1. What mixed graphs test

A mixed-graph set distributes information across two or more visual representations. One chart may show the number of applicants to an examination, while another shows the percentage who qualified. Alternatively, bars may represent annual production and a line may represent the percentage sold. Neither representation alone answers every question; the candidate must establish the mathematical relationship between them.

Common combinations include bars and lines sharing a horizontal axis, a pie chart accompanied by a table of totals, and two separate charts describing different aspects of the same categories. The shared link may be a year, quarter, district, product or population group. Before calculating, confirm that both sources refer to the same category, period and coverage.

CSAT questions commonly ask for totals, ratios, percentage changes, weighted averages, rankings or conclusions supported by the data. A question may also be impossible to determine because a necessary total is absent. Recognising such insufficiency is as important as performing arithmetic. Do not assume missing values from general knowledge or from the apparent shape of a graph.

Bar plus line: often links an absolute quantity with a rate, percentage or price.
Pie chart plus table: often links category shares with totals or per-unit values.
Two charts: may require matching categories before deriving a third quantity.

2. Read the visual language before calculating

Start with the title, legend, horizontal categories and vertical scales. Note whether quantities are expressed in units, thousands, lakh or crore. A value of 80 on an axis labelled thousand units means 80,000 units. Likewise, ₹5 crore and ₹500 lakh are equal, although their displayed numbers differ greatly. Unit conversion should precede addition or comparison.

In a dual-axis chart, bars may use the left axis while the line uses the right axis. Their apparent intersection has no inherent numerical meaning. A bar reaching 100 thousand units and a line reaching 80% cannot be compared as though they represent the same variable. Check for truncated axes, unequal intervals and explicitly printed data labels before estimating values.

Read the percentage base carefully. Qualification rate usually means qualified candidates divided by applicants, but a question may instead give qualified candidates as a percentage of those who appeared. Similarly, profit as a percentage of cost differs from profit as a percentage of revenue. The words surrounding the chart determine which denominator is valid.

Distinguish flows from stocks and annual values from cumulative values. Quarterly sales are a flow over a period; inventory at quarter-end is a stock at a particular time. Adding cumulative monthly totals double-counts earlier observations. Also, unsold current production is not necessarily closing inventory because opening stock, returns or transfers may exist.

Write a short unit label beside every derived quantity.
Treat missing observations as unknown, not zero.
Use printed values where available; avoid extracting false precision from an approximate diagram.

Mixed-graph solution sequence

1. Identify the quantity asked.
2. Read titles, legends, axes, units and percentage bases.
3. Match the relevant categories across representations.
4. Write the relationship and derive only necessary values.
5. Calculate, using cancellation or safe approximation.
6. Check units, denominator and plausibility against the options.

3. Core calculations and denominator discipline

When a bar supplies a total and a line supplies a percentage, multiply them to obtain the corresponding quantity. If production is P and the percentage sold is s, units sold equal P × s/100. Units not sold from that production equal P × (100 − s)/100, provided the percentage specifically refers to current production.

For comparisons over time, percentage change equals (new value − old value)/old value × 100. The earlier value is the base. A rise in a rate from 40% to 50% is 10 percentage points but a 25% relative increase. These two descriptions are not interchangeable. Reverse questions also require care: if sales after a 20% increase are 120, earlier sales were 120/1.20, or 100.

Aggregate rates normally require weighting. If one centre qualifies 50% of 100 applicants and another qualifies 80% of 400 applicants, their combined qualification rate is (50 + 320)/(100 + 400) × 100 = 74%. The simple average, 65%, gives equal weight to centres of unequal size and is incorrect.

For pie charts, category quantity equals total × sector percentage/100, or total × sector angle/360. Shares from different years cannot establish absolute growth unless the respective totals are known. A category's share can fall even while its absolute quantity rises if the overall total grows sufficiently.

Revenue = quantity sold × selling price per unit.
Overall rate = sum of relevant outcomes / sum of relevant base quantities × 100.
Ratio comparisons can often be simplified by cancelling a shared total or common unit.

Hypothetical quarterly production, sales percentage and selling price
Quarter	Production: thousand units	Current production sold: %	Selling price: ₹ per unit
Q1	100	80	50
Q2	120	75	60
Q3	150	80	50
Q4	130	90	80

4. Worked mixed-graph example

The table below represents a hypothetical mixed-graph set: bars show quarterly production, a line shows the percentage of that quarter's production sold, and an accompanying table gives selling prices. Assume the reported sales are entirely from the corresponding quarter's production. These figures are illustrative examination data, not observations about an actual enterprise.

For Q2, production is 120 thousand units and 75% is sold. Sales therefore equal 90 thousand units. At ₹60 per unit, revenue is ₹54 lakh. A useful conversion is that thousand units multiplied by rupees per unit gives thousand rupees; divide this result by 100 to express it in lakh rupees.

Across all quarters, production totals 500 thousand units and sales total 407 thousand units. The overall sold proportion is therefore 81.4%, not the simple average of the four percentages, which is 81.25%. Production volumes provide the weights. The small difference illustrates why apparently close answers still require the correct method.

The highest production occurs in Q3, but the highest revenue occurs in Q4. Q3 sells 120 thousand units at ₹50 each, whereas Q4 sells 117 thousand at ₹80 each. Thus, neither the tallest production bar nor the highest sales quantity alone identifies the highest revenue. The required ranking depends on the variable named in the question.

Quarterly sales, in thousand units: Q1 = 80; Q2 = 90; Q3 = 120; Q4 = 117.
Quarterly revenue, in ₹ lakh: Q1 = 40; Q2 = 54; Q3 = 60; Q4 = 93.6.
Current production not sold, in thousand units: Q1 = 20; Q2 = 30; Q3 = 30; Q4 = 13.

5. An efficient CSAT solving strategy

Read the question before doing extensive calculations. Identify the target variable and locate only the values needed for it. If the question asks about revenue, production alone is insufficient: first derive sales and then apply price. A compact scratch table with category, total, rate and derived quantity reduces repeated graph reading and transcription errors.

Estimate before calculating exactly. Compare products, cancel common factors and use familiar fractions where helpful: 75% is three-fourths and 12.5% is one-eighth. Approximation is useful when options are well separated, but close alternatives require exact arithmetic. Never round intermediate values so heavily that a ranking or answer choice may change.

Finish with a plausibility check. A sold percentage between 75% and 90% must produce an aggregate within that interval. Revenue must carry a currency unit, while a ratio is dimensionless. If an answer contradicts these checks, inspect the denominator, axis or conversion. In a qualifying examination, dependable selection of solvable sets is preferable to spending excessive time on one calculation-heavy question.

Separate information explicitly provided from quantities that must be derived.
Do not infer causation merely because two plotted variables move together.
Where required bases are missing, assess whether the answer is genuinely indeterminate.

Real-world case studies

NFHS: percentages and population bases

National Family Health Survey reports present indicators such as anaemia prevalence for defined population groups. Comparing state percentages identifies relative prevalence, not the absolute number affected. Estimating counts requires corresponding population bases for the same group and period. This illustrates why a percentage chart cannot automatically be interpreted as a headcount chart.

Central Electricity Authority: capacity versus generation

Central Electricity Authority publications report installed electricity capacity and electricity generation. Capacity is commonly expressed in MW, while generation is reported in energy units such as million units. A source's share of installed capacity need not equal its share of generation. Interpreting these together requires attention to units, reporting periods and utilisation rather than comparison of bar heights alone.

Previous year questions

No source-linked PYQ is available here yet. Use the practice questions below.

Practice questions

Practice MCQ 1 · Easy

A mixed graph shows production through bars and the percentage of that production sold through a line. The printed values are: January: production = 80 thousand units; sold = 75%. February: production = 120 thousand units; sold = 60%. March: production = 100 thousand units; sold = 90%. How many units of the production of these three months were sold altogether?

A. 210 thousand
B. 222 thousand
C. 225 thousand
D. 240 thousand

Practice MCQ 2 · Easy

A pie chart shows the sector-wise allocation of a district's annual development budget. Education occupies 90° and Health occupies 60°. An accompanying bar chart shows that the district's total development budget is ₹240 crore. By how much does the allocation to Education exceed that to Health?

A. ₹15 crore
B. ₹30 crore
C. ₹40 crore
D. ₹20 crore

Practice MCQ 3 · Easy

In a mixed graph, bars show the sales revenue of three products and a line shows their selling prices per unit. Each product is sold at the stated price throughout the period. Product P: revenue = ₹12 lakh; price = ₹40. Product Q: revenue = ₹18 lakh; price = ₹60. Product R: revenue = ₹20 lakh; price = ₹80. What is the ratio of the numbers of units sold of P, Q and R?

A. 6 : 6 : 5
B. 3 : 3 : 4
C. 6 : 9 : 10
D. 2 : 3 : 4

Practice MCQ 4 · Easy

A bar chart shows that examination centres X and Y had 2,000 and 3,000 applicants, respectively. A line graph shows that 25% of the applicants at X and 40% of those at Y qualified. What percentage of the applicants at the two centres combined qualified?

A. 32.5%
B. 35%
C. 34%
D. 37.5%

Practice MCQ 5 · Easy

Two pie charts show the distribution of a company's annual sales revenue among products. Product K accounts for 30% in Year 1 and 24% in Year 2. An accompanying bar chart gives total sales revenue for Year 1 as ₹80 crore, but the Year 2 total is missing. Which one of the following conclusions is necessarily correct?

A. Revenue from K fell by 20%.
B. Revenue from K increased if and only if total revenue in Year 2 exceeded ₹100 crore.
C. Revenue from K remained unchanged if total revenue in Year 2 was ₹96 crore.
D. Revenue from K must have fallen because its share fell.

Practice MCQ 6 · Moderate

A pie chart shows the allocation of 5,000 hectares among four crops: Wheat = 144°, Rice = 108°, Pulses = 72°, and Oilseeds = 36°. A line graph gives their respective yields as 3, 4, 2 and 1.5 tonnes per hectare. What is the ratio of the combined output of Wheat and Rice to the combined output of Pulses and Oilseeds?

A. 12 : 5
B. 24 : 7
C. 9 : 2
D. 48 : 11

Practice MCQ 7 · Moderate

A company's mixed graph shows annual revenue through bars and profit as a percentage of cost through a line: Year 1: revenue = ₹144 lakh; profit = 20% of cost. Year 2: revenue = ₹180 lakh; profit = 25% of cost. Year 3: revenue = ₹224 lakh; profit = 40% of cost. If revenue equals cost plus profit, what is the ratio of total profit to total cost over the three years?

A. 31 : 106
B. 17 : 60
C. 31 : 137
D. 3 : 10

Practice MCQ 8 · Moderate

Bars show cumulative sales from the beginning of a financial year, while a line shows the selling price applicable to all units sold in each quarter: End of Q1: cumulative sales = 20 thousand units; Q1 price = ₹100. End of Q2: cumulative sales = 50 thousand units; Q2 price = ₹120. End of Q3: cumulative sales = 90 thousand units; Q3 price = ₹150. End of Q4: cumulative sales = 140 thousand units; Q4 price = ₹160. Approximately what percentage of the year's sales revenue was earned in Q3 and Q4 together?

A. 64.29%
B. 68.57%
C. 71.43%
D. 75.00%

Practice MCQ 9 · Moderate

A bar chart gives registered candidates at centres A, B and C as 1,200, 1,500 and 1,800, respectively. A line graph gives absentee percentages among registered candidates as 10%, 20% and 25%, respectively. An accompanying table gives qualification rates among those who actually appeared as 25%, 30% and 40%, respectively. Across the three centres, what is the ratio of qualified candidates to absent candidates?

A. 13 : 10
B. 39 : 29
C. 49 : 29
D. 39 : 121

Practice MCQ 10 · Moderate

A factory's bar chart gives quarterly production, in thousand units, as Q1 = 100, Q2 = 120, Q3 = 150 and Q4 = 130. A line graph shows the percentage of each quarter's own production sold during that quarter as 80%, 75%, 80% and 90%, respectively. A table records additional sales from inventory available at the beginning of each quarter as 5, 10, 15 and 20 thousand units, respectively. Inventory at the beginning of Q1 was 25 thousand units. There were no losses, returns or other stock movements. What was inventory at the end of Q4?

A. 43 thousand units
B. 75 thousand units
C. 93 thousand units
D. 68 thousand units

Practice MCQ 11 · Difficult

A recruitment agency received 20,000 applications. A pie chart distributes them among centres A, B and C as 40%, 35% and 25%, respectively. A two-line graph shows the following percentages: A: appeared as a percentage of applicants = 75%; qualified as a percentage of those appearing = 20%. B: appeared = 80%; qualified = 25%. C: appeared = 90%; qualified = 40%. An accompanying table gives: A: women among qualified candidates = 45%; joining rate among qualified women = 80%; joining rate among qualified men = 90%. B: corresponding percentages = 40%, 75%, 80%. C: corresponding percentages = 50%, 90%, 70%. All candidates are classified as women or men. What is the ratio of women to men among all candidates who joined?

A. 10 : 11
B. 277 : 330
C. 277 : 316
D. 5 : 6

Practice MCQ 12 · Difficult

Bars show that a firm sold 120 thousand units in Year 1 and 160 thousand units in Year 2. Pie charts distribute the units sold among products A, B and C: Year 1: A = 30%, B = 40%, C = 30%. Year 2: A = 25%, B = 45%, C = 30%. A table gives selling prices per unit: Year 1: A = ₹100, B = ₹120, C = ₹150. Year 2: A = ₹120, B = ₹100, C = ₹180. The cost per unit sold was ₹60 for A, ₹80 for B and ₹100 for C in both years. Profit is sales revenue minus the cost of units sold, with no other expenses. Approximately by what percentage did total profit increase from Year 1 to Year 2?

A. 48.84%
B. 39.84%
C. 33.33%
D. 52.50%

Practice MCQ 13 · Difficult

A mixed graph for three divisions of a company shows annual costs through bars and profit as a percentage of revenue through a line: Division A: cost = ₹80 crore; profit = 20% of revenue. Division B: cost = ₹100 crore; profit = 25% of revenue. Division C: cost = ₹120 crore; profit = 40% of revenue. In the following year, the costs of A, B and C rise by 25%, 20% and 10%, respectively. The company sets a uniform profit margin, measured as profit divided by revenue, for all three divisions. What should this uniform margin be if combined profit is to increase by exactly 20% over the first year? Assume revenue equals cost plus profit.

A. 30%
B. 33⅓%
C. 45.45%
D. 31.25%

Practice MCQ 14 · Difficult

A bar chart gives the populations of districts A, B and C as 40, 60 and 100 thousand, respectively. A pie chart shows the allocation of a total gross water supply of 20 million litres per day: A = 25%, B = 35%, C = 40%. A line graph shows distribution losses as a percentage of each district's gross allocation: A = 20%, B = 10%, C = 25%. The authority may freely revise the allocation shares, but each district's loss percentage remains unchanged. What is the minimum percentage increase in total gross water supply required to ensure that every district receives at least 90 litres per person per day after losses?

A. 10%
B. 12.5%
C. 15%
D. 20%

Practice MCQ 15 · Difficult

A company's workforce data are presented in mixed charts. Bars show total annual salary payments of ₹60 crore in Year 1 and ₹84 crore in Year 2. A line shows the average annual salary per employee as ₹6 lakh and ₹7 lakh, respectively. Every employee worked for the full relevant year, and these averages equal total salary payments divided by employee numbers. Pie charts show employee distribution across departments: Year 1: A = 30%, B = 45%, C = 25%. Year 2: A = 25%, B = 50%, C = 25%. An accompanying table gives women as a percentage of each department's employees: Year 1: A = 40%, B = 60%, C = 32%. Year 2: A = 48%, B = 54%, C = 40%. All employees are classified as women or men. Approximately by what percentage did the number of men increase from Year 1 to Year 2?

A. 15.47%
B. 20.00%
C. 25.11%
D. 13.40%

Mixed graphs