RRB Group D Mathematics Formulas
Prepare for RRB Group D Mathematics with our comprehensive guide! Explore essential topics like the Number System and Percentage, and test your knowledge with our expertly crafted Multiple Choice Questions (MCQs
|
Topic |
Formula |
Example |
|
Simple Interest (SI) |
SI = (P * R * T) / 100 |
SI for a principal of Rs. 5000 at 10% interest for 2 years = (5000 * 10 * 2) / 100 = Rs. 1000 |
|
Compound Interest (CI) |
CI = P * [1 + R/100]n – P |
CI for a principal of Rs. 10000 at 10% interest compounded annually for 2 years = 10000 * [1 + 10/100]^2 – 10000 = Rs. 2100 |
|
Percentage |
A% of B = (A/100) * B |
20% of 500 = (20/100) * 500 = 100 |
|
Profit & Loss |
Profit = SP – CP |
Profit earned by selling an article for Rs. 120 after buying it for Rs. 100 = 120 – 100 = Rs. 20 |
|
Time and Work |
W1/T1 = W2/T2 |
If A can do a work in 10 days and B can do the same work in 15 days, then A and B together can do the work in (10 * 15) / (10 + 15) = 6 days |
|
Ratio and Proportion |
a/b = c/d |
If a:b = 3:4 and b:c = 5:6, then a:b:c = 15:20:24 |
|
Average |
Average = (Sum of terms) / (Number of terms) |
Average of 10, 15, 20, 25 and 30 = (10 + 15 + 20 + 25 + 30) / 5 = 20 |
|
Speed, Time and Distance |
Speed = Distance / Time |
Speed of a train traveling 100 km in 2 hours = 100/2 = 50 km/hr |
|
Mixture and Alligation |
Rule of Alligation |
To find the ratio of two liquids A and B to be mixed to get a mixture of desired concentration C: (C – B) / (A – C) |
|
Area and Volume |
Formulas for different shapes (e.g., triangle, rectangle, circle, sphere, cone) |
Area of a rectangle with length 10 cm and breadth 5 cm = 10 * 5 = 50 sq cm |
1. If the sum of two numbers is 45 and their difference is 15, what are the two numbers?
a) 30, 15
b) 20, 25
c) 18, 27
d) 22, 23
Answer: b) 20, 25
2. A train travels 300 km in 4 hours. What is its speed in km/h?
a) 75
b) 60
c) 80
d) 90
Answer: a) 75
3. If the radius of a circle is 7 cm, what is its circumference? (Use π = 22/7)
a) 14 cm
b) 44 cm
c) 154 cm
d) 154/7 cm
Answer: b) 44 cm
4. Solve for x: 3x – 5 = 16
a) 7
b) 5
c) 6
d) 9
Answer: a) 7
5. The product of two consecutive even integers is 288. What are the integers?
a) 12, 14
b) 16, 18
c) 18, 20
d) 20, 22
Answer: c) 18, 20
6. If the area of a rectangle is 48 square meters and its length is 8 meters, what is its width?
a) 4 meters
b) 6 meters
c) 8 meters
d) 12 meters
Answer: a) 4 meters
7. The sum of three consecutive odd integers is 63. What is the smallest integer?
a) 19
b) 21
c) 23
d) 25
Answer: a) 19
8. A right-angled triangle has legs of length 5 cm and 12 cm. What is the length of the hypotenuse?
a) 13 cm
b) 10 cm
c) 15 cm
d) 17 cm
Answer: a) 13 cm
9. If 20% of a number is 40, what is the number?
a) 100
b) 150
c) 200
d) 250
Answer: c) 200
10. Solve for y: 4y + 7 = 19
a) 3
b) 4
c) 5
d) 6
Answer: c) 5
11. The perimeter of a square is 36 cm. What is the length of each side?
a) 6 cm
b) 8 cm
c) 9 cm
d) 12 cm
Answer: b) 8 cm
12. If the selling price of an item is Rs. 450 and the profit percentage is 20%, what is the cost price?
a) Rs. 375
b) Rs. 400
c) Rs. 420
d) Rs. 480
Answer: a) Rs. 375
13. If a car travels at a speed of 60 km/h, how long will it take to cover a distance of 240 km?
a) 2 hours
b) 3 hours
c) 4 hours
d) 5 hours
Answer: c) 4 hours
14. Solve the equation: 2x – 5 = 7
a) 6
b) 7
c) 8
d) 9
Answer: c) 8
15. The sum of the angles in a triangle is 180 degrees. If two angles are 45 degrees and 75 degrees, what is the measure of the third angle?
a) 45 degrees
b) 60 degrees
c) 75 degrees
d) 90 degrees
Answer: b) 60 degrees
16. A rectangular garden has a length of 15 meters and a width of 8 meters. What is the area of the garden?
a) 100 square meters
b) 120 square meters
c) 150 square meters
d) 180 square meters
Answer: c) 150 square meters
17. If a box contains 24 chocolates and 6 chocolates are taken out, what percentage of chocolates remains in the box?
a) 75%
b) 60%
c) 50%
d) 40%
Answer: a) 75%
18. The ratio of boys to girls in a class is 3:2. If there are 15 girls, how many boys are there?
a) 10
b) 15
c) 18
d) 20
Answer: c) 18
19. A circle has a radius of 5 cm. What is its area? (Use π = 22/7)
a) 25π square cm
b) 50π square cm
c) 75π square cm
d) 100π square cm
Answer: a) 25π square cm
20. If the interest on a sum of money is Rs. 300 at an annual rate of 6%, what is the principal amount?
a) Rs. 2,000
b) Rs. 3,000
c) Rs. 4,000
d) Rs. 5,000
Answer: b) Rs. 3,000
21. If a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?
a) 22 cm
b) 32 cm
c) 36 cm
d) 48 cm
Answer: c) 36 cm
21. If a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?
a) 22 cm
b) 32 cm
c) 36 cm
d) 48 cm
Answer: c) 36 cm
22. A train covers a distance of 400 km in 5 hours. What is its average speed?
a) 60 km/h
b) 80 km/h
c) 100 km/h
d) 120 km/h
Answer: b) 80 km/h
23. If 15% of a number is 45, what is 40% of the same number?
a) 120
b) 135
c) 150
d) 180
Answer: c) 150
24.If the ratio of the lengths of two sides of a triangle is 3:4 and the perimeter is 28 cm, what are the lengths of the sides?
a) 6 cm, 8 cm, 14 cm
b) 7 cm, 9 cm, 12 cm
c) 5 cm, 10 cm, 13 cm
d) 9 cm, 12 cm, 16 cm
Answer: a) 6 cm, 8 cm, 14 cm
25.The sum of three consecutive integers is 57. What are the integers?
a) 18, 19, 20
b) 18, 20, 22
c) 19, 20, 21
d) 20, 21, 22
Answer: c) 19, 20, 21
26.. The perimeter of a regular hexagon is 60 cm. What is the length of each side?
a) 8 cm
b) 10 cm
c) 12 cm
d) 15 cm
Answer: b) 10 cm
27. If the difference between a number and its square is 24, what is the number?
a) 6
b) 8
c) 10
d) 12
Answer: b) 8
28. If the sum of three consecutive even integers is 54, what is the smallest integer?
a) 16
b) 18
c) 20
d) 22
Answer: b) 18
29.. If a cube has a volume of 125 cubic cm, what is the length of each side?
a) 3 cm
b) 4 cm
c) 5 cm
d) 6 cm
Answer: a) 3 cm
30. A shop sells a shirt for Rs. 800 after a discount of 20%. What is the original price of the shirt?
a) Rs. 640
b) Rs. 720
c) Rs. 960
d) Rs. 1000
Answer: d) Rs. 1000
31. If the interest on a sum of money is Rs. 450 at an annual rate of 9%, what is the principal amount?
a) Rs. 4000
b) Rs. 5000
c) Rs. 6000
d) Rs. 7000
Answer: a) Rs. 4000
32. The area of a right-angled triangle is 24 square cm, and one leg is 6 cm. What is the length of the other leg?
a) 4 cm
b) 6 cm
c) 8 cm
d) 12 cm
Answer: a) 4 cm
33. A box contains 120 chocolates. If 25% of them are dark chocolates, how many dark chocolates are there?
a) 20
b) 30
c) 40
d) 50
Answer: b) 30
34. If a rectangle has a length of 12 cm and a diagonal of 15 cm, what is its width?
a) 9 cm
b) 12 cm
c) 15 cm
d) 18 cm
Answer: a) 9 cm
35. If the sum of two numbers is 56, and their difference is 8, what are the two numbers?
a) 32, 24
b) 30, 26
c) 28, 28
d) 36, 20
Answer: b) 30, 26
36. The area of a square is 121 square units. What is the length of each side?
a) 9 units
b) 11 units
c) 13 units
d) 15 units
Answer: b) 11 units
37.. If a number is increased by 25% and then decreased by 20%, what is the net percentage change?
a) 5%
b) 2%
c) 3%
d) 1%
Answer: a) 5%
38. A rectangular prism has dimensions of 5 cm, 8 cm, and 12 cm. What is its volume?
a) 384 cubic cm
b) 480 cubic cm
c) 560 cubic cm
d) 720 cubic cm
Answer: a) 384 cubic cm
39. If the area of a circle is 154 square cm, what is its radius? (Use π = 22/7)
a) 7 cm
b) 5 cm
c) 6 cm
d) 8 cm
Answer: b) 5 cm
40. The sum of the ages of John and Mary is 50. If John is 8 years older than Mary, what is Mary’s age?
a) 19 years
b) 21 years
c) 23 years
d) 25 years
Answer: b) 21 years
41. A train travels at a speed of 90 km/h. How far will it travel in 3 hours?
a) 180 km
b) 240 km
c) 270 km
d) 300 km
Answer: d) 300 km
42. If the average of five numbers is 18, and four of the numbers are 15, 20, 25, and 18, what is the fifth number?
a) 14
b) 18
c) 22
d) 26
Answer: a) 14
RRB Group D Number System MCQ Questions
|
Number System |
Formula |
Description |
|
Natural numbers (N) |
N = {1, 2, 3, …} |
Set of positive whole numbers |
|
Whole numbers (W) |
W = {0, 1, 2, 3, …} |
Set of natural numbers and zero |
|
Integers (Z) |
Z = {…,-3, -2, -1, 0, 1, 2, 3, …} |
Set of all whole numbers, positive and negative, and zero |
|
Rational numbers (Q) |
Q = {a/b |
a, b ∈ Z, b ≠ 0} |
|
Irrational numbers (I) |
I = {x ∈ R |
x ∉ Q} |
|
Real numbers (R) |
R = Q ∪ I |
Set of all rational and irrational numbers |
|
Complex numbers (C) |
C = {a + bi |
a, b ∈ R} |
1. What is the smallest prime number?
a) 0
b) 1
c) 2
d) 3
Answer: c) 2
2. What is the sum of the first 50 natural numbers?
a) 1275
b) 1275
c) 1325
d) 1375
Answer: a) 1275
3. If a number is divisible by both 4 and 9, what is it divisible by?
a) 18
b) 36
c) 72
d) 144
Answer: c) 72
5. What is the smallest three-digit prime number?
a) 101
b) 103
c) 107
d) 109
Answer: b) 103
7. What is the greatest common divisor (GCD) of 24 and 36?
a) 6
b) 8
c) 12
d) 18
Answer: a) 6
8. What is the product of the first 10 prime numbers?
a) 2,520
b) 18,906
c) 23,100
d) 29,856
Answer: a) 2,520
9. If a number is divisible by both 6 and 9, what is it divisible by?
a) 18
b) 36
c) 54
d) 72
Answer: b) 36
10. What is the square root of 144?
a) 10
b) 12
c) 14
d) 16
Answer: b) 12
11. Which of the following is a prime number?
a) 25
b) 33
c) 47
d) 50
Answer: c) 47
12. What is the next prime number after 89?
a) 91
b) 93
c) 97
d) 99
Answer: c) 97
13. What is the LCM of 12 and 18?
a) 18
b) 24
c) 36
d) 48
Answer: c) 36
14. What is the LCM of 12 and 18?
a) 18
b) 24
c) 36
d) 48
Answer: c) 36
15. What is the remainder when 47 is divided by 5?
a) 0
b) 1
c) 2
d) 3
Answer: d) 3
16. What is the sum of the first 100 odd numbers?
a) 5000
b) 10000
c) 2500
d) 12500
Answer: b) 10000
17. What is the sum of the first 50 positive even numbers?
a) 2500
b) 2550
c) 2600
d) 2650
Answer: a) 2500
18. Which of the following is a composite number?
a) 29
b) 37
c) 49
d) 53
Answer: c) 49
19. What is the product of the first 5 prime numbers?
a) 120
b) 210
c) 230
d) 260
Answer: a) 120
20. What is the least common multiple (LCM) of 15, 20, and 25?
a) 60
b) 75
c) 100
d) 150
Answer: c) 100
21. What is the square of the sum of 9 and 7?
a) 256
b) 324
c) 400
d) 484
Answer: b) 324
22. What is the remainder when 135 is divided by 8?
a) 1
b) 3
c) 5
d) 7
Answer: c) 5
23. What is the sum of the first 15 prime numbers?
a) 319
b) 400
c) 447
d) 543
Answer: c) 447
24. Which of the following is a perfect square?
a) 42
b) 64
c) 79
d) 93
Answer: b) 64
25. What is the greatest prime factor of 72?
a) 3
b) 5
c) 7
d) 13
Answer: a) 3
26. What is the product of the first 4 composite numbers?
a) 30
b) 42
c) 60
d) 72
Answer: a) 30
27. What is the sum of the first 20 positive odd numbers?
a) 200
b) 400
c) 600
d) 800
Answer: b) 400
28. What is the smallest composite number?
a) 0
b) 1
c) 4
d) 6
Answer: d) 6
29. What is the next perfect square after 144?
a) 169
b) 196
c) 225
d) 256
Answer: b) 196
30. What is the next perfect square after 144?
a) 169
b) 196
c) 225
d) 256
Answer: b) 196
RRB Group D Percentage MCQ Questions
|
Formula |
Description |
Example |
|
P% of A = (P/100) * A |
Calculates the percentage P of a quantity A. |
Find 20% of 500. P = 20, A = 500. <br>(20/100) * 500 = 100 |
|
Increase = [(P/100) * A] + A |
Calculates the new value after a percentage increase. |
The price of a book increases by 10%. Original price = ₹100, P = 10. <br>Increase = [(10/100) * 100] + 100 = ₹110 |
|
Decrease = A – [(P/100) * A] |
Calculates the new value after a percentage decrease. |
The cost of a laptop decreases by 15%. Original cost = ₹50000, P = 15. <br>Decrease = 50000 – [(15/100) * 50000] = 42500 |
|
(New value – Old value)/Old value * 100 |
Calculates the percentage change between two values. |
The salary of an employee increases from ₹20000 to ₹22000. Find the percentage increase. <br>(22000 – 20000)/20000 * 100 = 10% |
|
(Sum of percentages)/Number of percentages |
Calculates the average of multiple percentages. |
Find the average of 20%, 30%, and 40%. <br>(20 + 30 + 40)/3 = 30% |
1. If the price of a product is increased by 20%, by what percentage should it be reduced to bring it back to its original price?
a) 15%
b) 16.67%
c) 20%
d) 25%
Answer: b) 16.67%
2. If a number is increased by 25% and then decreased by 20%, what is the net percentage change?
a) 5%
b) 2%
c) 3%
d) 1%
Answer: a) 5%
3. A shopkeeper offers a discount of 15% on a shirt. If the original price is Rs. 800, what is the discounted price?
a) Rs. 680
b) Rs. 720
c) Rs. 760
d) Rs. 850
Answer: c) Rs. 760
4. If 30% of a number is 45, what is 150% of the same number?
a) 200
b) 225
c) 250
d) 275
Answer: b) 225
5. A student scored 360 out of 500 in an exam. What is the percentage scored by the student?
a) 72%
b) 76%
c) 80%
d) 90%
Answer: a) 72%
6. If the population of a town increased from 20,000 to 25,000, what is the percentage increase?
a) 20%
b) 25%
c) 30%
d) 35%
Answer: b) 25%
7. If the value of a car depreciated by 15% each year, what is the approximate value of the car after 3 years if its original value was Rs. 50,000?
a) Rs. 31,875
b) Rs. 32,500
c) Rs. 33,125
d) Rs. 33,750
Answer: a) Rs. 31,875
8. A store is offering a sale with a discount of 40%. If a shirt originally costs Rs. 1200, what is the discounted price?
a) Rs. 720
b) Rs. 800
c) Rs. 900
d) Rs. 1000
Answer: c) Rs. 900
9. If the price of a product is reduced by 30%, by what percentage should it be increased to bring it back to its original price?
a) 30%
b) 40%
c) 42.86%
d) 50%
Answer: b) 40%
10. A company’s profit increased from Rs. 50,000 to Rs. 60,000. What is the percentage increase in profit?
a) 10%
b) 15%
c) 20%
d) 25%
Answer: a) 10%
11. If a commodity is sold at a loss of 20%, what is the selling price if the cost price is Rs. 500?
a) Rs. 400
b) Rs. 450
c) Rs. 480
d) Rs. 520
Answer: a) Rs. 400
12. A salary is increased by 15% one year and then decreased by 10% the next year. What is the net percentage change in the salary over the two years?
a) 3.5%
b) 5%
c) 7.5%
d) 10%
Answer: a) 3.5%
13. If the original price of a mobile phone is Rs. 20,000 and it is sold at a discount of 25%, what is the discounted price?
a) Rs. 14,000
b) Rs. 15,000
c) Rs. 16,000
d) Rs. 18,000
Answer: b) Rs. 15,000
14. If the population of a city decreased from 150,000 to 120,000, what is the percentage decrease?
a) 15%
b) 20%
c) 25%
d) 30%
Answer: c) 25%
15. If the price of a book is increased by 10% and then decreased by 5%, what is the net percentage change in the price?
a) 5%
b) 4.5%
c) 3%
d) 2.5%
Answer: d) 2.5%
16. A student scored 85 out of 100 in one subject and 90 out of 100 in another subject. What is the overall percentage scored by the student?
a) 87.5%
b) 88%
c) 88.5%
d) 89%
Answer: a) 87.5%
17. If the value of a car appreciated by 10% each year, what is the approximate value of the car after 4 years if its original value was Rs. 80,000?
a) Rs. 104,800
b) Rs. 105,000
c) Rs. 106,120
d) Rs. 106,480
Answer: a) Rs. 104,800
18. A store is offering a sale with a discount of 50%. If a product originally costs Rs. 2000, what is the discounted price?
a) Rs. 1000
b) Rs. 1100
c) Rs. 1200
d) Rs. 1300
Answer: a) Rs. 1000
19. If the original price of a laptop is Rs. 40,000 and it is sold at a profit of 15%, what is the selling price?
a) Rs. 41,500
b) Rs. 42,000
c) Rs. 43,000
d) Rs. 44,000
Answer: a) Rs. 41,500
20. A student answered 80 out of 100 questions correctly in an exam. What is the percentage of correct answers?
a) 80%
b) 85%
c) 90%
d) 95%
Answer: a) 80%
21. If a shirt is sold at a profit of 25%, and the selling price is Rs. 625, what is the cost price of the shirt?
a) Rs. 480
b) Rs. 500
c) Rs. 520
d) Rs. 540
Answer: d) Rs. 540
22. The price of a watch is increased by 15% and then decreased by 10%. If the original price was Rs. 800, what is the final price?
a) Rs. 732
b) Rs. 750
c) Rs. 765
d) Rs. 780
Answer: c) Rs. 765
23. If a product is sold at a loss of 12.5%, what is the selling price if the cost price is Rs. 640?
a) Rs. 550
b) Rs. 560
c) Rs. 580
d) Rs. 600
Answer: c) Rs. 580
24. The population of a city increased from 80,000 to 100,000. What is the percentage increase in population?
a) 15%
b) 20%
c) 25%
d) 30%
Answer: b) 20%
25. If the original price of a camera is Rs. 25,000 and it is sold at a discount of 20%, what is the discounted price?
a) Rs. 18,000
b) Rs. 19,000
c) Rs. 20,000
d) Rs. 22,000
Answer: a) Rs. 18,000
26. A student scored 75 marks out of 100 in a subject. What is the percentage scored by the student?
a) 65%
b) 70%
c) 75%
d) 80%
Answer: c) 75%
27. If the price of a book is increased by 12% and then decreased by 8%, what is the net percentage change in the price?
a) 3.36%
b) 3.84%
c) 4.32%
d) 4.80%
Answer: a) 3.36%
28. A store is offering a discount of 30%. If a product originally costs Rs. 1500, what is the discounted price?
a) Rs. 950
b) Rs. 1000
c) Rs. 1050
d) Rs. 1100
Answer: a) Rs. 950
29. If a commodity is sold at a profit of 10%, what is the selling price if the cost price is Rs. 450?
a) Rs. 490
b) Rs. 495
c) Rs. 500
d) Rs. 505
Answer: b) Rs. 495
30. A shopkeeper offers a discount of 18% on a refrigerator. If the original price is Rs. 22,000, what is the discounted price?
a) Rs. 18,040
b) Rs. 18,160
c) Rs. 18,240
d) Rs. 18,360
Answer: d) Rs. 18,360