RRB Group D Mathematics Previous Year Question Paper Solved with Shortcuts
Welcome aspirants! If you are preparing for upcoming railway examinations like RRB Group D, RRB NTPC, or RRB ALP, mastering the Mathematics section is critical for scoring top percentile ranks. In this article, we break down real exam questions from the previous year paper with step-by-step traditional methods alongside Wisdom Helps short tricks to help you solve questions in under 15 seconds.
📌 Essential Mathematics Formulas & Shortcuts
Review these important formulas frequently tested in competitive railway exams:
| Topic | Standard Formula / Speed Trick |
|---|---|
| Average | Total Sum = n × Average |
| Average Speed | Avg Speed = 2xy / (x + y) (When distance is constant) |
| LCM & HCF | LCM × HCF = Product of Two Numbers (N1 × N2) |
| Effective CI (2 Years) | Effective Rate = x + y + (x × y) / 100 % |
| Discount % (Buy X Get Y) | Discount % = [Free Quantity / Total Quantity] × 100 |
📝 Solved Questions with Step-by-Step Solutions
Question: The average age of 26 students in a class is 26 years. If the age of the teacher is included, the average age of the entire group becomes 27 years. What is the age of the teacher (in years)?
Sum of ages of 26 students = 26 × 26 = 676 years
Sum of ages including teacher (27 people) = 27 × 27 = 729 years
Teacher's Age = 729 − 676 = 53 years
New Average = 27
Increase for existing 26 students = 26 × 1 = 26
Teacher's Age = 27 + 26 = 53 Years
Question: If 20% of a number is added to 90, the result is the same number. Find 80% of that same number.
Let the number be x.
20% of x = (1/5)x
Given: (1/5)x + 90 = x ⇒ x − (1/5)x = 90 ⇒ (4/5)x = 90
x = (90 × 5) / 4 = 112.5
Now, 80% of the number = 112.5 × (80 / 100) = 90
Question: Smriti travels to a shopping mall at a speed of 21 km/h and returns along the same route at a speed of 69 km/h. Find her average speed for the whole journey.
Since distance is constant, apply the harmonic average speed formula:
Average Speed = 2xy / (x + y)
= (2 × 21 × 69) / (21 + 69) = 2898 / 90 = 32.2 km/h
Question: An article was bought for ₹8,900. It was marked up by 40% above the cost price and then sold at a discount of 5% on the marked price. What was the profit percentage on the transaction?
Ignore the actual cost value ₹8,900 as percentage profit is requested!
Let Cost Price (CP) = 100%
Marked Price (MP) = 140%
Discount = 5% of 140 = 7%
Selling Price (SP) = 140 − 7 = 133%
Profit Percentage = 133% − 100% = 33%
Question: Which of the following ratios is equivalent to 3 : 2?
Check option 54 : 36.
Divide both terms by 18: 54/18 = 3 and 36/18 = 2.
Ratio = 3 : 2
Question: If tan θ = 12 / 5, find the value of sec θ.
tan θ = Opposite / Adjacent = 12 / 5
Using Pythagorean Triplet (5, 12, 13), Hypotenuse = 13.
sec θ = Hypotenuse / Adjacent = 13 / 5
Question: The Total Surface Area (TSA) of a solid right circular cylinder is 542. If its Curved Surface Area (CSA) is 2/5 of its TSA, find its CSA.
CSA = (2 / 5) × 542
Multiply numerator and denominator by 2 to make the denominator 10:
CSA = (4 × 542) / 10 = 2168 / 10 = 216.8
Question: Two numbers have an HCF of 18 and an LCM of 1512. If one of the numbers is 126, find the positive difference between the two numbers.
Formula: HCF × LCM = Number1 × Number2
18 × 1512 = 126 × Number2
Number2 = (18 × 1512) / 126 = 216
Difference = 216 − 126 = 90
Question: A scheme offers "Buy 6, Get 4 Free". What is the effective discount percentage?
Discount % = [Free Articles / Total Articles] × 100
Total Articles = 6 + 4 = 10
Discount % = (4 / 10) × 100 = 40%
Question: What will be the total amount on a principal sum of ₹6,800 at 15% per annum compounded annually for 2 years?
Effective Compound Interest Rate for 2 years = 15 + 15 + (15 × 15)/100 = 32.25%
Total Amount Rate = 100% + 32.25% = 132.25%
Total Amount = 6800 × (132.25 / 100) = 68 × 132.25 = 8993
(Tip: Use Digit Sum matching in exams to verify choices instantly!)
💡 Key Exam Tips for RRB Mathematics Section
- Focus on Speed & Accuracy: Practice solving questions using shortcuts like Effective Percentages, Digit Sum, and Triplet Recognition to save critical exam time.
- Memorize Basic Squares & Cubes: Learn squares up to 30 and cubes up to 15 to perform fast Mental Math.
- Analyze PYQs: Previous Year Questions give you direct insight into the exam pattern and question weightage for topics like Arithmetic, Algebra, and Mensuration.
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