Fastest growing languages of India — Hindi (first), Kashmiri (second), Gujarati & Meitei alias Manipuri (third), Bengali (fourth) — based on 2011 census of India Gujarati & Meitei are so close in the
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Women in a tribal (Gond adivasi) village, Umaria district, India. Picture taken during a meeting organised by Ekta Parishad about land rights, the main grievance of the Adivasi people.
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1. Reading a table before calculating
A table presents observations at the intersection of rows and columns. Rows may identify districts, companies, years or population groups; columns may show applicants, expenditure, output, percentages or other variables. The first task is to understand what each cell represents. A number such as 250 is meaningless until its category, period and unit are known. It could mean 250 persons, 250 thousand tonnes or ₹250 crore.
Read the title, row labels, column headings, units and footnotes before attempting arithmetic. Check whether the period is a calendar year, a financial year or a point-in-time reference date. A table of stocks, such as population on a specified date, differs from a table of flows, such as annual migration. Similarly, a cumulative figure includes earlier periods and must not be treated as an additional, independent annual observation.
Identify whether entries are absolute numbers, percentages, ratios or index values. Blank cells, dashes and zeroes are not automatically interchangeable: a dash may mean unavailable, not applicable or negligible, depending on the legend. If a question provides insufficient information to interpret an entry, do not invent a value. This reading discipline prevents more errors than faster multiplication alone.
- Mark the required category, time period and unit mentally before selecting values.
- Check whether totals include all categories and whether categories overlap.
- Treat footnotes as part of the data, not as optional background.
2. Core calculations and the correct denominator
Most table questions use a small set of operations: addition, subtraction, ratios, percentages, averages and growth rates. A category’s share equals its value divided by the relevant total, multiplied by 100. A selection rate equals selected candidates divided by applicants, multiplied by 100. Percentage change equals the new value minus the old value, divided by the old value, multiplied by 100. Although similar in appearance, these expressions answer different questions.
Direction matters in comparisons. If A is 25% greater than B, then A equals 1.25 times B; consequently, B is 20% less than A, not 25% less. Likewise, a rate rising from 15% to 20% increases by 5 percentage points but by approximately 33.33% relative to its initial level. CSAT options may deliberately place these two results close together.
An overall rate is usually a weighted average. If groups contain different numbers of applicants, their selection rates cannot simply be added and divided by the number of groups. Instead, divide total selections by total applicants. For other applications, use the corresponding weights: quantities for average purchase prices, student numbers for combined class averages, and relevant population counts for combined population rates.
- Average per unit = total quantity ÷ number of units.
- Weighted average = sum of each value multiplied by its weight ÷ sum of weights.
- For successive changes, multiply growth factors; a 20% rise followed by a 20% fall produces a net fall of 4%.
A reliable table-solving sequence
- 1. Read the question and identify the required quantity.
- 2. Check the table’s labels, units, period and footnotes.
- 3. Extract only the relevant cells.
- 4. Choose the correct denominator and operation.
- 5. Simplify, compare or calculate to the precision required by the options.
- 6. Check plausibility and match the result to the question wording.
3. Worked interpretation of an illustrative table
The accompanying table is hypothetical and represents recruitment data for four districts. Applicants total 5,000 and selections total 900. Therefore, the overall selection rate is 18%. District D has the largest number selected, 315, and the highest selection rate, 22.5%. District C has the most applicants, 1,500, but its selection rate is only 15%. The largest denominator does not necessarily produce the highest rate.
Districts A and B each have 180 selected candidates, but their rates differ because A has 1,200 applicants while B has 900. Their respective rates are 15% and 20%. District B’s rate is therefore 5 percentage points higher, or approximately 33.33% higher relative to A’s rate. Meanwhile, B contributes 20% of all selections because 180 divided by 900 equals 0.20. This happens to equal its own selection rate, but the denominators are different.
For A and B together, divide 360 selections by 2,100 applicants to obtain approximately 17.14%. Averaging their two rates gives 17.5%, which is incorrect because the groups have unequal sizes. Across all four districts, the simple average of the rates is 18.125%, not the correct combined rate of 18%. Even a small discrepancy can determine the correct option.
- District D’s share of total selections is 315 ÷ 900 × 100 = 35%.
- District C’s share of total applicants is 1,500 ÷ 5,000 × 100 = 30%.
- The difference between applicants and selections is 4,100; this does not establish how many candidates actually appeared for the examination.
| District | Applicants | Selected | Selection rate |
|---|---|---|---|
| A | 1,200 | 180 | 15% |
| B | 900 | 180 | 20% |
| C | 1,500 | 225 | 15% |
| D | 1,400 | 315 | 22.5% |
| Total | 5,000 | 900 | 18% |
4. Efficient calculation and option elimination
Read the question before performing detailed calculations. A question asking for the highest selection rate requires comparison of selected-to-applicant ratios, not every total in the table. Cancel common factors before multiplying. To compare a/b and c/d for positive denominators, compare ad and bc. Cross-multiplication is useful when decimal division would be lengthy, although easy benchmark fractions may be quicker.
Memorise common fraction-percentage equivalents: one-half is 50%, one-third is approximately 33.33%, one-fourth is 25%, one-fifth is 20%, one-eighth is 12.5%, and one-sixth is approximately 16.67%. For example, 225 out of 1,500 can be simplified to 15 out of 100. Recognising such relationships reduces arithmetic and lowers the chance of copying a number incorrectly.
Use approximation only when the options are sufficiently separated. If possible answers are 12%, 18%, 30% and 45%, a rough estimate may suffice; if they are 18.0% and 18.1%, exact calculation may be necessary. Establish bounds before calculating: a combined rate with positive weights must lie between the smallest and largest subgroup rates. An answer outside that range can immediately be rejected.
- Keep intermediate fractions exact and round only the final result when practical.
- Convert units consistently: one lakh equals 100,000 and one crore equals 100 lakh.
- If a long set is consuming disproportionate time, mark it for review rather than letting it crowd out easier questions.
5. Inference limits and common traps
A table supports only conclusions justified by its definitions and entries. Higher district expenditure does not establish better administrative performance unless relevant outcomes and needs are known. More selected candidates do not necessarily imply a fairer or easier recruitment process. Similarly, two variables moving together do not establish that one caused the other. Distinguish numerical description from explanation.
Watch for totals that are counted twice. If a table lists male applicants, female applicants and all applicants, adding all three columns duplicates the population. Percentages may not sum to exactly 100 because of rounding; alternatively, they may exceed 100 when respondents can choose multiple answers. The table’s structure and notes determine which interpretation is valid.
Missing information can sometimes be recovered using a genuine total, but only if the listed components are mutually exclusive and exhaustive. A percentage without its denominator usually cannot yield an absolute count. Similarly, a rise in nominal expenditure does not prove an equivalent rise in real expenditure without price information. For every statement-based question, ask whether the conclusion must follow, merely could follow, or cannot be established.
- Do not infer appearance, eligibility or withdrawal figures from applicant and selection counts alone.
- For an index with base year equal to 100, distinguish index-point changes from percentage changes.
- Recheck the selected option against the exact wording: highest number, highest share and highest growth are different demands.
Real-world case studies
Census of India 2011: identifying the literacy denominator
Census literacy rates refer to the population aged seven years and above. Calculating a state’s literacy rate using its entire population would therefore use the wrong denominator. Combining district literacy rates also requires weighting by the respective populations aged seven and above, rather than taking an ordinary average.
NFHS-5: comparing indicator-specific populations
The National Family Health Survey, NFHS-5, conducted during 2019–21, publishes state and district fact sheets. Indicators refer to different populations: stunting concerns children under age five, while several women’s health indicators concern specified groups aged 15–49. These percentages cannot be added or directly converted into counts without the appropriate population base. Survey weighting also means published aggregate estimates should not be reconstructed by simply averaging subgroup percentages.
Previous year questions
No source-linked PYQ is available here yet. Use the practice questions below.
Practice questions
Practice MCQ 1 · Easy
The table shows the number of books borrowed from three public libraries during a month. | Library | Books borrowed by adults | Books borrowed by children | |---|---:|---:| | P | 360 | 240 | | Q | 420 | 180 | | R | 300 | 300 | How many books were borrowed by children from the three libraries together?
- A. 680
- B. 720
- C. 780
- D. 1080
Practice MCQ 2 · Easy
A district's expenditure on four sectors is given below. These are the only sectors included in the expenditure total. | Sector | Expenditure (₹ crore) | |---|---:| | Roads | 54 | | Drinking water | 36 | | Health | 30 | | Education | 60 | What percentage of the total expenditure was incurred on drinking water?
- A. 15%
- B. 18%
- C. 25%
- D. 20%
Practice MCQ 3 · Easy
The annual output of four production units is shown below. | Unit | Output in 2023 (tonnes) | Output in 2024 (tonnes) | |---|---:|---:| | P | 80 | 100 | | Q | 120 | 144 | | R | 150 | 180 | | S | 200 | 230 | Which unit recorded the highest percentage increase in output from 2023 to 2024?
- A. P
- B. Q
- C. R
- D. S
Practice MCQ 4 · Easy
The table gives the number of trainees enrolled at two skill-development centres. Each trainee is counted once. | Centre | Male trainees | Female trainees | |---|---:|---:| | Urban | 180 | 120 | | Rural | 140 | 160 | What is the ratio of female trainees to all trainees at the two centres combined?
- A. 7 : 8
- B. 8 : 15
- C. 7 : 15
- D. 14 : 15
Practice MCQ 5 · Easy
The following table shows cumulative expenditure on a project from the beginning of a financial year up to the end of each quarter. | Quarter ending | Cumulative expenditure (₹ lakh) | |---|---:| | June | 45 | | September | 110 | | December | 185 | | March | 260 | What was the expenditure during the October–December quarter alone?
- A. ₹65 lakh
- B. ₹75 lakh
- C. ₹110 lakh
- D. ₹185 lakh
Practice MCQ 6 · Moderate
Recruitment examination data for three centres are given below. Each applicant belongs to exactly one centre. | Centre | Applicants | Percentage of applicants who appeared | Percentage of those appearing who qualified | |---|---:|---:|---:| | P | 1200 | 75% | 20% | | Q | 800 | 90% | 25% | | R | 1000 | 80% | 30% | What percentage of all candidates who appeared at these centres qualified?
- A. 20%
- B. 24%
- C. 25%
- D. 30%
Practice MCQ 7 · Moderate
The table gives the number of students and their average marks in three sections of a school. | Section | Number of students | Average marks | |---|---:|---:| | P | 40 | 54 | | Q | 60 | 66 | | R | Not shown | 72 | The average marks of all students in these three sections together are 66. How many students are in Section R?
- A. 80
- B. 60
- C. 100
- D. 120
Practice MCQ 8 · Moderate
The following table describes cultivation in a region during a year. The areas under the three crops are separate and together constitute the entire cultivated area. | Crop | Area (hectares) | Yield (tonnes per hectare) | |---|---:|---:| | P | 120 | 2.5 | | Q | 80 | 3.0 | | R | 100 | 1.8 | In the following year, the region's total production increased by 30%, while its total cultivated area increased by 20%. What was the overall yield in the following year?
- A. 2.40 tonnes per hectare
- B. 2.50 tonnes per hectare
- C. 2.64 tonnes per hectare
- D. 2.60 tonnes per hectare
Practice MCQ 9 · Moderate
A survey recorded the use of solar energy and biogas in two villages. Households in the two villages are distinct. The columns for solar energy and biogas each include households using both. | Village | Total households | Using solar energy | Using biogas | Using both | |---|---:|---:|---:|---:| | P | 200 | 80 | 65 | 25 | | Q | 300 | 120 | 100 | 40 | Among all households using at least one of these two energy sources, what percentage use exactly one?
- A. 47%
- B. 78⅓%
- C. 65%
- D. 83⅓%
Practice MCQ 10 · Moderate
The table shows examination results for two streams, which together account for all candidates in each year. | Year | Stream | Candidates appearing | Candidates passing | |---|---|---:|---:| | 2023 | P | 100 | 90 | | 2023 | Q | 400 | 240 | | 2024 | P | 400 | 340 | | 2024 | Q | 100 | 50 | Consider the following statements: 1. The overall pass rate increased by 12 percentage points from 2023 to 2024. 2. The pass rate increased in each stream separately. 3. Stream P's share of all successful candidates increased from 2023 to 2024. Which of the above statements are correct?
- A. 1 only
- B. 2 and 3 only
- C. 1 and 2 only
- D. 1 and 3 only
Practice MCQ 11 · Difficult
A trader purchased a commodity from three suppliers as shown below. | Supplier | Quantity purchased (kg) | Purchase price (₹ per kg) | Percentage rejected on arrival | |---|---:|---:|---:| | P | 400 | 50 | 10% | | Q | 600 | 40 | 5% | | R | 500 | 44 | 4% | The trader paid for the entire purchased quantity and incurred an additional ₹4500 in transport costs. Rejected quantities had no sale value. Of the accepted quantity, two-thirds was sold at ₹60 per kg. Subsequently, 20% of the remaining quantity spoiled and had no sale value. There were no other costs or receipts. At what price per kg must the remaining saleable quantity be sold to earn a profit of 20% on the total purchase and transport cost?
- A. ₹70
- B. ₹72
- C. ₹75
- D. ₹80
Practice MCQ 12 · Difficult
The table describes employees in three offices before any transfers. | Office | Total employees | Women as a percentage of the office's employees | |---|---:|---:| | P | Not shown | 40% | | Q | 300 | 60% | | R | Not shown | 25% | Together, the offices have 1000 employees, of whom 40% are women. Some women are transferred from Q to R, with no other transfers, recruitment or departures. After the transfer, women constitute the same percentage of employees in Q and R. How many women were transferred?
- A. 100
- B. 80
- C. 120
- D. 60
Practice MCQ 13 · Difficult
A survey of 1000 households recorded enrolment in three schemes, X, Y and Z. | Enrolment category | Number of households | |---|---:| | X | 520 | | Y | 460 | | Z | 380 | | Both X and Y | 240 | | Both X and Z | 200 | | Both Y and Z | 180 | | None of the three | 180 | Each single-scheme count includes households also enrolled in other schemes. Each pairwise count includes households enrolled in all three schemes. A one-time payment of ₹200 is made to each household enrolled in exactly one scheme, ₹350 to each household enrolled in exactly two schemes, and ₹500 to each household enrolled in all three. These payments are mutually exclusive; households enrolled in none receive nothing. What is the total payment?
- A. ₹2.17 lakh
- B. ₹2.61 lakh
- C. ₹2.85 lakh
- D. ₹2.45 lakh
Practice MCQ 14 · Difficult
An election has only two candidates, A and B, and three polling areas. The table gives the initial count. Turnout is the percentage of registered voters who cast a vote; the valid-vote percentage is calculated among votes cast. | Area | Registered voters | Turnout | Valid votes as a percentage of votes cast | A's share of initially valid votes | |---|---:|---:|---:|---:| | R | 12000 | 75% | 80% | 60% | | S | 10000 | 80% | 90% | 45% | | T | 8000 | 75% | 80% | Not shown | On verification, 5% of the votes initially counted for A in R and 10% of the votes initially counted for B in S are declared invalid. No other vote changes its status, and no vote is transferred between candidates. What is the minimum number of initially valid votes that A must have received in T to finish with a lead of at least 1000 votes?
- A. 2360
- B. 2450
- C. 2540
- D. 2648
Practice MCQ 15 · Difficult
The table gives the initial populations of two towns and the newcomers who subsequently settle in them from outside both towns. | Town | Initial population | Initial literacy rate | Number of newcomers | Literacy rate among newcomers | |---|---:|---:|---:|---:| | P | 40000 | 70% | 10000 | 80% | | Q | 60000 | 50% | 10000 | 60% | After all newcomers settle, x literate persons move from P to Q and 2x illiterate persons move from Q to P. No person moves more than once. There are no other population changes, and nobody's literacy status changes. The two towns then have equal literacy rates. What is the total number of persons who moved between the two towns?
- A. 11250
- B. 7500
- C. 15000
- D. 3750
Further reading
- UPSC Civil Services Examination notification: Preliminary Examination scheme and General Studies Paper II syllabus, upsc.gov.in.
- UPSC official previous question papers: Civil Services Preliminary Examination, General Studies Paper II.
- NCERT Mathematics, Class VII: Comparing Quantities and Data Handling.
- NCERT Mathematics, Class VIII: Comparing Quantities and Data Handling.
- Census of India 2011: Primary Census Abstract and census concepts, censusindia.gov.in.
- Ministry of Health and Family Welfare and International Institute for Population Sciences: NFHS-5 India Report and state fact sheets.
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