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# PERCENTAGE & PROPORTION

## PERCENTAGE & RATIO PROPORTION SET12

Q.1 A cloth merchant has announced 25% rebate in prices. If one needs to have a rebate of \$40, how many shirts costing \$32 each should he purchase? A) 2 B) 5 C) 10 D) 18 Ans. B C.P. of one shirt = \$32 Rebate on one shirt = 0.25 × 32 = \$8 To get a rebate of \$40, number of shirts to be bought = = 5 Q.2 750 candidates appeared in an examination. 70% of the girls and 65% of the boys passed the examination. If total pass percentage was 67%, find the number of boys that appeared in the examination. A) 400 B) 430 C) 440 D) 450 Ans. D Apply the Rule of Alligation- 70 65 67 2 3 Thus, ratio is: 2:3 Since we have to find boys, then = 3/5 * 750 = 450 Q.3 An employer reduces the number of employees by th and increases their wages by th. What is the ratio of the total wages paid to the employees before the hike and after that? A) 10.0 : 11 B) 11.0 : 10 C) 10.5 : 10 D) 10.5 : 12 Ans. C Let the initial number of employees = n New number of employees = n Let initial wages = x New wages = x ? Ratio of total wages before and after the change = (nx) : = 21 : 20 = 10.5 : 10 Q.4 Aman’s salary is 25% higher than that of Balraj’s. By how much percent is Balraj’s salary lower than that of Aman’s? A)25% B)20% C)15% D)10% Ans. B Let Balraj’s salary be Rs.100 Aman’s salary will be Rs.125 A – B = 125 – 100 = 25 B’s salary is ( ) 100 = 20% Q.5 If the price of sugar goes up by 10%, what should be the percentage reduction in the quantity consumed so that the total expenditure on sugar remains the same? A) 10 % B) 9 % C) 8 % D) 7 % Ans. B Percentage reduction in quantity consumed = × 100 = × 100 = % = 9 % Q.6 In Lok Sabha elections there are two candidates-A & B contesting from North delhi seat. 3/5th of the people promise to vote for A, & the rest promise to vote for B. If 10% of the people who promised to vote for A did not vote & 20% of the people who promised to vote for B did not vote. If B got 6400 votes, how much was the margin of victory for A ? A) 5500 B) 8800 C) 4400 D) 4000 Ans. C Let total votes be X, It is given 3/5th of people =i.e. 3/5*100=60% (Here we have considered people be 100) Now, 10% of the people who promised to vote for A did not vote Then, People voted for A= 60% of x-10% of 60% of x = 0.54 x People voted for B= 40% of x – 20 % of 40 % of x = 0.32 x Now find margin victory for A= i.e. 0.54-0.32= 0.22 x Then, acc to question If B got 6400 votes 0.32x (calculated value of B)= 6400 X= 20000 how much was the margin of victory for A ? i.e. 0.22 (Calculated value of A)=0.22*20000=4400 Votes Q.7 Out of 54600 candidates for an examination, 35% failed to pass while 15% passed with honours. Find the number of candidates who passed the examination but failed to obtain honours. A) 43680 B) 35990 C) 27300 D) None of these Ans. C Total Candidates = 54600 %age of the candidates who failed to pass and who passed with honours (35% + 15%) = 50% %age of candidates who passed but failed to obtain honours. (100 – 50%) = 50% 50 % of 54600 = 27300

## PERCENTAGE & RATIO PROPORTION SET10

Q.1 In a military camp, the food available is enough for 500 soldiers for 10 days. If 300 soldiers are sent to another camp, how long will the available food last?A) 15 daysB) 18 daysC) 20 daysD) 25 daysAns. D 500 Soldiers can eat food for 10 days1 Soldier can eat food for 5000 days200 Soldier can eat food for days = 25 days Q.2 A man loses 12 1/2% of his money. He spends 70% of the remaining and is still left with \$210. How much money did he have initially?A) \$357B) \$443C) \$800D) None of theseAns. C Let total amount = \$xLost amount = = Remaining amount = x – x = x According to question= 210x = \$800 Directions : The following questions are based on the given information:a) Candidates appeared 10,500b) Passed in all five subjects 5,685c) Passed in three subjects only 1,498d) Passed in two subjects only 1,250e) Passed in one subject only 835f) Failed in English only 78g) Failed in Maths only 275h) Failed in Physics only 149i) Failed in Chemistry only 147j) Failed in Biology only 221 Q.3 How many candidates failed in all three subjects? A) 4,815 B) 3317 C) 2,687 D) 362 Ans. D Candidates failed in all three subjects==(Candidate appeared) – (Candidate passed in one, two, three or five subjects+ Candidates failed in any subject)= 10,500-(5,685 + 1,498 + 1,250 + 835 + 78+ 275 + 149 + 221)=362 Q.4 How many candidates passed in at least four subjects? A) 6,555 B) 5,685 C) 1,705 D) 870 Ans. A Candidate passed in at least four subjects=( Candidate passed in four subjects + Candidate passed in all five subjects)=(78+ 275 + 149 + 147 + 221) + 5,685=6,555 Q.5 How many candidates failed because of having failed in four or less subjects? A) 4,815 B) 4,453 C) 3,618 D) 2,368 Ans. BCandidates failed in four or less subjects= (Candidates failed in only one subject) + (Candidates failed in only two subjects) + (Candidates failed in only three subjects) + (Candidates failed in only four subjects)= ( 78 + 275 + 149 + 147 + 221) + (1,498 + 1,250 + 835)=4,453

## PERCENTAGE & RATIO PROPORTION SET9

Q.1 A man does not want to change his expenditure for the consumption of sugar. If the prices of sugar increases by 60%, then the man must reduce his consumption by :A) 35 %B) 60 %C) 37 ½ %D) 40 %Ans. C60 / 160 * 100 = 37 1/2b Q.2 A tank is filled 10% in an hour & 8% of the water is emptied in the next hour. If it is repeated again, Find the percentage of tank filled with water ?A) 4 %B) 20 %C) 17.66 %D) 19 %Ans. CTank will be filled 10% in first hour .In next hour 8 % of it = 10 * 8/100 = 8 % of the tank is emptied. Remaining water after the second hour is 9.2%. Again in the third hour 10% tank is filled, it becomes 19.2%.Again, 8% of it i.e. 19.2 * *8/100= 1.536 % is emptied in the fourth hour ,So remaining water is 19.2 – 1.536 = 17.66 % Q.3 A garrison of 450 men have sufficient provision for 16 weeks .After 6 weeks 50 men more came in. How long the provision will last ?A) 9B) 10C) 11D) 12Ans. A16 weeks – 6 weeks = 10 weeksFor 450 men, 450 * 10Here it is given,Additional 50 men came,Thus, 450*10/450+50= 9 Q.4 A can do a piece of work in 24 days. If b is 60% more efficient than A, then the no. of days required by B to do the same piece of work is :A) 18B) 15C) 17D) 12Ans. B1/24*160/100=1/15=15 Q.5 Two jars having equal capacity are filled with a mixture of alcohol & water in the proportion of 2:1 & 1:1. These two were emptied into a third jar. What is the proportion of water & alcohol in the third jar ?A) 5/6 : 7/6B) 5/3 : 7/3C) 6/5 : 6/7D) None of the aboveAns. AAlcohol : Water = 2:1 & Alcohol : Water = 1:12/3 : 1/3 ½ : ½So, water part= 1/3 + ½ ; Alcohol part = 2/3 +1/25/6 : 7/6

## PERCENTAGE & RATIO PROPORTION SET8

Q.1 The population of a city is 5,00,000 out of which 52% are males and rest are females. The overall literacy rate in the city is 70% and 60% of the males are literate. Find the number of educated females in the city and percentage literacy among females. A) 194000, 80.83% B) 50000, 20.83% C) 2,40,000, 50.02% D) 1,40,000, 40.02% Ans. A Total population = 5, 00,000Number of males = = 2, 60,000Literate males = = 1,56,000Number of females = 5,00,000 – 2,60,000 = 2,40,000Overall literate population = = 3,50,000Literate females = Overall literate population – literate males= 3,50,000 – 1,56,000 = 1,94,000Literate percentage among females = = 80.83% Q.2 The ratio of the prices of the keyboard and the monitor is 1 : 4. If the price of the monitor increases by 20% and the ratio decreases by 5%, what is the percentage increase/decrease in the price of the keyboard ? A) 20% increase B) 4% decrease C) 6% increase D) None of these Ans. B According to question,¼ * x/1.2y = 20/100x/4.8y = 20/100or x= 96%x has gone down by 4% Q.3 In an examination, the number of those who passed and the number of those who failed were in the ratio 5 : 2. Had 25 more appeared, and 5 less passed, the ratio of passed to failed would have been 3 : 2. Find the number of candidates who appeared, initially. A) 215 B) 210 C) 200 D) 175 Ans. D Number of those who passed to number of those failed = 5 : 2Let number of students who passed = 5xand number of students who failed = 2xTotal number of students = 5x + 2x = 7x When 25 more students appeared then total students = 7x + 25When students increased, 5 less passedNow number of students passed = 5x – 5Number of students who failed = (7x + 25) – (5x – 5)= 7x + 25 – 5x + 5 = 2x + 30New ratio of passed to failure = 3 : 2 According to question ? 2 (5x – 5) = 3 (2x + 30)10x – 10 = 6x + 90 ? 10x – 6x = 90 + 10 4x = 100, x = 25Hence number of students who appeared =7xor 7 × 25 = 175. Q.4 750 candidates appeared in an examination. 70% of the girls and 65% of the boys passed the examination. If total pass percentage was 67%, find the number of boys that appeared in the examination. A) 400 B) 430 C) 440 D) 450 Ans. D Apply the Rule of Alligation : Girls Boys70 65672 3 Or 3/5 * 750 = 450 boys Q.5 If the cost of 30 metres of cloth is Rs. 345.Find the cost of 16 metres of cloth ?A) 185B) 184C) 187D) 188Ans. B30 : 16 I I 345 : XOr X= 16*345/30= 184

## PERCENTAGE & RATIO PROPORTION SET7

Q.1 A candidate attempted 12 questions & secured full marks in all of them. If he obtained 60% in the test & all Questions carried equal marks then what is the number of questions in the test ? A) 36 B) 30 C) 25 D) 20 Ans. D Let no. of questions = x X * 60 % = 12 X * 60/100 = 12 X = 20 Q.2 Two equal glasses respectively 1/3rd & 1/4th full of milk. They are then filled up with water & the contents mixed in a tumbler. Find the ratio of milk & water in a tumbler ? A) 7 : 17 B) 2 : 5 C) 9 : 21 D) 3 : 5 Ans. A Ist glass = Milk : water = 1/3 : 2/3 2nd glass= Milk : Water= ¼ : ¾ Milk = 1/3 + ¼ = 7/12 Water = 2/3 + ¾ = 17/12 Now, find ratio of milk : Water = 7/12 * 12/17 = 7 : 17 Q.3 A & B are two alloys of gold & copper by mixing metals in proportions 7 : 2 & 7 : 11. If equal quantities of alloys are melted to form as third alloy C in the proportion of Gold & Copper in C will be : A) 5 : 7 B) 7 : 5 C) 5 : 9 D) 9 : 5 Ans. B Let quantitites of A & B each be 18 gm Therefore, in A mass of Gold = 7*18/9 = 14 gm & In A mass of Copper = 2*18/9 = 4 In B mass of Gold = 7*18/18 = 7 gm & In B mass of Copper = 11*18/18 = 11 gm Therefore, total quantity of Gold in C = 14+7 = 21 gm & total quantity of copper in C = 4+11 = 15gm Therefore required ratio = 21 : 15 =7 : 5 Q.4 If 1/3 rd of liquid contents of a can evaporates on the first day & 3/4th of the remaining evaporates on the second day. The fractional part of the original contents remaining at the closing of the second day is : A) ½ B) 1/6 C) 4/7 D) 7/12 Ans. B IInd day, 2/3 evaporates (therefore, 1-2/3 = 1/3) Now,1/3 of ¾ (3/4 is given in question) =¼ remains Thus remaining amount is: ¼ * 2/3 = 1/6 of original contents PASSAGE: There are 2500 students in a school . Ratio of number of boys & girls is 3:2. All students play different games like Hockey, Boxing, Tennis, Football & Volleyball. 28% girls play hockey. 16% boys like Tennis. 1/5th of the boys play Volleyball. In Tennis, ratio of girls & boys is 2:3. 25% of the total number of students prefer Boxing. In Volleyball, Number of girls 60 % of number of boys involved in this game. 22% girls like football. Rest girls are in Boxing. 18% boys play Hockey & rest play Football. Q.5 How many girls play tennis & Volleyball together ? A) 340 B) 400 C) 380 D) 320 Ans. A 160 + 180 = 340 Q.6 The number of boys who prefer Boxing is what percent of the total number of students in the school ? A) 10.8 % B) 18.6 % C) 12 % D) 9 % Ans. B 465/2500 * 100 = 18.6 % Q.7 How many girls prefer Boxing ? A) 180 B) 220 C) 160 D) 200 Ans. C Number of players who play Hockey : 1000- (Number of girls who play games other than Hockey) 1000 – 280+160+220+180 1000-840 = 160 Q.8 Total number of boys in Hockey is what percent of the total number of girls in the same game ? A) 103.70 % B) 117.43 % C) 80.36 % D) 96.43 % Ans. D 270/280*100 = 96.43 Q.9 How many boys like Football ? A) 270 B) 240 C) 225 D) 300 Ans. C 1500 – (Number of boys who play games other than football) 1500- (270 + 465 + 240 + 300) 1500 – 1275 = 225

## PERCENTAGE & RATIO PROPORTION SET6

Q.1 Sum of Rs. 312 was divided among 100 boys & girls in such a way that each boy gets Rs.3.60 & each girl Rs.2.40. Find the no. of girls ?A) 40B) 41C) 42D) 43Ans. A312/100=3.12 360 24031272 48Or 72:48=3:2Or 2/5*100=40 Q.2 In what ratio must water be mixed with milk to gain 20% by selling mixture at cost price ?A) 1:5B) 5:1C) 1:4D) 4:1Ans. AC.P.=100/120*1=5/60 15/61-1/5 5/6-0=1/6 =5/6Therefore,1/6:5/6=1:5 Q.3 Indian electricity prices have risen from Rs. 6.4 to Rs.6.5 per unit.Arvi’s factory expected to use 600 units in the next billing period. He installed solar panels at the start of that period. This reduced his electricity usage by 90%.How much did Arvi’s bill increase ? A) Rs. 6 B) Rs. 38 C) Rs. 39 D) Rs. 54 Ans. A Number of units of electricity used in the factory = 600Number of units of electricity used after installing solar panels = 600 90% of 600 = 60Increase in the cost of one unit electricity = Rs 6.5-6.4=0.1 Increase in Arvi’s bill = Rs 0.1 × 60 = Rs 6 Passage:A company having 450 employees has sent all its employees for training in one or more areas out of HRM, Computer skills & Financial skills. The employees are classified into two categories : Officers & Clerks, who are in the ratio 4 :5. 10% of the officers takes training only in computer skills , 16 % of clerks takes training only in HRM, which is equal to the number of officers taking only in Financial skills both. 6% of the total employees takes training in all the three ,of which two-thirds are officers. 10 % of total employees takes training in Computer skills & HRM both which is five times the number of clerks taking training in Computer skills & Financial skills . 10 % of the clerks taking training in HRM & Computer skills both. The number of officers taking training only in HRM is 25% of the number of clerks taking training only in HRM. 20% of the total number of employees takes training only in Computer skills . Number of clerks taking training in HRM & Financial skills both is 20 % of the total number of clerks. Q.4 How many total clerks takes training in Computer skills but not in HRM ? A) 113 B) 70 C) 88 D) 79 Ans. B Q.5 Total how many officers takes training in HRM ? A) 128 B) 118 C) 92 D) 110 Ans. C Q.6 How many total clerks takes training in Financial Skills ? A) 106 B) 115 C) 97 D) 124 Ans. D 74+41+9 = 124 Q.7 How many total employees takes training in financial skills but not in HRM ? A) 135 B) 162 C) 164 D) 106 Ans. B 74+40+48 = 162 Q.8 What percent of the total number of Officers takes training in Computer Skills but not in Financial Skills ? A) 25 % B) 15 % C) 40 % D) 11 % Ans. D % = Officers taking training in Computer skills but not in financial skills/ Total number of officers * 100 (20+2)/200 * 100 = 11 % Explanation: Number of officers = 450*4/(4+5) = 450 * 4/9 = 200Number of Clerks = 450 – 200 = 250Officers in Computer skills = 10/100 * 200 = 20Clerks in HRM =16/100 * 250 = 40 (Officers in Financial skills)Clerks in HRM = 50 % of officers in HRM & Financial skills Therefore, Officers in HRM & Financial skills = 40*100/50 = 80Total employees taking training in all three = 6/100*450 = 27Officers in all three = 2/3*27 = 18Therefore, clerks in all three= 27-18 = 9***Employees taking training in HRM & Computer skills = 10/100*450 = 45Employees in HRM & computer skills = 5* clerks in computer skills & financial skillsThus, Clerks in computer skills & Financial skills = 45/5 =9Clerks in HRM & Computer skills =10% of 250=25Officers only in HRM =25% of clerks in HRM25/100*40=10Clerks in HRM & Financial skills = 20% of 250 = 50

## PERCENTAGE & RATIO PROPORTION SET5

Q.1 Milk vendor has 2 cans of milk. First contains 25% water & rest milk. Second contains 50% water. How much milk should he mix from each of the container so as to get 12 litres of milk such that ratio is 3:5 ?A) 4 litresB) 5 litresC) 6 litresD) 7 litresAns. CLet the cost of 1 litre milk be Re. 1Milk in 1 litre mix. in 1st can = 3 litre, C.P. of 1 litre mix. in 1st can Re. 34 4Milk in 1 litre mix. in 2nd can = 1 litre, C.P. of 1 litre mix. in 2nd can Re. 12 2Milk in 1 litre of final mix. = 5 litre, Mean price = Re. 58 8By the rule of alligation, we have: C.P. of 1 litre mixture in 1st can   C.P. of 1 litre mixture in 2nd can     34Mean Price5812 1818   Ratio of two mixtures = 1 : 1 = 1 : 1.8 8 So, quantity of mixture taken from each can = 1 x 12 = 6 litres.2 Q.2 We have 100 litres of Vodka & take 10 litre & add 10 litre of water. Then after 3 processes what is the quantity of Vodka ?A) 27 litreB) 28 litreC) 29 litreD) 30 litreAns. AOriginal quantity is 100 & if we take 10 litre then 90% is left i.e. 0.9Then, V=100*(0.9)3Or V=72.9Or water=100-72.9=27.1 litre Q.3 Tea worth Rs.126/kg & Rs.135/kg are mixed with third variety in ratio 1:1:2.If mixture is worth Rs.153/kg by the price of third variety/kg will be :A) 175.5B) 180.2C) 175.1D) 180.6Ans. A126      135      x1kg      1kg      2kg         153Or 126+135+2x=4*153Or 261+2x=6122x=351X=175.5 Q.4 Discount on Rs. 2562 due 4 months hence is Rs.122. Rate % is ?A) 2%B) 3%C) 4%D)5%Ans. D2562-122=2440122*100  /2440=5% Q.5 729 ml of mixture contains milk & water in the ratio of 7:2. How much water is to be added to get a new mixture containing milk & water in the ratio of 7:3 ?A) 80 mlB) 81 mlC) 82 mlD) 83 mlAns. BMilk=729*7/9 = 567 mlWater=729-567=162 mlOr 567/162+x=7/3Or 1701=134+7xX=81 ml

## PERCENTAGE & RATIO PROPORTION SET4

Q.1 In Delhi University, some students appeared for the papers of ten subjects, each constituting of 100 marks. A student has to score 50 marks in order to pass in a subject i.e. overall one need to score fifty percent of the total marks. Find the probability of overall passing of a student, if he got failed in eight subjects?A) 1457/13231B) 1458/13232C) 1459/13234D) 1460/13235Ans. ARange of the marks in the subjects in which the student has failed = 0 – 392.Range of the marks in the subjects in which the student has passed = 100 – 200Total possibilities of total marks = 393 × 101 = 39693Possibilities in which he is passing (scoring 500 marks) are as follows.(108 and 392), (109, 391), (110, 390) ………… (200, 300)There are a total of 93 cases, when sum of the marks is 500.In the same way, there are 92 cases when sum of the marks is 501.In the same way, there are 91 cases when sum of the marks is 502….In the same way, there is 1 case when sum of the marks is 592.So, total number of cases in which he is pass = (1+93)/2 × 93 = 4371Probability = 4371/39693 = 1457/13231 Q.2 From the salary of a person 10% is deduced as house rent. He spends 15% of the rest on children’s education and 10% of the balance on clothes. After this expenditure, he is left with \$1377. What is his salary?A) \$2200B) \$2000 C) \$1900D) \$1840 Ans. B Let x be the total salary.According to the question, On solving for x, we get x = \$2000 Q.3 When processing flower-nectar into honey by honey bees, considerable amount of water gets reduced. How much flower nectar must be processed to yield 1kg honey if nectar contains 50% water & honey obtained from this nectar contains 15% water.A) 1.4 kgB) 1.5 kgC) 1.6 kgD) 1.7 kgAns. DFlower nectar contains 50% of non-water partIn honey non-water part contains 85% (100-15)Therefore, 0.5*amount of flower nectar=0.85*amount of honey=0.85*1kgTherefore, amount of flower-nectar needed=0.85/0.5*1kg=1.7kg Q.4 Ravi had 500Rs. & he wanted to lend it out to Manish & Siddharth. Manish is willing to give double rate of interest that Siddharth is willing to give. If Siddharth gives 15% & Ravi wants to double his money in 5 years. How should Ravi split his money ?A) 2 : 1B) 3 : 1C) 1 : 2D) 1 : 3Ans. ARavi wants to double in 5 years, then100/5 = 20%15% 30%20%10 5=2 :1 Q.5 In what ratio should rice of Rs. 10 & Rs.15 & 20 should be mixed to get price of Rs.17/kg ?A) 1:1:3B) 2:1:1C) 3:1:1D) 1:1:2Ans. A10 20 15 2017 173 7 3 23:3:9In this we have taken 9, because of Rs.20 kgOr 1:1:3

## PERCENTAGE & RATIO PROPORTION SET3

Q.1 Student secured 30% in the first paper out of 180. How much should he score in the 2nd paper out of 150, if he get atleast 50% overall marks ?A) 109 B) 110 C) 111 D) 112 Ans. A 0.3*180 = 54 In 2nd paper=0.5*(150+180) = 165 Therefore, 165 – 54 = 109 PASSAGE: Growth of the aircraft services is driven by the increase in the number of the people using aircraft services & the increase in per person use of the airplanes. In 2019 it expected that there will be 200 million aircraft service users in India or about 20% of the population will generate 50 billion Rs. in aircraft services revenue. Services revenues should expand from 50 billion Rs. to 150 billion Rs. by 2014, while the no. of users should grow to over 560 million or to about half the population of India in the same period. Q.2 What is the estimated population of India in 2010 ? A) 1000 crore B) 100 crore C) 98 crore D) 115 crore Ans. A It is given 200 million = 20% of population So, Population = 200*100/20 = 1000 million Q.3 What will be the simple average growth rate of population of India in the given period 2010-2014 ? A) 2% B) 4.5% C) 3% D) 4% Ans. C Population in 2010 = 1000million Population after 4 yrs i.e. in 2014 = 560*2 = 1120 million Thus average growth = 1120-1000 / 1000*4 * 100 Or 120 / 1000*4 * 100 =12/4 % =3 % Q.4 If 50% of the population of any country can afford aircraft services use, it is economically developed. Can we say India will be a developed country in 2013 ? A) Yes B) No C) Can’t say D) Data inadequate Ans. D As information regarding2013 is not known Q.5 What will be the % growth of the revenues of the aircraft services in the given period 2010-2014 ? A) 230% B) 200% C) 260% D) 300% Ans. B Revenue in 2010 = 50 billion Revenue in 2014 = 150 billion Thus % growth = 150-50 / 50 * 100 100/50 * 100 =200 % Q.6 What will be the growth in % of aircraft services users in India by 2014 ? A) 150 % B) 100 % C) 200 % D) 180 % Ans. D Users in 2010 = 200 million Users in 2014 = 560 million Thus, growth in % = 560-200 / 200 * 100 =360/200*100 =180 %