1. Prologue
  2. [Block#2] %, STD and Stat
    1. Percentages, Profit loss SI-CI
    2. Ratio Proportion
    3. Time speed distance Work (TSDW)
    4. Statistics-Data interpretation (DI)
      1. Stat#1: Calculation type
      2. Stat#2: Data Interpretation sets
      3. Stat#3: Theory / definition type MCQs
  3. Appendix Download link: Topic wise Sorted NCERTs


  1. In the previous article, we saw how to prepare number system, surds-indices, linear and quadratic equations for CDS maths paper. click me
  2. Now in this second article, we’ll see how to approach percentage, profit-loss, simple-compound interest rate, time-speed-distance-work and statistics-Data interpretation related problems.
  3. In the third article, we’ll see how to approach geometry, trigonometry and remaining misc. Topics. click me


[Block#2] %, STD and Stat

topics in this block avg. MCQs in each of the last four CDS exams. priority
Profit loss, SI-CI, ratio-proportion 5 medium*
Time Speed Distance Work 7 high
statistics and Data interpretation 6 high

*medium priority because in last two exams (of 2013), barely 3 and 2 MCQs respectively. The average is “5” only because in earlier times, they used to ask a lot from here. Still 2-3 MCQs are good because you hardly need to memorize any formulas.

Percentages, Profit loss SI-CI

Unlike the IBPS questions, here % or compound interest rate doesn’t require lengthy multiplication or division. Most of the time the numerators will be easily cut.

7_8 Comparing Quantities introduces to %, simple interest rates, profit IAK
8_8 Comparing Quantities compound interest rates IAK*

* IAK=”I already know”. Meaning you can ignore this chapter, if you’re basics are already good. (i.e. you’ve already cleared written stage of bank, SSC or LIC.)

You can even ignore above NCERTs, and directly use methods explained in following articles:

  1. Concepts of Marked Price and Successive Discounts (Profit-Loss) without (stupid) formulas
  2. Compound Interest Rate, Population Growth without Formulas
  3. Alligation: Advanced applications in Interest rates, Profit-loss, Average Wages (Wine-Water Concept) <=master this technique because often interest rate problems in CDS are based on this theme.
  4. Product Consistency: If Sugar price increases then consumption should be Decreased by What %, Time-Speed-Distance problems,

Then do Sarvesh Kumar’s chapters on: percentages, profit loss and discount, and CI/SI/installments. In each of them solve all illustrations/examples, introductory exercises and level1 exercises. you may ignore the ‘loan-installment’ related problems because I didn’t see them in last 5 years’ papers.

Demo MCQs from previous CDS Exam


  1. A sum of money is lent on simple interest triples itself in 15 years and six months. In how many years will it be doubled?
  2. A men has invested Rs. 1000 on simple interest of certain rate, and Rs. 1500 at 2% higher rate. The total interest accumulated in three years is Rs. 390. What is the rate of interest for Rs. 1000?
  3. A man has borrowed Rs. 40,000 at 8% simple interest rate per and. At the end of second-year he has paid back certain amount, and at the end of fifth year, he gave Rs. 35,960 and cleared the debt. What is the amount did he pay back after the second year?
  1. What is the least number of complete years in which a sum of money @20% compound interest rate will be more than doubled? (7/6/5/4)
  2. An amoun of Rs. X @20%compound interest rate per year, becomes Rs.Y after three years. What is the ratio of Y:X?
  1. A trader marks 10% higher than the cost price. He gives discount of 10% on the marked price. In this kind of sales how much percent does the trader gain or loss?
  2. By selling 8 dozen pencils, a shopkeeper gains the selling price of 1 dozen pencils. What is the gain?

Ratio Proportion

Usually one or two MCQs from this portion each year. But still, the cost: benefit is great because no formulas to memorize.

7_8 Comparing Quantities basics of Ratios IAK
8_13 Direct and Indirect Proportions basics of variation IAK
  • Since they’re not asking anything from definitions, you may directly goto Sarvesh Kumar chapter on Ratio proportion variations without touching NCERTs.
  • Solve all the examples and questions upto level 1. (For rock solid grip, you may even do upto level II).
  • also see this article: [Aptitude] Partnership and profit-sharing made Easy.

Demo MCQs from previous CDS exams

  1. in a class, number of boys is more than the number of girls by 12% of the total students. what is the ratio of number of boys to that of girls?
  2. if (a+b)(a-b)=1:5 then what is the ratio of (a2-b2): (a2+b2)?(**Note: for these type of questions, first finish the quadratic equation block.)
  1. Rs.8400 is to be divided among A,B and C in the ratio of (1/5): (1/6) : (1/10). What is the share of A.
  2. A bag contains Rs.112 in the form of Rs.1, 50 paisa and 10 paisa coins in the ratio of 3:8:10. Find the number of 50 paisa coins.
  1. Monthly income of A and B in the ratio of 4:3. Each saves Rs.600. if expenditure ratio is 3:2, then what find monthly income of A.
  2. Wages of laborers has increased in the ratio of 22:25 and their number has decreased in the ratio of 3:2. What was the original wage bill of the factory, if the present bill is Rs.5000
  1. x varies directly as y and inversely as square of z. when y=4, z=14, x=10. IF y=16, z=7 then what is x?
  2. x varies inversely as the square of y in way that if x=1 then y=6. if y=3 find value of x.

Time speed distance Work (TSDW)

In this portion, NCERT not much useful because it runs on the LCM method and doesn’t dwell on all variety of questions, besides nothing asked from theory/definition.

TSDW is made up of two topics

  1. Time speed distance: related to cars, trains, platforms, boats etc.
  2. Time speed work: related to “A can complete a work in….”, “pipe A can fill the tank in …” etc.

All of these can be solved through just one formula: STD (speed x time =distance). Go through following articles:

Time-speed-Distance Time-speed-work
  1. Trains, Platforms TSD (Time, Speed, Distance) made easy
  2. Boats and Streams made-easy using our STD-Table Method
  3. Average Speed made easy without Formulas
  4. STD table : Application in train man bridge, time and work problems
  5. Time n Distance: Early and late to office (shortcut using product consistency method)
  6. Product Consistency: Time-Speed-Distance problems
  1. [Speed Time Work] Two Men can finish a work, A is 3x more efficient than B, B leaves before completion & variety of cases
  2. [Speed Time Work] Three men can finish a work in x days, A & B start work, C joins after x day, share in wages & other special cases
  3. Time n Work: 4 men and 6 women can complete a work in 8 Days then

Once you’ve got the idea of STD method, solve all the examples and questions given in Sarvesh Kumar’s book under the chapters:

  • time and work (upto level 1)
  • time speed and distance (upto level 1)

Then CDS MCQs will be a walk in the park.

TSD: Demo MCQs from Previous CDS Exams

  1. two trains travel in same direction at 50 and 32 kmph speed respectively. Man in the slower train observe that 15 seconds elapse before faster train completely passes him. Find length of the faster train.
  2. Two trains with length 100m and 150m respectively are travelling in opposite direction at speed of 75kmph and 50 kmph respectively. Find the time taken by them to cross each other.
  3. Two cars A and B start simultaneously from a certain    place at the speed of 30 km/hr and 45 km/hr respectively. The car B reaches the destination 2 hours earlier than A. What is the distance between the starting point and destination?
  1. boat covers 9km downstream in two hours and takes 6 hours to cover the same in upstream. Find the speed of boat in still water.
  2. Speed of boat in still water is 11kmph, it can go upstream 12 km and return downstream to the engine point in 2 hours and 45 minutes. Find the speed of the stream.
  1. A biker travels a distance of 200km @constant speed. had the speed increased by 5kmph, journey time would have reduced by 2 hours. Find speed of the bike.
  2. Boy walks at speed of 2.5kmph from home and reaches the school 12 minutes late. Next day he walks at 4kmph and arrives 15 minutes early. Find the distance between school and home.
  1. A man can walk upwhill at 2.5kmph and downhill at 3.25 kmph. if total time taken to go up and down the hill is 4 hours 36 minutes, find the total distance covered by the man
  2. Biker complete journey in 10 hours. he covers half the distance @30kmph and remaining @70kmph. Find total distance covered.

TSW: Demo MCQs from previous CDS exam

  1. A, B and C take individually 2, 3 and 4 days to finish a job. If they work together and get 3900 for completion of work, what is the share of “Y” in the money received?
  2. A can finish a work in 15 days, B in 20 days and C in 25 days. All these three worked together and earned Rs. 4,700. What is the share of C?
  1. A can finish a job in 24 days. If B is 60% more efficient than A, then how many days does B require to do the same work?
  2. A person can do a job as fast as his two sons working together. If one son does the job in six days and the other son in 12 days, how many days does it take the father to finish the job?
  1. four taps can individually fill up the tank in 1,2,3 and 6 hrs respectively. if all of them opened simultaneously, then how many minutes will it take to fill up the tank?
  2. two taps can fill a tub in 5 and 7 minutes respectively. A pipe can empty it in three minutes. if all thee opened simultaneously, in how many minutes will the tub be filled completely?
  1. If six men and eight boys can do a piece of work in 10 days while 26 men and 48 boys can do the same work into days, what is the time taken by 15 men and 20 boys in doing the same type of work
  2. 42 men take 25 days to dig a pond. If the phone would have to be dug in 14 days, then what is the number of men required to be employed?
MDW related
  1. If 18 men can earn Rs. 1440 in five days, how many men can earn Rs. 1920 in eight days?
  2. The hostel charges 35 students for 24 days in Rs. 6300. In how many days will the hostel charges Rs. 3375 for 25 students.
  3. 18 men can earn Rs.360 in 5 days.How much money will 15 men earn in 9 days?

Statistics-Data interpretation (DI)

average 6MCQ per exam in last four exams from this section. But in the CDS maths paper, the statistics-DI portion differs from SSC-CGL / IBPS type exams because

  1. Theory / definition based MCQs asked.
  2. For data interpretation they don’t ask conventional pie-chart, bar-graph related cases. Instead they give frequency chart and you’ve to find mean / median / mode. (i.e. like the “stat” portion in the UPSC GS mains paper II under old syllabus.) Therefore you’ve to mugup those special formulas for continuous series etc.

Stat#1: Calculation type

first observe the MCQs

Weighted average  (wine-water) AM (Arithmetic mean)
  1. The mean weight of 150 students in a certain class is 60 kg.The mean weight of boys from the class is 70 kg, while that of girls is 55 kg.What is the number of girls in the class?
  2. A boy travels a distance of 8 km at the rate of 4 km/h, 6 km at the rate of 3 km/h and 4 km at the rate of 2 km/h.What is the average speed for the entire journey?
  3. A person invested part of Rs.45,000 at 4% and the rest at 6%.If his annual income from both are equal, then what is the average rate of interest?
  1. Nine numbers are written in ascending order. The middle number is the average of the nine numbers. The average of the first five larger numbers is 68 and that of the five smaller numbers is 44.What is the sum of all nine numbers?
  2. A batsman scores 80 runs in his sixth innings thus increases his average by 5.What is his average after six innings?
GM (Geometric Mean) HM (Harmonic Mean)
find geometric mean of 125, 729, 1331

  1. 495
  2. 1485
  3. 2221
  4. none of above
Consider these pairs: I (8,12); II (9, 11); III (6,24). Which of them have same harmonic mean?

  1. I and ii
  2. ii and iii
  3. I and ii
  4. all of them

Now how to prepare? Go through following articles

Weighted average (wine-water) Arithmetic mean
  1. Alligations,Mixtures,Alloys: Water,Milk,Wine mixing: Weighted Average Made Easy for CSAT,CAT,CMAT,IBPS Aptitude
  2. Alligation: Advanced applications in Interest rates, Profit-loss, Average Wages (Wine-Water Concept)

then Sarvesh Kumar chapter on Alligiation. (upto level1)

  1. Averages: More than two elements added / removed : shortcut technique explained
  2. Averages: Entry / Removal of 1 element => Increase / Decrease in Average Shortcut method explained
  3. also this YouTube video on [Statistics for GS] Wrong Observation to Correct Average (shortcut Method).flv

then Sarvesh Kumar chapter on Averages. (upto level1)

For geometric and harmonic mean

In the NCERT zip folder, I’ve included a word file giving the formulas and a few theory points. read it then pick a few random numbers and find their GM, HM on your own.
you’ll also find a few MCQs of GM, HM in Sarvesh Kumar’s chapter on “Sequence, series and progressions”.

Stat#2: Data Interpretation sets

First Observe the MCQs from past exams

Q1. Consider following data

x 1 2 3 4 5
f 3 5 9 A 2

IF THE arithmetic mean is 2.96, what is the missing frequency “A”? (options: 4/6/7/8)

Q2. Consider following data

class interval 1-10 11-20 21-30 31-40 41-50 51-50
frequency 9 22 20 12 8 100 total frequency

What is the modal class?

  1. 10.5 to 20.5 only
  2. 10.5-20.5  and 20.5-30.5
  3. 20.5-30.5 only
  4. there is modal class

Q3. for the following table, median is 14.4 and total frequency is 20.

class 0-6 6-12 12-18 18-24 24-30
fr. 4 x 5 y 1

Now answer the following two questions:

  1. What is the value of x? (option: 4/5/6/7)
  2. what is the relation between x and y
    1. 2x=3y
    2. 3x=2y
    3. x=y
    4. 2x=y

As you can see these are not the typical Data interpretation sets you face in SSC or Bank or LIC type exams.

Anyways how to approach statistical DI sets?

  • In the NCERT zip file=>stat=>11_Stat_5_Measures of Central Tendency.pdf (i.e. class 11 NCERT statistics for economics –chapter 5)
  • You can also go through my YouTube Playlist of Stat lectures (click me):
  • In above youtube playlist page, watch video number 3,4,7,8,14,17. (Remaining topics were meant for old syllabus of UPSC General Studies mains paper II, hence useless.)
  • Then solve old CDS papers.

Stat#3: Theory / definition type MCQs

First observe the MCQs from previous CDS exams

  1. If the population figures are given for each State of India, then the data can be classified as?
    1. qualitative
    2. quantitative
    3. geographical
    4. chronological
  2. With the help of histogram one can prepare.
    1. fr. polygon
    2. fr. curve
    3. fr. distribution
    4. all of these
  3. When rectangles are drawn with the areas proportional to the frequencies of the respective class intervals, what is the diagram called? (ogive / frequency polygon / pie diagram / histogram)
  4. Assertion (A) The mean of first seven prime numbers is greater than their median. Reason (R) Mean is always greater than median.
  1. If every number of a finite set is increased by any number k, the measure of central tendency should also increase by k. Which one of the following measures of central tendency does not have this property?
    1. Arithmetic Mean
    2. Median
    3. Mid-range
    4. Geometric mean
  2. Suitable graph for representing the partitioning of total into subparts is
    1. ogive
    2. pictograph
    3. histogram
    4. pie chart
  3. Type of classification needed to enumerate female population of India?
    1. geographical
    2. qualitative
    3. chronological
    4. quantitative

For this type of theory, you’ve to refer to NCERTs. In the Zip file, I’ve given separate folder for “STAT” and within that stat folder, there are two sub-folders:

Contains following NCERT chapters.

  • 10_14 Statistics
  • 11_15 Statistics
  • 11_Stat_3_Organisation of Data
  • 11_Stat_4_Presentation of Data
  • 11_Stat_5_Measures of Central Tendency
  • Geometric and Harmonic Mean (word file)
  • Remaining chapters related to stat from class 7 to 11.
  • Read them if you’ve time left, else ignore.

this concludes second article, in the third and last article we’ll see how to prepare geometry, trigonometry and remaining misc. topics for the combined defense services exam.

Appendix Download link: Topic wise Sorted NCERTs

You’ve two choices

Choice #1: good internet connection: And you want to download entire zip file at once (size 35MB) then use following link: https://files.secureserver.net/0sYHJ029rgUbrg

Choice #2: not so good internet connection: and / or You want to download small zip files or selective topics only, then goto following link (e.g. geometry zip file separately, trigonometry zip file separately and so on) then use following link: https://files.secureserver.net/0fmaNqqBDslHlc