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All questions of CTET Practice Test (Mathematics) for CTET & State TET Exam
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Six-elevenths of a number is equal to 22% of second number. Second number is equal to the one-fourth of third number. The value of the third number is 2400. What is the 45% of the first number? - a)108.9
- b)111.7
- c)117.6
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
Six-elevenths of a number is equal to 22% of second number. Second number is equal to the one-fourth of third number. The value of the third number is 2400. What is the 45% of the first number?
a)
108.9
b)
111.7
c)
117.6
d)
None of these
|
Swati Chopra answered |
Two men undertook to do a job for Rs. 1960. One of them can do it alone in 7 days, and the other in 8 days. With the assistance of a boy they together complete the work in 3 days. How much money will the boy get ? - a)Rs. 300
- b)Rs. 325
- c)Rs. 385
- d)Rs. 425
Correct answer is option 'C'. Can you explain this answer?
Two men undertook to do a job for Rs. 1960. One of them can do it alone in 7 days, and the other in 8 days. With the assistance of a boy they together complete the work in 3 days. How much money will the boy get ?
a)
Rs. 300
b)
Rs. 325
c)
Rs. 385
d)
Rs. 425
|
Sravya Nambiar answered |
Let's assume that the amount of work done by the first man in one day is x and the amount of work done by the second man in one day is y.
- The first man can complete the job alone in 7 days, so in one day he completes 1/7th of the work, which can be represented as x = 1/7.
- Similarly, the second man can complete the job alone in 8 days, so in one day he completes 1/8th of the work, which can be represented as y = 1/8.
Combined work:
- When the two men work together, the total work done in one day is x + y.
- With the assistance of the boy, they complete the work in 3 days, which means they complete 1/3rd of the work in one day.
- So, we have the equation x + y + b = 1/3, where b represents the amount of work done by the boy in one day.
Finding the values of x, y, and b:
- We already know that x = 1/7 and y = 1/8.
- Substituting these values in the equation x + y + b = 1/3, we get 1/7 + 1/8 + b = 1/3.
- Finding a common denominator of 56, we get 8/56 + 7/56 + b = 18/56.
- Simplifying the equation, we have 15/56 + b = 18/56.
- Subtracting 15/56 from both sides, we get b = 3/56.
Calculating the boy's share of the money:
- Now that we know the amount of work done by the boy in one day is b = 3/56, we can calculate the boy's share of the money.
- The total amount of work is represented by 1, and the boy does 3/56th of the work.
- So, the boy's share of the money is (3/56) * 1960 = Rs. 105.
Therefore, the boy will receive Rs. 105, which is option C.
- The first man can complete the job alone in 7 days, so in one day he completes 1/7th of the work, which can be represented as x = 1/7.
- Similarly, the second man can complete the job alone in 8 days, so in one day he completes 1/8th of the work, which can be represented as y = 1/8.
Combined work:
- When the two men work together, the total work done in one day is x + y.
- With the assistance of the boy, they complete the work in 3 days, which means they complete 1/3rd of the work in one day.
- So, we have the equation x + y + b = 1/3, where b represents the amount of work done by the boy in one day.
Finding the values of x, y, and b:
- We already know that x = 1/7 and y = 1/8.
- Substituting these values in the equation x + y + b = 1/3, we get 1/7 + 1/8 + b = 1/3.
- Finding a common denominator of 56, we get 8/56 + 7/56 + b = 18/56.
- Simplifying the equation, we have 15/56 + b = 18/56.
- Subtracting 15/56 from both sides, we get b = 3/56.
Calculating the boy's share of the money:
- Now that we know the amount of work done by the boy in one day is b = 3/56, we can calculate the boy's share of the money.
- The total amount of work is represented by 1, and the boy does 3/56th of the work.
- So, the boy's share of the money is (3/56) * 1960 = Rs. 105.
Therefore, the boy will receive Rs. 105, which is option C.
In a classroom there are certain number of benches. If 6 students are made to sit on a bench, then to accommodate all of them, one more bench is needed. However, if 7 students are made to sit on a bench, then, after accommodating all of them, space for 5 students is left. What is the total number of students in the class? - a)30
- b)42
- c)72
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
In a classroom there are certain number of benches. If 6 students are made to sit on a bench, then to accommodate all of them, one more bench is needed. However, if 7 students are made to sit on a bench, then, after accommodating all of them, space for 5 students is left. What is the total number of students in the class?
a)
30
b)
42
c)
72
d)
None of these
|
Sparsh Das answered |
A Raymond’s Trader marked the selling price of an article at 10% above the cost price. At the same time of selling he allowed certain discount and suffers a loss of 1%. He allowed a discount of: - a)11%
- b)10%
- c)9%
- d)10.5%
Correct answer is option 'B'. Can you explain this answer?
A Raymond’s Trader marked the selling price of an article at 10% above the cost price. At the same time of selling he allowed certain discount and suffers a loss of 1%. He allowed a discount of:
a)
11%
b)
10%
c)
9%
d)
10.5%
|
Shounak Iyer answered |
A man starts running from point P at 11:00 a.m. with a speed of 10 km/hr. He runs for 2 hours and then takes a 1 hour rest. He continues the pattern till he is caught by another man who starts at 2:00 p.m. from point P and runs non-stop at a speed of 15 km/hr towards the first man. At what time (in p.m.) will the first man be caught? - a)6:20
- b)4:40
- c)6:00
- d)5:30
Correct answer is option 'B'. Can you explain this answer?
A man starts running from point P at 11:00 a.m. with a speed of 10 km/hr. He runs for 2 hours and then takes a 1 hour rest. He continues the pattern till he is caught by another man who starts at 2:00 p.m. from point P and runs non-stop at a speed of 15 km/hr towards the first man. At what time (in p.m.) will the first man be caught?
a)
6:20
b)
4:40
c)
6:00
d)
5:30
|
Arjun Datta answered |
The average weight of A, B and C is 55 kg. If the average weight of A and B be 50 kg and that of B and C be 53 kg, then the weight of B is- a)41 kg
- b)42 kg
- c)39.5 kg
- d)45 kg
Correct answer is option 'A'. Can you explain this answer?
The average weight of A, B and C is 55 kg. If the average weight of A and B be 50 kg and that of B and C be 53 kg, then the weight of B is
a)
41 kg
b)
42 kg
c)
39.5 kg
d)
45 kg
|
|
Sounak Sharma answered |
Given Information:
- Average weight of A, B and C = 55 kg
- Average weight of A and B = 50 kg
- Average weight of B and C = 53 kg
Calculating individual weights:
Let the weight of A, B, and C be denoted as A, B, and C respectively.
1. From the given information, we have:
A + B + C = 55 * 3 = 165 kg (1)
2. Also, A + B = 50 * 2 = 100 kg (2)
3. And, B + C = 53 * 2 = 106 kg (3)
Solving equations:
Subtracting equation (2) from equation (1), we get:
(A + B + C) - (A + B) = 165 - 100
=> C = 65 kg
Subtracting equation (3) from equation (1), we get:
(A + B + C) - (B + C) = 165 - 106
=> A = 59 kg
So, A = 59 kg, B = 41 kg, and C = 65 kg.
Conclusion:
Therefore, the weight of B is 41 kg, which is the correct answer.
In a class, the number of girls is 20% more than that of the boys. The strength of the class is 66. If 4 more girls are admitted to the class, the ratio of the number of boys to that of the girls is. - a)1: 2
- b)3 : 4
- c)1: 4
- d)3: 5
Correct answer is option 'B'. Can you explain this answer?
In a class, the number of girls is 20% more than that of the boys. The strength of the class is 66. If 4 more girls are admitted to the class, the ratio of the number of boys to that of the girls is.
a)
1: 2
b)
3 : 4
c)
1: 4
d)
3: 5
|
Prateek Ghosh answered |
In a business, Abhiram and Chiru invested amounts in the ratio 2: 1, whereas the ratio between amounts invested by Abhiram and Bikash was 3: 2. If Rs. 1,57,300 was their profit, how much amount did Bikash receive? - a)Rs. 72600
- b)Rs. 48400
- c)Rs. 36300
- d)Rs. 24200
Correct answer is option 'B'. Can you explain this answer?
In a business, Abhiram and Chiru invested amounts in the ratio 2: 1, whereas the ratio between amounts invested by Abhiram and Bikash was 3: 2. If Rs. 1,57,300 was their profit, how much amount did Bikash receive?
a)
Rs. 72600
b)
Rs. 48400
c)
Rs. 36300
d)
Rs. 24200
|
Ashutosh Banerjee answered |
The average monthly salary of the workers in a workshop is Rs. 8,500. If the average monthly salary of 7 technicians is Rs. 10,000 and the average monthly salary of the rest is Rs. 7,800, then the total number of workers in the workshop is - a)18
- b)20
- c)22
- d)24
Correct answer is option 'C'. Can you explain this answer?
The average monthly salary of the workers in a workshop is Rs. 8,500. If the average monthly salary of 7 technicians is Rs. 10,000 and the average monthly salary of the rest is Rs. 7,800, then the total number of workers in the workshop is
a)
18
b)
20
c)
22
d)
24
|
|
Aarav Majumdar answered |
In an entrance examination Rockie scored 56% marks, perry scored 92% marks and Srifi scored 634 marks. The maximum marks of the examination are 875, what are the average mark scored by all the three girls together: - a)929
- b)815
- c)690
- d)643
Correct answer is option 'D'. Can you explain this answer?
In an entrance examination Rockie scored 56% marks, perry scored 92% marks and Srifi scored 634 marks. The maximum marks of the examination are 875, what are the average mark scored by all the three girls together:
a)
929
b)
815
c)
690
d)
643
|
|
Madhavan Singh answered |
Four Iron metal rods of lengths 78 cm, 104 cm, 117 cm, and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut? - a)27
- b)36
- c)43
- d)400
Correct answer is option 'B'. Can you explain this answer?
Four Iron metal rods of lengths 78 cm, 104 cm, 117 cm, and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?
a)
27
b)
36
c)
43
d)
400
|
Saikat Sengupta answered |
Since each Iron rod must be cut into parts of equal length and
each part must be as long as possible, so HCF should be
taken.
HCF of 78, 104, 117 and 169 = 13.
No. of parts from 78cm. rod = 78 /13=6
No. of parts from 104 cm. rod =104/13=8
No. of parts from 117 cm. rod =117/ 13=9
No. of parts from 169 cm. rod =169 /13=13
Maximum no. of pieces = 6 + 8 + 9 + 13 = 36
each part must be as long as possible, so HCF should be
taken.
HCF of 78, 104, 117 and 169 = 13.
No. of parts from 78cm. rod = 78 /13=6
No. of parts from 104 cm. rod =104/13=8
No. of parts from 117 cm. rod =117/ 13=9
No. of parts from 169 cm. rod =169 /13=13
Maximum no. of pieces = 6 + 8 + 9 + 13 = 36
A, B and C can complete a work in 10, 12 and 15 days respectively. All three of them start together but after 3 days A leaves the job and B left the job 2 days before the work was completed. C completed the remaining work alone. In how many days was the total work completed? - a)25/9 days
- b)52/9 days
- c)26/9 days
- d)53/9 days
Correct answer is option 'B'. Can you explain this answer?
A, B and C can complete a work in 10, 12 and 15 days respectively. All three of them start together but after 3 days A leaves the job and B left the job 2 days before the work was completed. C completed the remaining work alone. In how many days was the total work completed?
a)
25/9 days
b)
52/9 days
c)
26/9 days
d)
53/9 days
|
|
Yash Malik answered |
A person scores 45% of the total marks in the exam and still fails by 40 marks. The passing percentage of the exam is 55%. What is the maximum marks of the exam? - a)300
- b)350
- c)400
- d)500
Correct answer is option 'C'. Can you explain this answer?
A person scores 45% of the total marks in the exam and still fails by 40 marks. The passing percentage of the exam is 55%. What is the maximum marks of the exam?
a)
300
b)
350
c)
400
d)
500
|
|
Priyanka Khanna answered |
Given:
- The person scores 45% of the total marks in the exam.
- The person fails by 40 marks.
- The passing percentage of the exam is 55%.
To find:
- The maximum marks of the exam.
Approach:
1. Let's assume the maximum marks of the exam as 'x'.
2. According to the given information, the person scores 45% of 'x' marks.
3. The passing percentage of the exam is 55%, which means the person should score at least 55% of 'x' marks to pass the exam.
4. The person fails by 40 marks, so the difference between the passing marks and the obtained marks is 40.
5. We can set up the following equation based on the above information:
55% of 'x' - 45% of 'x' = 40
6. Simplifying the equation:
0.55x - 0.45x = 40
0.1x = 40
x = 40 / 0.1
x = 400
Answer:
The maximum marks of the exam is 400. (Option C)
- The person scores 45% of the total marks in the exam.
- The person fails by 40 marks.
- The passing percentage of the exam is 55%.
To find:
- The maximum marks of the exam.
Approach:
1. Let's assume the maximum marks of the exam as 'x'.
2. According to the given information, the person scores 45% of 'x' marks.
3. The passing percentage of the exam is 55%, which means the person should score at least 55% of 'x' marks to pass the exam.
4. The person fails by 40 marks, so the difference between the passing marks and the obtained marks is 40.
5. We can set up the following equation based on the above information:
55% of 'x' - 45% of 'x' = 40
6. Simplifying the equation:
0.55x - 0.45x = 40
0.1x = 40
x = 40 / 0.1
x = 400
Answer:
The maximum marks of the exam is 400. (Option C)
A bus travels 2/5 of a total journey at its usual speed. The remaining distance was covered by bus at 6/7 of its usual speed. Due to slow speed it reaches its destination 50 minutes late. If the total distance is 200 kms, then what is the usual speed (in km/hr) of bus? - a)20.57
- b)24
- c)28
- d)26.52
Correct answer is option 'B'. Can you explain this answer?
A bus travels 2/5 of a total journey at its usual speed. The remaining distance was covered by bus at 6/7 of its usual speed. Due to slow speed it reaches its destination 50 minutes late. If the total distance is 200 kms, then what is the usual speed (in km/hr) of bus?
a)
20.57
b)
24
c)
28
d)
26.52
|
|
Pooja Khanna answered |
The weights of Mr. Gupta and Mrs. Gupta are in the ratio 7: 8 and their total weight, combined is 120 kg. After taking a dieting course Mr. Gupta reduces by 6 kg and the ratio between their weights changes to 5: 6. So, Mrs. Gupta has reduced by - a)2 kg
- b)4 kg
- c)3 kg
- d)5 kg
Correct answer is option 'B'. Can you explain this answer?
The weights of Mr. Gupta and Mrs. Gupta are in the ratio 7: 8 and their total weight, combined is 120 kg. After taking a dieting course Mr. Gupta reduces by 6 kg and the ratio between their weights changes to 5: 6. So, Mrs. Gupta has reduced by
a)
2 kg
b)
4 kg
c)
3 kg
d)
5 kg
|
|
Swati Chopra answered |
5 years ago the average age of a family which includes father, mother and a son was 35 years. 3 years ago the average age of father and mother was 46 years. What is the present age (in years) of the son? - a)20
- b)24
- c)26
- d)22
Correct answer is option 'D'. Can you explain this answer?
5 years ago the average age of a family which includes father, mother and a son was 35 years. 3 years ago the average age of father and mother was 46 years. What is the present age (in years) of the son?
a)
20
b)
24
c)
26
d)
22
|
|
Avantika Singh answered |
In an examination, 62% student passed in geography and 59% students passed in English. If 6% students failed in both the subjects, then what is the percentage of students who have passed in both the subjects? - a)25%
- b)27%
- c)29%
- d)31%
Correct answer is option 'B'. Can you explain this answer?
In an examination, 62% student passed in geography and 59% students passed in English. If 6% students failed in both the subjects, then what is the percentage of students who have passed in both the subjects?
a)
25%
b)
27%
c)
29%
d)
31%
|
Sravya Desai answered |
Two friends P and Q stared a business investing amount in the ratio of 5: 6. R joined them after 6 months investing an amount equal to that of Q’s amount. At the end of year, 20% profit was earned which was equal to Rs. 98,000. What was the share of R? - a)Rs. 2,10,00
- b)Rs. 1,05,000
- c)Rs. 1,750,0
- d)Rs. 2,25,00
Correct answer is option 'A'. Can you explain this answer?
Two friends P and Q stared a business investing amount in the ratio of 5: 6. R joined them after 6 months investing an amount equal to that of Q’s amount. At the end of year, 20% profit was earned which was equal to Rs. 98,000. What was the share of R?
a)
Rs. 2,10,00
b)
Rs. 1,05,000
c)
Rs. 1,750,0
d)
Rs. 2,25,00
|
|
Bhaskar Chaudhary answered |
Mr. X invested an amount for 2 years at 15% per annum at simple interest. Had the interest been compounded, he would have earned Rs. 450/- more as interest. What was the amount invested? - a)Rs. 22,000
- b)Rs. 25,000
- c)Rs. 18,000
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
Mr. X invested an amount for 2 years at 15% per annum at simple interest. Had the interest been compounded, he would have earned Rs. 450/- more as interest. What was the amount invested?
a)
Rs. 22,000
b)
Rs. 25,000
c)
Rs. 18,000
d)
None of these
|
|
Samarth Saini answered |
Amit sold a car at 5% profit and a bike at 10% profit, in whole transaction he gets Rs 15000 as a profit. If he sold the car at 5% loss and the bike at 15% profit, he gets Rs 5000 as a profit. Find the cost price of car? - a)80000
- b)140000
- c)160000
- d)120000
Correct answer is option 'B'. Can you explain this answer?
Amit sold a car at 5% profit and a bike at 10% profit, in whole transaction he gets Rs 15000 as a profit. If he sold the car at 5% loss and the bike at 15% profit, he gets Rs 5000 as a profit. Find the cost price of car?
a)
80000
b)
140000
c)
160000
d)
120000
|
|
Yash Malik answered |
Suresh solved 60% of the question in an examination correctly. If out of 71 Questions solved by Suresh, 37 questions are correct and out of remaining every 7 questions, 5 questions have been solved by Suresh correctly. Then find the total number of questions asked in the examination? - a)49
- b)120
- c)81
- d)111
Correct answer is option 'B'. Can you explain this answer?
Suresh solved 60% of the question in an examination correctly. If out of 71 Questions solved by Suresh, 37 questions are correct and out of remaining every 7 questions, 5 questions have been solved by Suresh correctly. Then find the total number of questions asked in the examination?
a)
49
b)
120
c)
81
d)
111
|
Atharva Shah answered |
What is the average of all numbers between 9 and 90 which are divisible by 8? - a)53
- b)52
- c)51
- d)50
Correct answer is option 'B'. Can you explain this answer?
What is the average of all numbers between 9 and 90 which are divisible by 8?
a)
53
b)
52
c)
51
d)
50
|
|
Anand Desai answered |
To find the average of all numbers between 9 and 90 that are divisible by 8, we need to first determine the count of such numbers and then calculate their sum. Finally, we can divide the sum by the count to find the average.
1. Count of numbers divisible by 8 between 9 and 90:
- The smallest number divisible by 8 in this range is 16.
- The largest number divisible by 8 in this range is 88.
- We can find the count by subtracting the two values and dividing by 8, and then adding 1 to include both ends of the range.
- Count = (88 - 16) / 8 + 1 = 11
2. Sum of numbers divisible by 8 between 9 and 90:
- To find the sum, we can use the formula for the sum of an arithmetic series: Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term.
- In this case, a = 16, l = 88, and n = 11.
- Sum = (11/2)(16 + 88) = 11 * 104 = 1144
3. Average:
- To find the average, we divide the sum by the count.
- Average = 1144 / 11 = 104.3636...
Since the question asks for the average as an integer, we need to round down to the nearest whole number. The largest whole number less than 104.3636 is 104. Therefore, the average of all numbers between 9 and 90 that are divisible by 8 is 104.
Therefore, the correct answer is option B) 52.
1. Count of numbers divisible by 8 between 9 and 90:
- The smallest number divisible by 8 in this range is 16.
- The largest number divisible by 8 in this range is 88.
- We can find the count by subtracting the two values and dividing by 8, and then adding 1 to include both ends of the range.
- Count = (88 - 16) / 8 + 1 = 11
2. Sum of numbers divisible by 8 between 9 and 90:
- To find the sum, we can use the formula for the sum of an arithmetic series: Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term.
- In this case, a = 16, l = 88, and n = 11.
- Sum = (11/2)(16 + 88) = 11 * 104 = 1144
3. Average:
- To find the average, we divide the sum by the count.
- Average = 1144 / 11 = 104.3636...
Since the question asks for the average as an integer, we need to round down to the nearest whole number. The largest whole number less than 104.3636 is 104. Therefore, the average of all numbers between 9 and 90 that are divisible by 8 is 104.
Therefore, the correct answer is option B) 52.
A is 1.5 times efficient than B therefore takes 8 days less than B to complete a work. If A and B work on alternate days and A works on first day, then in how many days the work will be completed? - a)17
- b)19
- c)19.5
- d)21
Correct answer is option 'B'. Can you explain this answer?
A is 1.5 times efficient than B therefore takes 8 days less than B to complete a work. If A and B work on alternate days and A works on first day, then in how many days the work will be completed?
a)
17
b)
19
c)
19.5
d)
21
|
|
Aaditya Joshi answered |
Chapter doubts & questions for CTET Practice Test (Mathematics) - Mathematics & Pedagogy Paper 2 for CTET & TET Exams 2024 is part of CTET & State TET exam preparation. The chapters have been prepared according to the CTET & State TET exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for CTET & State TET 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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Mathematics & Pedagogy Paper 2 for CTET & TET Exams
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