Simple Interest, Averages and Speed
Overview
Simple Interest, Averages, and Speed are high-scoring topics in Railway NTPC and Group D exams. Simple Interest uses the formula SI = (P×R×T)/100. Averages require finding the mean of a data set. Speed-Distance-Time problems use Speed = Distance/Time. Together these three topics contribute 4–7 questions per paper and can be solved quickly with the right shortcuts and formula recall.
Typed Notes
Simple Interest — Core Formula & Tricks
Simple Interest (SI) = (P × R × T) / 100. Principal (P) is the original sum, R is the annual rate of interest, and T is time in years. Amount (A) = P + SI. Exam tip: If SI doubles the principal, then R × T = 100. If SI is half the principal, R × T = 50. To find rate: R = (SI × 100) / (P × T). Railway papers often give three of the four variables and ask for the fourth. Always check whether time is given in months — convert months to years by dividing by 12 before applying the formula.
Averages — Formula, Shortcuts & Weighted Average
Average = Total Sum / Number of items. If the average of n numbers is A and one number is replaced by a new number, the new average = A + (new number − old number) / n. Weighted Average is used when two groups merge: Combined Average = (n1×A1 + n2×A2) / (n1 + n2). Exam shortcut: If average of first n natural numbers is asked, answer = (n+1)/2. Railway Group D frequently asks: 'Average of first 20 odd numbers = 20' and 'Average of first 20 even numbers = 21'. These are direct one-line answers worth memorising.
Speed, Distance & Time — Trains, Boats & Relative Speed
Speed = Distance / Time. For trains crossing a pole, use train's own length as distance. For trains crossing each other going in the same direction, Relative Speed = difference of speeds; opposite direction, Relative Speed = sum of speeds. Boats: Speed upstream = Boat speed − Stream speed; Speed downstream = Boat speed + Stream speed. Average speed for a round trip at speeds x and y = 2xy/(x+y). Convert km/h to m/s by multiplying by 5/18. Railway NTPC regularly tests train-crossing problems — always add lengths of both objects when two trains cross each other.
Mixed Application & Exam-Day Strategy
Railway papers often combine these topics: e.g., 'A person travels at two speeds — find average speed' or 'Find principal if SI earned in 3 years at 5% is ₹450.' Solve SI problems by isolating the unknown variable. For averages, draw a quick number line to check if the answer is reasonable. For speed problems, write D = S × T in a small table. Eliminate wrong options using unit sense — if answer should be in km/h, options in m/s are wrong. Attempt these questions first in the exam as they take under 60 seconds with practice.
Key Concepts
Revision ke liye ek nazar — exam se pehle yahi padhna hai.
- 01SI = (P × R × T) / 100; Amount = P + SI; where P = Principal, R = Rate % per annum, T = Time in years.
- 02Average = Sum of all observations / Number of observations; if one value changes, new average = old average ± (change / n).
- 03Speed = Distance / Time; Time = Distance / Speed; Distance = Speed × Time — memorise as the SDT triangle.
- 04Average Speed for equal distances = 2xy / (x + y), where x and y are the two speeds — NOT the simple average.
- 05Unit conversions: 1 km/h = 5/18 m/s; 1 m/s = 18/5 km/h — these appear directly in Railway exam options.
Questions & Solutions
Pehle khud try karo — phir solution kholo. Yahi tariqa topper banata hai.
A sum of ₹5,000 is invested at 8% per annum simple interest for 3 years. Find the total amount.
The average of 10 numbers is 40. If one number is replaced by 80 instead of 20, what is the new average?
A train 150 m long passes a pole in 15 seconds. Find its speed in km/h.
A man travels from A to B at 60 km/h and returns at 40 km/h. Find his average speed for the whole journey.
At what rate percent per annum will ₹2,000 amount to ₹2,500 in 5 years under simple interest?
SI = PRT/100; Amount = P + SI. Average = Sum/Count; use weighted average when groups merge. Speed = D/T; for trains add lengths; for round trips use harmonic mean formula 2xy/(x+y). Convert km/h to m/s using ×5/18. These three topics together offer 4–7 easy marks in Railway NTPC and Group D — master the formulas and unit conversions to score full marks quickly.
Chapter-end quiz
4 MCQsOption tap karo — turant pata chalega sahi ya galat, explanation ke saath.
Q1.Simple Interest on ₹1,200 at 10% per annum for 2 years is:
Q2.The average of first 15 odd natural numbers is:
Q3.A train 200 m long and another train 300 m long travel towards each other at 50 km/h and 70 km/h. Time to cross each other is:
Q4.1 km/h is equal to how many m/s?
Mark karo — dashboard par progress dikhega.