% of P = 4800

⇒ P = 60,000

And, 18% of P = (18/100) × 60,000 = 10,800

∴ 18% of P is 10,800

Given:

The height of a tomb increases by 22% in first year

In the next year, the height further increases by 10% and becomes 503.25.

Calculation:

Let the height of the tomb be x meters.

The height of a tomb after first year = x + 22% of x

⇒ 1.22x

The height of tomb next year = 503.25

⇒ 10% of 1.22x = 503.25
⇒ 1.1 × 1.22x = 503.25

⇒ x = 375

∴ The initial height of the tomb is 375 meters.

Given:

16% of overall voters are senior citizen

75% of the senior citizen voters voted

Calculation:

Let the number of voters be x

Number of senior citizen voters = 16% of x = 16/100x

Number of senior citizen who voted = 75% of 16/100x = 12/100x

Percentage of senior citizen votes = (12/100x)/x × 100

⇒ Percentage = 12/100 × 100

⇒ Percentage = 12

∴ Percentage of senior citizen votes is 12%

Given:

A number increases by 25% if 60 is added to it.

Formula:

Percentage increase = (new - actual)/actual × 100

Calculation:

Let the number be x.

⇒ x + 0.25x = x + 60

⇒ x = 60 × 4 = 240

New number = 240 + 600 = 840

Percentage increase = (840 – 240)/(240) × 100

⇒ (600/240) × 100

⇒ 250

∴ The number should increase by 250%.

Calculations :

Let the number be 'x' 

According to the question

18 % of x - 14 % of x = 45 

4 % of x = 45 

\( {4 \over 100}\) of x = 45 

4x = 45 × 100 

4x = 4500 

x = 4500/4 

x = 1125 

∴ The number is 1125

Given:

Population in 1912 = 12,000

Population in 1922 = 12,982

% increase in male population = 6%

% increase in female population = 10%

Concept:

The increased in male and female population is the difference of population in 1912 and 1922. 

Calculation:

Let, the male population in 1912 = x

the female population in 1912 = y

∵ In 1912;

x + y = 12,000      ------(1)

Increase in population = 12,982 - 12,000

= 982

∴ (6/100) × (x) + (10/100) × y = 982

⇒ 6x + 10y = 98200      ------(2)

Multiply (1) with 6 and subtract from (2);

⇒ 4y = 26,200

⇒ y = 6550

Putting the value of 'y' in (1);

⇒ x + 6556 = 12,000

⇒ x = 12,000 - 6550

⇒ x = 5450

∴ Male population = 5450

Female population = 6550

Given:

Number of days = 122

Concept used:

Number of days in a leap year is 366

Calculation:

Leap year = 366 days

Required% = (122/366) × 100

⇒ 33.33%

∴Required% is 33.33% 

Given:

The population of the city is 50,000

Calculation:

Let be assume population after 2 year is p

⇒ p = (50000) × (4/5) × (4/5)

⇒ p = 32000

∴ The required result will be 32,000.

Given that:

90% of 42% of 1200

Calculations:

⇒ (90/100) × (42/100) × 1200

⇒ (9 × 42 × 12)/10

= 453.6

∴ Required answer is 453.6.

Given:

A team wins 45 games.

The number of games won by the team is 60% of the number of games played.

Calculation:

Let the total number of games played be 100 units.

We can say that the number of games won by the team will be 60 units.

According to the question,

60 units = 45

⇒ 100 units = (45 × 100)/60 = 75

∴ The total number of games played by the team is 75.

Let the population of the city 2 years age be x

Then, According to question

x × (105/100) × (105/100) = 926100

⇒ x = 926100 × (20/21) × (20/21)

⇒ x = 2100 × 400 = 840000

∴ The population of the city 2 years ago was 840000

Calculation:

The present population of a city = 15,00,000

Birth rate and death rate = 3.5% , 1.5%

The rate of increment = 3.5% - 1.5%

⇒ 2%

The population of city after 3 years = 15,00,000 × 102/100× 102/100 × 102/100

⇒ 1591812

∴ The population of city after 3 years is 1591812.

Calculation:

Let the price of bike in the first year be Rs.M.

The price of a bike after four years = M × (110/100 × 105/100 × 85/100 × 110/100) = 1.079925M

⇒ 1.079925M - M = 2397.25

⇒ M ≈ Rs.30000

∴ the price of a bike in the first year is Rs.30000.