1.The difference between the value of a number increased by 25% and the value of the original number decreased by 30% is 22. What is the original number?
A. 70
B. 65
C. 40
D. 90
E. 75
Solutions
Short Trick :
Let the number be 100x.
If increased by 25% then it becomes 125x.
If decreased by 30%, then becomes 70x.
Now, according to question,
125x – 70x = 22
x = 2/5
original number = 100x ⇒ 100 × 2/5 = 40
Detailed Solution :
Say A is the original number.
Number value increased by 25%
⇒ A + (0.25A) = 1.25A
Number value decreased by 30%
⇒ A – (0.30A) = 0.70A
Given that, Difference between increased and decreased value is 22.
⇒ (1.25 – 0.70) × A = 22
⇒ 0.55A = 22
⇒ A = 22/0.55 = 40∴ 40 is the original value of the number
.
2.By mixing water with milk a dishonest milkman gains the profit of 11 1/9% . Find the quantity of water mixed by him with 1 litre of milk.
A. 1/9 litres
B. 1/8 litres
C. 1/10 litres
D. 1/11 litres
E. None of these
Solutions
Short Trick :
Let for 100 litres he gained profit of 11.11 litres.
∴ 100 litres = 11.11 litres
for 1 litre = ?
? = 0.1111 ⇒ 1/9
Detailed Solution :
To gain 11 1/9% the milkman has to mix 11 1/9 liter of water with 100 litres of pure milk.
If he does so, he can sell a litre of mixture [at the price of pure milk] while his investment is only 100 litre of pure milk.
∴ He is mixing 11 1/9 Liter water with 100 litre milk.
With 1 litre milk he has to mix litre of water.
Now, a litre of water
(100/9)/100 litre of water= 1/9 litre of water.
3.In a company, there are 75% skilled workers and remaining ones are unskilled. 80% of skilled workers and 20% of unskilled workers are permanent. If number of temporary workers is 126, then find the number of total workers.
A. 124
B. 388
C. 324
D. 360
E. None of these
Solutions
Let the total number of workers be ‘x’, then according to the question,
Skilled workers = 75% of x
Unskilled workers = (100-75)% = 25% of x,
Permanent workers = 20% of unskilled workers + 80% of skilled workers
= 20% of 25% of x + 80% of 75% of x
= x × (20/100) × (25/100) + x × (80/100) × (75/100)
= x {0.05 + 0.6} = 0.65x
According to the question, remaining workers are temporary whose number is 126,
⇒ (1 – 0.65)x = 126
⇒ 0.35x = 126
⇒ x = 126/0.35 = 360
Hence, the required number of workers is 360.
4. If the numerator of a certain fraction increased by 100% and the denominator is increased by 200%, the new fraction thus formed is 4/21. What is the original fraction?
A. 2/7
B. 3/7
C. 2/5
D. 4/7
E. None of these
Solutions
Let F be the original fraction.
As the numerator is increased by 100% and denominator is increased by 200%, the formed equation will be;
F [ (200/100) / (300/100) ] = 4/21
F [ 2/3 ] = 4/21
F = 4/21 * 3/2
F = 2/7
5.In a province, there are three types of cities: A, B and C. The number of cities A is 30% more than that of cities B and C together. Number of cities B is 20% of total cities. If the total number of cities is 10000, then how many type C cities are there ?
A. 200
B. 256
C. 312
D. 429
E. Given condition is not possible
Solutions
Let number of cities C be T.
Number of cities B is 20% of total cities. Total number of cities is 10000.
⇒ Number of cities B = 10000 × (20/100) = 2000
⇒ Number of cities A and C = 10000 – 2000 = 8000
⇒ Number of cities A = 8000 – T
The number of cities A is 30% more than that of cities B and C together.
⇒ 8000 – T = (T + 2000) × (1 + 30/100)
⇒ 8000 – T = 1.3T + 2600
⇒ T = 5400/2.3
We see that T is not a natural number, and hence cannot be the number of cities C.∴ Given condition is not possible.
6. Three contenders M, N and P battled in an election. Out of the total votes on a voter list 25% did not vote and 6.66% votes polled were invalid. P got 2450 valid votes, which were 40% more than that of N. If M got only 40% of the total votes, then what is the total number of votes?
A. 11000
B. 12000
C. 1400
D. 14000
E. None of the above
Solutions
Let the total number of votes be ‘x’
25% of x did not vote
No. of polled votes = x – (25/100)x
No. of polled votes = (100 – 25)/100 × x
No. of polled votes = (75/100)x
No. of polled votes = 75%
No. of polled votes = 0.75x
Of these, 6.66% of votes were invalid
No. of valid votes = 0.75x – (6.66/100) × 0.75x
No. of valid votes = 0.75x × (100 – 6.66)/100
No. of valid votes = 0.75x × (100 – 6 2/3 )/100
No. of valid votes = 0.75x × (100 – 20/3)/100
No. of valid votes = 0.75x × (300 – 20)/300
No. of valid votes = 0.75x × 280/300
No. of valid votes = 0.25x × 280/100
No. of valid votes = 0.7x
No. of valid votes = 0.7x
Now, M + N + P = 0.7x
We know, P = 2450 valid votes
P has 40% more votes than N.
⇒ 2450 = N + (40/100)N
⇒ 2450 = (140/100)N
⇒ 2450 = (7/5)N
⇒ 2450/7 × 5 = N
N = 350 × 5
N = 1750
M has 40% of total votes
⇒ 0.4x + 1750 + 2450 = 0.7x
⇒ 4200 = 0.7x – 0.4x
⇒ 4200 = 0.3x
⇒ 4200/0.3 = x
⇒ x = 14000∴ Total number of votes = 14000
7. Lavanya has to travel from Hyderabad to Chennai which is a certain distance apart. 23% of the distance is travelled by bus, 50%of the remaining by train and the rest of the distance which is 231 km by taxi. Find the distance between Hyderabad and Chennai in km.
A. 600
B. 550
C. 675
D. 590
E. None of these
Solutions
Let the total distance travelled = x km
23% of the distance is travelled by bus
Thus, the remaining distance = (100 – 23)% of x = 77% of x
50% of the remaining 77% of x is travelled by train = 0.5 × 0.77 = 0.385
38.5% of the distance is travelled by train
Thus, the remaining distance = [100 – (23 + 38.5)] = 38.5%
Thus 38.5% of x is travelled by taxi = 231 km
⇒ 38.5/100 × x = 231
⇒ x = (231 × 100)/38.5
⇒ x = 600 km
∴ Distance between Hyderabad and Chennai = 600 km
8. After a certain increase in the number of students the class becomes 3 times the half of its previous size. How much is the increase?
A. 25%
B. 30%
C. 35%
D. 40%
E. 50%
Solutions
Initial number of students = X
New number of students = 3X/2∴ Increase = X/2X × 100 = 50%
9. Direction: Based on the given information, determine the relation between the two quantities
Quantity A: 75% of a number when added to 75 is 20 less than the number. Then that number is:Quantity B: Fifth term of a G.P. is 2. Then 75% of the product of its first nine terms:
A. Quantity A > Quantity B
B. Quantity A < Quantity B
C. Quantity A ≥ Quantity B
D. Quantity A ≤ Quantity B
E. Quantity A = Quantity B
Solutions
First we will find Quantity A,
Quantity A:
Let the number be ‘x’.
75% of the number = 75% of x = 0.75x
According to the question,
0.75x + 75 = x – 20
⇒ 0.25x = 95
⇒ x = 95/0.25 = 380
∴ The number is 380.
Now,
Quantity B:
We know that for a G.P.-
nth term = arn-1
Where, a = 1st term, r = common ratio
⇒ 5th term = t5 = ar4 = 2
Product of its first nine terms = (a) × (ar) × (ar2) ×………× (ar8)
= a9 r1 + 2 + 3 + ….+ 8 = a9 r36 = (ar4)9 = 29 = 512
75% of the product of its first nine terms = (75/100) × 512 = 384∴ Quantity A < Quantity B
10. Compare the values of the two quantities in the question and answer.
Quantity 1: Find the value of x, such that 3 times the 35% of x is 40 less than 8/7 of x.Quantity 2: Find the value of x, such that 7 times the 70% of x is 1800 more than 6/11 of x.
A. Quantity 1 > Quantity 2
B. Quantity 1 < Quantity 2
C. Quantity 1 ≥ Quantity 2
D. Quantity 1 ≤ Quantity 2
E. Quantity 1 = Quantity 2
Solutions
Solving for Quantity 1:
⇒ 3 × 35% of x = (8/7) x – 40
⇒ 1.05x = (8/7) x – 40
⇒ 7.35x = 8x – 280
⇒ 8x – 7.35x = 280
⇒ 0.65x = 280
⇒ x = 430.77
⇒ Quantity 1 = 430.77
Solving for Quantity 2:
⇒ 7 × 70% of x = 1800 + (6/11) x
⇒ 4.9x = 1800 + (6/11) x
⇒ 53.9x = 19800 + 6x
⇒ 53.9x – 6x = 19800
⇒ 47.9x = 19800
⇒ x = 413.36
⇒ Quantity 2 = 413.36∴ Quantity 1 > Quantity 2
11. Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answer.
Quantity A: There were 2000 boys and 1600 girls appear in the examination. If 70% of boys and 60% of girls passed the exam then find the percentage of failed students?
Quantity B: Virat scored 140 runs which included 11 boundaries and 6 sixes. What percent of his total score did he make by running between the wickets?
A. Quantity A > Quantity B
B. Quantity A < Quantity B
C. Quantity A = Quantity B
D. Quantity A ≤ Quantity B
E. Quantity A ≥ Quantity B
Solutions
Quantity A:
Failed boys = (100 – 70)% of 2000 = 30% of 2000 = 600
Failed Girls = (100 – 60)%of 1600 = 40% of 1600 = 640
⇒ Percentage of failed students = (600 + 640)/(2000 + 1600) × 100 = 34.44%
Quantity B:
Total score = 140
⇒ Score made by virat by boundaries and sixes = 6 × 6 + 11 × 4 = 36 + 44 = 80
⇒ Runs made by running between the wickets = 140 – 80 = 60
⇒ Required % = 60/140 × 100 = 42.85%
∴ Quantity A < Quantity B
12. Directions: Given below is a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. You should use the given data and your knowledge of Mathematics to choose between the possible answer.
What is the minimum passing percentage in an exam?
I. Mohan scored 158 marks in an exam and failed by 114 marks.II. The maximum marks of the exam are 642 more than the marks obtained by Mohan.
A. The data in statement I alone are sufficient to answer the question
B. The data in statement II alone are sufficient to answer the question
C. The data in statement I alone or in statement II alone are sufficient to answer the question
D. The data in both the statement I and II are not sufficient to answer the question.
E. The data in both the statement I and II together are necessary to answer the question.
Solutions
From statement I:
Mohan scored 158 marks in an exam and failed by 114 marks.
⇒ Minimum passing marks = 158 + 114 = 272 …(i)
Statement I alone is not sufficient to answer the question.
From statement II:
The maximum marks of the exam are 642 morethan the marks obtained by Mohan.
Statement II alone is not sufficient to answer the question.
From statement I & II together:
Maximum marks of the exam = 158 + 642 = 800
If the minimum passing percentage be x, then
Hence, both the statements are necessary to answer the questions.
13. The below question is asked followed by three statements. You have to study the question and all the three statements given and decide whether any information provided in the statement(s) are redundant and can be dispensed with while answering the question?
What is the amount saved by Sahil per month from his salary?
(I) Sahil spends 25% of his salary on food, 35% on medicine and education and Rs 2400 on entertainment.
(II) Sahil spends Rs.4000 per month on food.
(III) Sahil spends Rs.5600 per month on medicine and education.
A. Only I
B. Only II
C. Both II and III
D. 1 and II or III
E. None of these
Solutions
Given, the percentage of salary, Sahil spends on food is 25% and on medicine and education is 35% and Rs 2400 on entertainment in statement(1) and the actual amount spent on food in Rs in statement (2) and the actual amount spent on medicine and education in statement (3).
Based on above statement, either statement (2) or statement (3) can be dispensed.
14. Direction: Given below is a question and some statements given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. You should use the given data and your knowledge of Mathematics to choose between the possible answers.
How many marks did zaheer get in chemistry?
I. He got 60% on an average in hindi, chemistry and physics.
II. In chemistry he got 15% more than the average marks.
A. The data in statement I alone is sufficient to answer.
B. The data in statement II alone is sufficient to answer
C. The data either in statement I alone or in statement II alone.
D. The data in both the statements I and II even together are not sufficient to answer
E. The data in both the statements I and II together are necessary to answer the question.
Solutions
From statement I:
He got 60% marks on an average in hindi, chemistry and physics.
Data in statement I is not sufficient to answer the question, as the maximum marks of each subject is not given.
From statement II:
In chemistry he got 15% more than the average marks.
Same as statement I maximum marks are not given so we can say that equation II is not sufficient to answer the question.
Hence, data in statement I and statement II are not sufficient to answer the question, as the maximum marks of each subject is not given.
15. Directions: In each of the following questions, a question is asked followed by three statements. While answering the question, you may or may not require the data provided in all the statements. You have to read the question and the three statements and then decide upon whether the question can be answered with any one or two of the statements or all the three statements are required to answer the question.
How Much vote did the winner get in the election out of 20 lakh electorates?
(I) He defeated his rival by 3 lakh votes
(II) He get 150% of votes of that his rival
(III) Only 75% votes were polled
A. Only I and II
B. Only I and III
C. I, II and III
D. Only III
E. III and Either I or II
Solutions
Let the winner got x number of votes
And his rival got y votes
Now, by statement I, we know that x = y + 300000
By statement II, we know that x = 150% of y = 150y/100
By statement III, we know that x + y = 75% of 2000000 = 1500000
Therefore by using any of the 2 statements(I or II) and third statement, we can get 2 different equations in x and y and hence find their values.
Here x = 900000 and y = 600000
