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All questions of Elementary Mathematics for CDS Exam
A man, his wife & his son works in a park. Man works for 2 days, woman for 
son for 4 days. Ratio of daily wages of man & woman is 7 : 4 & that of man & child is 7 : 3. If total incomes is Rs. 12000. Find the daily income of man (in Rs.). - a)2100
- b)1200
- c)900
- d)600
Correct answer is option 'A'. Can you explain this answer?
A man, his wife & his son works in a park. Man works for 2 days, woman for son for 4 days. Ratio of daily wages of man & woman is 7 : 4 & that of man & child is 7 : 3. If total incomes is Rs. 12000. Find the daily income of man (in Rs.).
son for 4 days. Ratio of daily wages of man & woman is 7 : 4 & that of man & child is 7 : 3. If total incomes is Rs. 12000. Find the daily income of man (in Rs.). a)
2100
b)
1200
c)
900
d)
600
|
Notes Wala answered |
The angle of elevation of the top of a tree at a point B due east of the tree is 60° and at a point A due west of the tree is 30°. If the distance between A and B is 100 m. Then the height of tree(in m) is ? - a)20√3
- b)25√3
- c)30√3
- d)15√3
Correct answer is option 'B'. Can you explain this answer?
The angle of elevation of the top of a tree at a point B due east of the tree is 60° and at a point A due west of the tree is 30°. If the distance between A and B is 100 m. Then the height of tree(in m) is ?
a)
20√3
b)
25√3
c)
30√3
d)
15√3
|
Advait Singh answered |
4 units → 100m
√3 units → 25√3m
CD = 25√3
Ifx= -5 and y = -2, then the value of x3 - 3x2 + 3x + 3y + y3 + 3y2 - a)-217
- b)+167
- c)-167
- d)-215
Correct answer is option 'A'. Can you explain this answer?
Ifx= -5 and y = -2, then the value of x3 - 3x2 + 3x + 3y + y3 + 3y2
a)
-217
b)
+167
c)
-167
d)
-215
|
|
Advait Singh answered |
Required value = (-5)3 - 3(-5)3 + 3(-5) + 3(-2) + (-2)3 + 3(-2)2
= -125 - 75 - 15 - 6 - 8 + 12 = -217
= -125 - 75 - 15 - 6 - 8 + 12 = -217
Kamlesh halwai sells rasgullas at Rs. 120 per kg. A rasgulla is made up of Sugar, Maida & Milk in the ratio 5 : 2 : 3. The ratio of prices of sugar, maida & milk is 1 : 5 : 5. Thus he gains 33 1/3% profit. Find the amount invested in sugar per kg of rasgulla? - a)60
- b)30
- c)52.5
- d)15
Correct answer is option 'D'. Can you explain this answer?
Kamlesh halwai sells rasgullas at Rs. 120 per kg. A rasgulla is made up of Sugar, Maida & Milk in the ratio 5 : 2 : 3. The ratio of prices of sugar, maida & milk is 1 : 5 : 5. Thus he gains 33 1/3% profit. Find the amount invested in sugar per kg of rasgulla?
a)
60
b)
30
c)
52.5
d)
15
|
|
Advait Singh answered |
150 workers were engaged to finish a piece of work in a certain number of days. Four workers dropped on the second day, four more workers dropped on third day and so on. It takes 8 more days to finish the work now, find the number of days in which the work was completed? - a)28
- b)24
- c)25
- d)30
Correct answer is option 'C'. Can you explain this answer?
150 workers were engaged to finish a piece of work in a certain number of days. Four workers dropped on the second day, four more workers dropped on third day and so on. It takes 8 more days to finish the work now, find the number of days in which the work was completed?
a)
28
b)
24
c)
25
d)
30
|
|
Notes Wala answered |
A man and a woman working together can do a certain work in 22 hrs. If their skills for doing the work are in the ratio 5 : 4. Then how many days will woman takes to finish the work? - a)44 hrs
- b)48 ½ hrs
- c)49 ½ hrs
- d)50 hrs
Correct answer is option 'C'. Can you explain this answer?
A man and a woman working together can do a certain work in 22 hrs. If their skills for doing the work are in the ratio 5 : 4. Then how many days will woman takes to finish the work?
a)
44 hrs
b)
48 ½ hrs
c)
49 ½ hrs
d)
50 hrs
|
|
Advait Singh answered |
In this given figure D, E and F are the mid points of the sides AB, BC and CA respectively and x, y and z are the midpoints of DE, EF and FD respectively. It is given that the area of triangle ABC is 48√3 cm2 and triangle XYZ also inscribes a circle. Find the diameter (in cm) of in-circle of triangle XYZ, if ∆ABC is an equilateral triangle.
- a)4√3
- b)8
- c)6√3
- d)2
Correct answer is option 'D'. Can you explain this answer?
In this given figure D, E and F are the mid points of the sides AB, BC and CA respectively and x, y and z are the midpoints of DE, EF and FD respectively. It is given that the area of triangle ABC is 48√3 cm2 and triangle XYZ also inscribes a circle. Find the diameter (in cm) of in-circle of triangle XYZ, if ∆ABC is an equilateral triangle.
a)
4√3
b)
8
c)
6√3
d)
2
|
|
Advait Singh answered |
then the value of x + y + z is
Neha’s weight is 140% of tina’s weight Mina’s weight is 90% of Lina’s weight. Lina’s weight is twice as much as that of Tina. If Neha’s weight is x% of Mina’s weight then x is equal to- - a)64 (2/3)
- b)77 (7/9)
- c)90
- d)128 (4/7)
Correct answer is option 'B'. Can you explain this answer?
Neha’s weight is 140% of tina’s weight Mina’s weight is 90% of Lina’s weight. Lina’s weight is twice as much as that of Tina. If Neha’s weight is x% of Mina’s weight then x is equal to-
a)
64 (2/3)
b)
77 (7/9)
c)
90
d)
128 (4/7)
|
|
Advait Singh answered |
, then, a4 + b4 =? 
The Ratio of the No. of boys to that of girls in a school is 5 : 3. If 70% of boys and 80% of the girls are scholarship holders then the percentage of students who do not get scholarship is - a)35.5%
- b)30%
- c)26 (1/4)%
- d)27%
Correct answer is option 'C'. Can you explain this answer?
The Ratio of the No. of boys to that of girls in a school is 5 : 3. If 70% of boys and 80% of the girls are scholarship holders then the percentage of students who do not get scholarship is
a)
35.5%
b)
30%
c)
26 (1/4)%
d)
27%
|
|
Advait Singh answered |
Product of two co-prime numbers is 221. Then their LCM is- - a)221
- b)17
- c)19
- d)1
Correct answer is option 'A'. Can you explain this answer?
Product of two co-prime numbers is 221. Then their LCM is-
a)
221
b)
17
c)
19
d)
1
|
|
Advait Singh answered |
HCF of two-prime numbers = 1
∴ Product of numbers = their LCM = 221
∴ Product of numbers = their LCM = 221
Ram aims to score an average of 85 percent marks in quarterly and half yearly exams but his average in quarterly is 5 percent less than his target and that in half yearly is 3 percent marks more than his aim. This difference between the total marks scored in both the exams is 48. Total marks aimed by Ram is. - a)510
- b)530
- c)480
- d)490
Correct answer is option 'A'. Can you explain this answer?
Ram aims to score an average of 85 percent marks in quarterly and half yearly exams but his average in quarterly is 5 percent less than his target and that in half yearly is 3 percent marks more than his aim. This difference between the total marks scored in both the exams is 48. Total marks aimed by Ram is.
a)
510
b)
530
c)
480
d)
490
|
|
Advait Singh answered |
is 
The sum of the reciprocals of the ages of two brothers Mahesh Babu and Ravi Teja is five times the difference of the reciprocals of their ages. If the ratio of the product of their ages to the sum of their ages is 14.4 : 1, find their ages. - a)36 and 24 yr
- b)24 and 20 yr
- c)18 and 15 yr
- d)12 and 9 yr
Correct answer is option 'A'. Can you explain this answer?
The sum of the reciprocals of the ages of two brothers Mahesh Babu and Ravi Teja is five times the difference of the reciprocals of their ages. If the ratio of the product of their ages to the sum of their ages is 14.4 : 1, find their ages.
a)
36 and 24 yr
b)
24 and 20 yr
c)
18 and 15 yr
d)
12 and 9 yr
|
Abhijeet Malik answered |
A took 15 s to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68 m/min. Find the area of the field. - a)45 sq m
- b)35 sq m
- c)60 sq m
- d)30 sq m
Correct answer is option 'C'. Can you explain this answer?
A took 15 s to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68 m/min. Find the area of the field.
a)
45 sq m
b)
35 sq m
c)
60 sq m
d)
30 sq m
|
|
Advait Singh answered |
A, B & C enter into a partnership by making investment in the ratio 3 : 5 : 7. After a year C invests another Rs 3, 37, 600 while A withdraws Rs 45600. Ratio of investments then change to 24 : 59 : 167. How much did A invest initially? (in Rs) - a)47,200
- b)45,600
- c)1,41,600
- d)6,86,054
Correct answer is option 'C'. Can you explain this answer?
A, B & C enter into a partnership by making investment in the ratio 3 : 5 : 7. After a year C invests another Rs 3, 37, 600 while A withdraws Rs 45600. Ratio of investments then change to 24 : 59 : 167. How much did A invest initially? (in Rs)
a)
47,200
b)
45,600
c)
1,41,600
d)
6,86,054
|
|
Advait Singh answered |
A and B started a business with Rs. 20000 and Rs. 35000 respectively. They agreed to share the profit in the ratio of their capital. C joins the partnership after 1 year with the condition that A, B and C will share profit equally and pays Rs. 220000 as premium for this, to be shared between A and B. This is to be divided between A and B in the ratio of - a)10 : 1
- b)1 : 10
- c)9 : 10
- d)10 : 9
Correct answer is option 'B'. Can you explain this answer?
A and B started a business with Rs. 20000 and Rs. 35000 respectively. They agreed to share the profit in the ratio of their capital. C joins the partnership after 1 year with the condition that A, B and C will share profit equally and pays Rs. 220000 as premium for this, to be shared between A and B. This is to be divided between A and B in the ratio of
a)
10 : 1
b)
1 : 10
c)
9 : 10
d)
10 : 9
|
|
Shreya Ahuja answered |
Solution:
Given, A invested Rs. 20000, B invested Rs. 35000 and C joined after 1 year.
Let the total profit be x.
Ratio of profit sharing between A and B = 20000 : 35000 = 4 : 7
Profit sharing ratio of A, B and C = 1 : 1 : 1
Step 1: Calculation of profit sharing between A and B before C joins the partnership.
Total profit = x
Profit sharing of A = (4/11)x
Profit sharing of B = (7/11)x
Step 2: Calculation of total profit sharing after C joins the partnership.
Let the total profit after C joins be y.
Now, the profit sharing ratio between A, B and C is 1 : 1 : 1
Profit sharing of A = (1/3)y
Profit sharing of B = (1/3)y
Profit sharing of C = (1/3)y
Total amount invested by A and B = Rs. 55000
Premium amount paid by C = Rs. 220000
This premium amount is to be shared between A and B in the ratio of their capital.
Ratio of capital of A and B = 20000 : 35000 = 4 : 7
Step 3: Calculation of premium amount to be shared between A and B.
Premium amount to be shared between A and B = (4/11) x 220000 = Rs. 80000
Ratio of sharing of premium amount between A and B = 4 : 7
Step 4: Calculation of profit sharing ratio of A and B after sharing of premium amount.
Profit sharing of A = (1/3)y + (4/11) x 80000
Profit sharing of B = (1/3)y + (7/11) x 80000
Step 5: Calculation of y.
Profit sharing of A = Profit sharing of B
(1/3)y + (4/11) x 80000 = (1/3)y + (7/11) x 80000
(3/11) x 80000 = (4/11) y - (7/11) y
(3/11) x 80000 = -(3/11) y
y = - Rs. 240000
Since profit cannot be negative, the partnership is in loss.
Ratio of sharing of premium amount between A and B = 4 : 7
Premium amount to be shared between A and B = (4/11) x 220000 = Rs. 80000
Ratio of profit sharing between A and B after sharing of premium amount = 1 : 10
Hence, option B is the correct answer.
Given, A invested Rs. 20000, B invested Rs. 35000 and C joined after 1 year.
Let the total profit be x.
Ratio of profit sharing between A and B = 20000 : 35000 = 4 : 7
Profit sharing ratio of A, B and C = 1 : 1 : 1
Step 1: Calculation of profit sharing between A and B before C joins the partnership.
Total profit = x
Profit sharing of A = (4/11)x
Profit sharing of B = (7/11)x
Step 2: Calculation of total profit sharing after C joins the partnership.
Let the total profit after C joins be y.
Now, the profit sharing ratio between A, B and C is 1 : 1 : 1
Profit sharing of A = (1/3)y
Profit sharing of B = (1/3)y
Profit sharing of C = (1/3)y
Total amount invested by A and B = Rs. 55000
Premium amount paid by C = Rs. 220000
This premium amount is to be shared between A and B in the ratio of their capital.
Ratio of capital of A and B = 20000 : 35000 = 4 : 7
Step 3: Calculation of premium amount to be shared between A and B.
Premium amount to be shared between A and B = (4/11) x 220000 = Rs. 80000
Ratio of sharing of premium amount between A and B = 4 : 7
Step 4: Calculation of profit sharing ratio of A and B after sharing of premium amount.
Profit sharing of A = (1/3)y + (4/11) x 80000
Profit sharing of B = (1/3)y + (7/11) x 80000
Step 5: Calculation of y.
Profit sharing of A = Profit sharing of B
(1/3)y + (4/11) x 80000 = (1/3)y + (7/11) x 80000
(3/11) x 80000 = (4/11) y - (7/11) y
(3/11) x 80000 = -(3/11) y
y = - Rs. 240000
Since profit cannot be negative, the partnership is in loss.
Ratio of sharing of premium amount between A and B = 4 : 7
Premium amount to be shared between A and B = (4/11) x 220000 = Rs. 80000
Ratio of profit sharing between A and B after sharing of premium amount = 1 : 10
Hence, option B is the correct answer.
= 3, then 
=? 
be 1, then the value of 8x10 + 
will be. 
The average age of eleven players of a cricket team decreases by 2 months when two new players are included in the team replacing two players of age 17 years and 20 yrs. The average age of new players is - a)17 yrs 1 month
- b)17 yrs 7 month
- c)17 yrs 11 month
- d)18 yrs 3 month
Correct answer is option 'B'. Can you explain this answer?
The average age of eleven players of a cricket team decreases by 2 months when two new players are included in the team replacing two players of age 17 years and 20 yrs. The average age of new players is
a)
17 yrs 1 month
b)
17 yrs 7 month
c)
17 yrs 11 month
d)
18 yrs 3 month
|
|
Advait Singh answered |
Six straight, zigzagging lines are drawn inside a rectangle. The drawing starts at the top left vertex and ends at the top right vertex. What is the minimum possible sum of the lengths of these 6 segments?
- a)10
- b)50
- c)75
- d)5
Correct answer is option 'A'. Can you explain this answer?
Six straight, zigzagging lines are drawn inside a rectangle. The drawing starts at the top left vertex and ends at the top right vertex. What is the minimum possible sum of the lengths of these 6 segments?
a)
10
b)
50
c)
75
d)
5
|
|
Advait Singh answered |
Make six copies of the 1 by 8 rectangle and place them next to each as shown below, so they make a 6 by 8 rectangle. The minimum distance from the top left vertex to the bottom right vertex is a straight line, so minimum sum will be 10.
A sphere with centre O is situated at the top of a pole as shown in the figure. An observer on the ground is at a distance of 100 m from the foot of the pole. The angles of elevation from the observer to the points P and Q on the sphere are 30° and 60° respectively. Then the radius (in m) of the sphere is
- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
A sphere with centre O is situated at the top of a pole as shown in the figure. An observer on the ground is at a distance of 100 m from the foot of the pole. The angles of elevation from the observer to the points P and Q on the sphere are 30° and 60° respectively. Then the radius (in m) of the sphere is
a)
b)
c)
d)
|
|
Advait Singh answered |
A man purchased 70 story books. But he found that he could get 8 extra books by spending 564 more and then the overall average price per book would be reduced by 2 Rs. The previous average price of each book was. - a)100
- b)90
- c)83
- d)84
Correct answer is option 'B'. Can you explain this answer?
A man purchased 70 story books. But he found that he could get 8 extra books by spending 564 more and then the overall average price per book would be reduced by 2 Rs. The previous average price of each book was.
a)
100
b)
90
c)
83
d)
84
|
|
Advait Singh answered |
Let the previous average price be Rs x
According to the question
70x + 564 = (x - 2) 78
70x + 564 = 78x - 156
8x = 720
x = 90
is equal to 
A certain number when divided by 899 leaves the remainder 65. when the same number is divided by 31, the remainder is: - a)2
- b)3
- c)4
- d)1
Correct answer is option 'B'. Can you explain this answer?
A certain number when divided by 899 leaves the remainder 65. when the same number is divided by 31, the remainder is:
a)
2
b)
3
c)
4
d)
1
|
|
Advait Singh answered |
∵ 899 is divided by 31 and leaves 0.
∴ required remainder = remainder by 65/31 = 3
∴ required remainder = remainder by 65/31 = 3
Without stoppage a train travels at an average speed of 75 km per hour and with stoppage it covers same destination at an average speed of 60 km/hr. How many minutes per hour does the train stop? - a)15 min
- b)8 min
- c)12min
- d)10 min
Correct answer is option 'C'. Can you explain this answer?
Without stoppage a train travels at an average speed of 75 km per hour and with stoppage it covers same destination at an average speed of 60 km/hr. How many minutes per hour does the train stop?
a)
15 min
b)
8 min
c)
12min
d)
10 min
|
|
Advait Singh answered |
The total earnings of A, B and C are Rs. 76000 and they save 30%, 25% and 20% of their incomes respectively. If their savings are in the ratio of 4 : 5 : 6, then the total earnings of A and B is more than the earnings of C by - a)Rs. 2000
- b)Rs. 3000
- c)Rs. 6000
- d)Rs. 4000
Correct answer is option 'D'. Can you explain this answer?
The total earnings of A, B and C are Rs. 76000 and they save 30%, 25% and 20% of their incomes respectively. If their savings are in the ratio of 4 : 5 : 6, then the total earnings of A and B is more than the earnings of C by
a)
Rs. 2000
b)
Rs. 3000
c)
Rs. 6000
d)
Rs. 4000
|
|
Akshay Datta answered |
Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? - a)20 hours
- b)30 hours
- c)15 hours
- d)25 hours
Correct answer is option 'A'. Can you explain this answer?
Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
a)
20 hours
b)
30 hours
c)
15 hours
d)
25 hours
|
|
Advait Singh answered |
Part filled by A in 1 hour = (1/36); Part filled by B in 1 hour = (1/45);
Part filled by (A + B) In 1 hour =(1/36)+(1/45)=(9/180)=(1/20)
Hence, both the pipes together will fill the tank in 20 hours.
Part filled by (A + B) In 1 hour =(1/36)+(1/45)=(9/180)=(1/20)
Hence, both the pipes together will fill the tank in 20 hours.
Chapter doubts & questions for Elementary Mathematics - CDS (Combined Defence Services) Mock Test Series 2025 2025 is part of CDS exam preparation. The chapters have been prepared according to the CDS exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for CDS 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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CDS (Combined Defence Services) Mock Test Series 2025
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