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# Aptitude Questions with Explanations --- PERCENTAGES Solved Problems 2

## Percentages - Solved Problems 2

For percentages concept and Formulae   - Percentages - Concept
For Practice problems on Percentages  - Percentages Solved Examples 1

Aptitude Questions with Explanations -- Percentages Solved Problems 21
A student has to get 35% of marks to pass the examination. Gupta got 81 marks and failed by 24 marks,. What is the maximum mark?
a)250         b)280      c)300         d)425
Explanation:    Maximum marks = 100%
Pass percentage = Pass marks
=>       35% = 81 + 24 => 35% = 105
Maximum marks 100% =
105 / 35
x 100

Quantitative Aptitude - Percentages Solved Problems 22
A student has to get 44% of marks to pass the examination. Sharma got 192marks and got 16 marks more than the necessary to pass the exam. What is the maximum mark?
a)   400      b) 240         c) 250                d) 520
Explanation :  Maximum marks = 100%
Pass percentage = Pass marks
=>    44% = 192 - 16
=> 44% = 176
Maximum marks 100% =
176 / 44
x 100
= 400

Arithmetic Questions with answers - Percentages Solved Problems 23
In an examination Kiran got 27% of total marks and failed by 39. While Srisri got 63% of total marks got 69 marks more than the necessary to pass the exam. What are the maximum marks?
a) 400         b) 300           &c) 250         d) 200
Explanation: Kiran got 27% of total marks but failed by 39 marks

Pass marks =27% of maximum marks + 39
Srisri got 63% of total marks got which are 69 marks more than the pass marks
Pass marks = 63% of maximum marks – 69
27% of maximum marks+39= 63% of maximum marks-69
36% of maximum marks =  108
Maximum marks = 300
Aptitude Questions and Answers    Percentages Solved Problems 24
In a school of 1800 students, 40% are boys. 30% of the girls and 50% of the boys failed the exam. What % of students in the school passed the exam?
a) 62%        b) 63%      c) 45%         d) 50%
Explanation :     Total students are  100%
Boys are 40% , then girls are 60%
30% of the girls failed the exams =>
30 / 100
x 60 = 18% girls failed in the exam
50% of the boys failed the exams =>
50 / 100
x 40  = 20% boys failed in the exam
Total % of students failed in the exam = 20 % + 18% = 38%
Percentage of students passed the exam = 100 % - 38% = 62%

Aptitude Questions with Solutions    Percentages Solved Problems 25
60 litres of a mixture of milk and water contain 35% of water. If 10 litres of milk is added, what will be the percentage of water in the resultant mixture?
a) 35%       b) 30%           c) 40%     d) 45%
Explanation :  Water in the mixture = 35/100 x 60 = 21
Milk in the mixture = 60-21= 39 liters
10 litres of milk is added , the total mixture=60 +10 =70 litres
Percentage of water in the resultant mixture =
21 / 70
x 100 %
= 30%
Quantitative Aptitude Question - Percentages Solved Problems 26
A bucket contains 250 lit. of pure milk. At 9’O clock 20% of this is taken out and replaced by water. At 10’O clock 20% of the mixture is taken out and replaced by water. Again at 11’O clock 20% of the mixture is taken out and replaced by water. What is the percentage of milk in the final mixture?
a) 128 lt        b) 200 lt         c) 64 lt.        d) 140 lt
Explanation:  Pure milk = 250 lts initially
For every hour 20% is taken out  => 80% remains
Percentage of milk in the final mixture =
250 x
80 / 100
x
80 / 100
x
80 / 100
= 250 x
4 / 5
x
4 / 5
x
4 / 5
=128 lts
Aptitude Questions with answer   Percentages Solved Problems 27
In an organization, the number of male employees is less than that of female employees by 30%, by what percentage the number of female employees is more than that of male employees?
a) 43 6/7 %    b) 42 6/7 %      c) 44 2/7 %      d) 41 6/7 %
Explanation :
If a value A is less than by B by x% , the B is
x / 100-x
x 100% more than A
Required percentage =
30 / 100-30
x 100 %
=
30 / 70
x 100%  =42 6/7%

Alternate Method :
Let number of female employees be 100.
Male employees are 30% less than female employees => 30
Required percentage =
30 / 70
x 100%
=42 6/7%

Quantitative Aptitude Questions   Percentages Solved Problems 28
The price of wheat is increased by 25%, by what percentage the consumption of sugar be reduced so that the expenditure on this account remains constant?
a) 9 1/11%                        b) 18 2/11%                      c) 20 %         d) 33 1/3 %
Explanation : If the price of a commodity is increase by x% , to keep the expenditure constant ,  the percentage consumption in the consumption of that commodity must be
(
x / (100+x)
) x 100%
The price of wheat is increased by 25%.
To keep the expenditure on this account remains constant, the % decrease in the consumption of wheat must be reduced by =>
25 / (100+25)
x 100%
=>
25 / 125
x 100% = 20%

Aptitude Questions with Explanations   Percentages Solved Problems 29
The price of an article has been reduced by 20%. In order to restore the original price, the new price must be increased by :
a) 33 1/3%                        b) 11  1/9%                         c) 9  1/11%                    d) 66  2/3%

Explanation:

Let original price = Rs.100
Price after reduction= Rs.80
To restore the original price , the price must be increased on Rs.80=Rs.20
Increase on Rs.100 = (
20 / 80
)×100)%=25%

Arithmetic Questions and Answers     Percentages Solved Problems 30
In an examination, 30% and 35% students respectively failed in Mathematics and physics while 27% students failed in both the subjects. If the number of students passing the examination is 496 , what is the total number of students who appeared in the examination?
a)760            b)800                    c)840        d)960
Explanation:
Percentage of students passing the examination
={ 100 –(30 + 35 – 27) }%
= { 100 – 38 } % = 62%
Let the total number of students appearing in the examination be N
Given 62% of N = 496
ð
62 / 100
x  N = 496 > N =
(496 x 100) / 62
ð  N=800
Therefore 800 students appearing in the examination.

Numerical Ability Solved Questions    Percentages Solved Problems 31
The maximum marks per paper in  3 subjects in Mathematics , Physics and Chemistry are set in the ratio 1 : 2 : 2 respectively. Shastri obtained 50% in Mathematics, 60% in Physics and 65% in Chemistry papers. What is overall percentage marks did he get overall?
a)55%        b)60%      c)65%          d)68%
Explanation : Ratio of maximum marks in 3 subjects = 1:2:2
Ratio of the marks got in Mathematics, Physics and Chemistry
=
50 / 100
x 1  :
60 / 100
x 2 :
65 / 100
x 2
= 0.5 : 1.2 : 1.3
Overall percentage of marks in 3 subjects =
(0.5 + 1.2 + 1.3) / (1+2+2)
x 100%
=
3 / 5
x 100%
= 60%
Aptitude Questions with Explanations    Percentages Solved Problems 32
In a tooth paste market survey, 30% opted for Colgate, whereas 50% opted for Pepsi dent. The remaining people were not certain of any product. If the difference between those who opted for Pepsident and those who are uncertain was 540, how many people were covered in the survey ?
a)1800    b)1440        c)1200        d)800
Explanation : Let the number of individuals involved in the survey be N.
Percentage of those who were not certain = 100- ( 30+50) = 20%
The difference between those who opted for Pepsident and those who are uncertain was 540.
50% of N – 20% of N = 540
ð   30% of N = 540
N=1800

Aptitude Questions and Answer     Percentages Solved Problems 33
If the price of petrol is increased by 25% , then find the percentage decrease in the consumption of the petrol of user , who can afford only  a 10% increase in expenditure ?
a)10%                    b)11%      c)12%           d)20%
Explanation :  Price x Consumption= Expenditure
1  x  1       = 1
Let new consumption be x.
Price is increased by 25% and he can afford only 10% increase in expenditure.
1.25  X   x/100       =1.1
=> x =
1.1 / 1.25
x 100%
=> x=  88%

Consumption can be 88% , the consumption must be reduced by 12%

Quantitative Aptitude Questions and answers   Percentages Solved Problems 34
The population of village increases at the rate of 4% per annum. There is an additional increase of 1% in the population due to the influx of job seekers. Therefore the percentage increase in the population after 2 years will be
a)10%          b)10.25%       c)11%     d)15%
Explanation : First increase is 4% , due to influx of job seeks 1% increase
So total increase is 5% per annum
After two years  , the percentage increase will be => 5 + 5 +
(5 x 5) / 100
%
= 10.25%

Aptitude Questions with Explanations    Percentages Solved Problems 35
A spends 80% of his salary and B spends 75% of his salary. Their total income is Rs 18000. Find the income of A , if the savings of A and B are equal?
a)Rs 8000      b)Rs 10000      c)Rs 12000       d)Rs 15000
Explanation: Let salaries of each one be 100%.
Savings of A = (100% - 80%)= 20% of his salary
Savings of B = (100% - 75%) = 25% of his salary.
Given that , the savings of both of them are same.
20% of A’s salary = 25% of B’s salary
A’s salary  : B’s salary = 25 : 20 = 5 : 4
ð  A’s salary = Rs 18000 x $\frac{5}{9}$  = Rs Rs 10000

Quantitative Aptitude             Percentages Solved Problems 36
1296 pencils were distributed equally among students in such a way that the number of pencils received by each student is 25% of the total number of students, How many pencils did each student receive?
a)15            b)17     c)18        d)72
Explanation : Let the number of student be  N.
Then each student got = 25% of N = ¼ of N
25% of N  x N = 1296  => ¼ of N x N  = 1296
ð  N2 = 1296 x 4 =5184
ð  N= 72
Each student got = 25% of 72 = ¼ of 72 = 18

Arithmetic Word Problems with Answer    Percentages Solved Problems 37
A person saves 20% of his income. If his income is increased by 20% and he saves 25% of the new income, by what per cent his actual savings will decrease?
a)25%       b)30%         c)40%             d)50%
Explanation: Let initial income= Rs 100
Initial savings = 20% of Rs 100 = Rs  20
Income after 20% increase = 100 x
120 / 100
= Rs 120
New savings = 25 % of Rs 120 = Rs 30
Increase in savings = Rs 30 – Rs 20 = Rs 10
Therefore, percentage increase in savings =
10 / 20
x 100% = 50%

Aptitude Questions and Answer         Percentages Solved Problems 38
A number is increased by 10% and again increased by 205. By what percentage should the increased number be reduced so as to get back the original number ?
a)24.24%     b)30%        c)37.25%     d)32%
Explanation : Net increase = 10 + 20 +
10x20 / 100
%
= 32%
Let the original number be 100.
Then new number (number after increase) = 132
To get back the original value , the number must be reduced by =
32 / 132
x 100 %
= 24.24%

Aptitude Questions with Explanations     Percentages Solved Problems 39
The total salary of A and B in an organization is Rs 30000. If the salary of A increase by 8% and salary of B increase by 10%, then their total salary would increase to Rs 32600. Find the salary of B ?
a)Rs 6000               b)Rs 10000                        c)Rs 8000                d)Rs 12000
Explanation: Let the total salary is completely B’s.
Then increase in the salary is 10% 30000 = Rs 3000
Therefore , increased salary = Rs 30000 + Rs 3000 = Rs 30000
But the actual increase in salary = 32600
Difference = Rs 33000 - Rs 32600 = Rs 400
Rs 400 is 2%( that is 10% - 8% = 2 %) of the A’s salary.
A’s salary =
400 / 2
x 100 = Rs 20000
B’s salary = Rs 30000 – Rs 20000
= Rs 10000

Aptitude Questions with Solutions        Percentages Solved Problems 40
800 candidates of a college appeared for an examination. 40% of the candidates appeared are female candidates and 12.5% of the female candidates failed in the examination. What percentages of male candidates failed if the total pass percentage of the 85% ?
a)16 2/3%               b)15%      c)18%       d)20%
Explanation : Total female candidates = 800 x
40 / 100
= 320
Total male candidates = 800 x
60 / 100
= 480
Total number of candidates failed = 15 % of 800 = 120
Total number of female candidates failed = 12.5% of 320 = 40
Therefore total number of male candidates failed = 120 –40 = 80
Percentage of male candidates failed in the examination =
80 / 480
x 100 %
= 16 2/3%

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