The following table shows the production of five types of cars (in thousands) by a company from 2015 to 2020. Study the table and answer the questions that follow.
| Year/Car Type | A | B | C | D | E |
|---|---|---|---|---|---|
| 2015 | 100 | 150 | 120 | 180 | 200 |
| 2016 | 120 | 160 | 130 | 190 | 210 |
| 2017 | 130 | 170 | 140 | 200 | 220 |
| 2018 | 140 | 180 | 150 | 210 | 230 |
| 2019 | 150 | 190 | 160 | 220 | 240 |
| 2020 | 160 | 200 | 170 | 230 | 250 |
What is the approximate average production of all car types in the year 2018?
Answer: B
Read the 2018 row of the table and average the five figures.
\[ 140 + 180 + 150 + 210 + 230 = 910 \]
\[ \frac{910}{5} = 182 \text{ thousand} \]
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The following chart gives the percentage of the different subject teachers in a particular school. Total number of teachers is 1600.
| Subject | Teachers (%) |
|---|---|
| Physics | 12% |
| History | 14% |
| Hindi | 15% |
| English | 21% |
| Mathematics | 22% |
| Chemistry | 16% |
What is the number of male teachers of mathematics if the ratio of mathematics teachers of male to female is 3 : 1 ?
CBSE Assistant Secretary - 2024,
Answer: B
The number is 264.
Mathematics teachers are 22% of all teachers.
\[ 22\% \text{ of } 1600 = \frac{22}{100} \times 1600 = 352 \]
The male to female ratio is 3 : 1, so males are three of every four mathematics teachers.
\[ \frac{3}{4} \times 352 = 264 \]
There are 264 male mathematics teachers. The option 352 is all the mathematics teachers, 88 is the female share (one quarter of 352) and 176 is half of them.
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Study the table and answer the question. Number of new patients admitted and number of patients discharged in four hospitals A, B, C and D in different months of certain year are given in the table.
| Hospitals | August New Admi. | Discharge | September New Admi. | Discharge | October New Admi. | Discharge | November New Admi. | Discharge |
|---|---|---|---|---|---|---|---|---|
| A | 80 | 56 | 64 | 78 | 87 | 69 | 58 | 74 |
| B | 89 | 74 | 88 | 62 | 62 | 77 | 79 | 72 |
| C | 75 | 58 | 59 | 78 | 85 | 88 | 83 | 73 |
| D | 76 | 87 | 86 | 72 | 82 | 68 | 79 | 82 |
During August to October, which hospital has seen the maximum increase in the number of patients ?
CBSE Assistant Secretary - 2024,
Answer: C
The maximum increase was in hospital A.
The change in the number of patients each month is new admissions minus discharges. Adding August, September and October:
Hospital A's net increase of 28 is the largest. B is close at 26, C actually fell, and D rose by 17. November is outside the period asked about.
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Marks obtained by Sunita in her pre-board examination are as follows :
| Subject | Marks |
|---|---|
| English | 72 |
| Hindi | 84 |
| Mathematics | 96 |
| Science | 80 |
| Social Science | 68 |
If a pie chart is constructed for the above data, then what will be the angle of the sector representing marks obtained by Sunita in Mathematics ?
CTET - 2023,
Answer: C
The angle for Mathematics is 86.4°.
The total of all marks is 72 + 84 + 96 + 80 + 68 = 400. A sector's angle is its share of 360°:
\[ \theta = \frac{96}{400} \times 360^\circ = 86{\cdot}4^\circ \]
75.6° is the angle for Hindi (84 marks), 72° would be 80 marks out of 400, which is Science, and 64.8° is the angle for English (72 marks).
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In class III, 150 children were asked to name their one favourite fruit and results for 5 favourite fruits were written in the form of the following table :
| Name of the Fruit | Number of Children |
|---|---|
| Apple | 28 |
| Guava | 26 |
| Mangoes | 44 |
| Banana | 14 |
| Grapes | 28 |
Choose the correct option :
CTET - 2024,
Answer: D
The correct statement is Ten children do not like any fruit given in the table.
Add the children in the table:
\[ 28 + 26 + 44 + 14 + 28 = 140 \]
150 children were asked, so 150 − 140 = 10 children named some other fruit.
The other statements fail on the numbers. Apple (28) and Guava (26) are not equal. Grapes minus Banana is 28 − 14 = 14, not 16. Mangoes and Banana together make 44 + 14 = 58, while twice Guava is 2 × 26 = 52, so that is not 'two times' either.
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The time spent by a student during a day in different activities is represented by sectors of central angles in a pie chart as given below :
School-90°
Homework-60°
Play-60°
Sleep-120°
Others-30°
What is the difference between the time spent by the student in the activities 'sleep' and 'school'?
CTET - 2024,
Answer: B
The difference is 2 hours.
A pie chart for one day represents 24 hours by 360°, so each degree is 24/360 = 1/15 hour. Sleep has 120° and school 90°:
\[ \begin{aligned} &(120^{\circ} - 90^{\circ}) \times \frac{24}{360} \\ &= 30 \times \frac{1}{15} = 2 \end{aligned} \]
Sleep is 8 hours and school 6 hours. Four hours is the time for play or homework (60°), not the difference asked for; 3 hours would need a gap of 45°, and 1½ hours a gap of 22.5°.
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If Red part in the following pie chart is 40, what is White part?
| Part | Share of the pie |
|---|---|
| Yellow | \( \frac{1}{4} \) |
| Blue | \( \frac{1}{8} \) |
| White | \( \frac{1}{8} \) |
| Red | \( \frac{1}{2} \) |
CTET - 2018,
Answer: B
The White part is 10.
Red is \( \frac{1}{2} \) of the chart and equals 40, so the whole chart is 80. White is \( \frac{1}{8} \) of the chart:
\[ \text{White} = \frac{1}{8} \times 80 = 10 \]
As a check, Yellow is 20 and Blue is 10, and \( 40 + 20 + 10 + 10 = 80 \). 20 is the Yellow part, 5 would follow from taking 40 as the whole, and 12 has no basis.
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A geometric representation, showing the relationship between a whole and its part, is
CTET - 2018,
Answer: B
It is a pie chart.
A pie chart is a circle divided into sectors, each sector's angle proportional to the part it represents (part/whole × 360°). It therefore shows at a glance how a whole is split into its parts, for example how a family's income is spent.
A bar graph and a pictograph compare separate quantities side by side, and a histogram shows the frequencies of a grouped continuous variable. None of them is designed to show parts of one whole.
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In a class, teacher prepared following table showing colours of eyes of 40 students :
| Blue eye | Brown eye | Black eye | |
|---|---|---|---|
| Boys | 5 | 4 | 11 |
| Girls | 7 | 3 | 10 |
Teacher told four students to write one statement each about this table on black-board. They wrote :
(a) Number of boys and girls are equal.
(b) Mostly students have black eye.
(c) Total number of students having blue eyes is odd.
(d) Total number of students having brown eyes is odd.
Choose the correct option :
CTET - 2026,
Answer: B
The correct option is (a), (b) and (d) are true but (c) is false.
From the table:
Option 1 wrongly rejects (d), option 3 wrongly rejects (a) and accepts (c), and option 4 accepts (c) and rejects (d).
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A pie chart is constructed for the following data :
| Month | January | February | March | April | May | June |
| Number of computers sold | 500 | 700 | 840 | 750 | 890 | 820 |
What will be the difference between the central angles of the sectors representing the number of computers sold in March and January ?
CTET - 2026,
Answer: C
The difference is 27.2°.
In a pie chart each value's central angle is its share of 360°. The total number of computers sold is
\[ 500 + 700 + 840 + 750 + 890 + 820 = 4500 \]
March exceeds January by 840 − 500 = 340 computers, so
\[ \begin{aligned} \text{difference} &= \frac{340}{4500} \times 360^\circ \\ &= 27.2^\circ \end{aligned} \]
Each computer is worth 0.08°. 28.8° would need a difference of 360 computers and 28° one of 350, so a slip in the subtraction or the total gives those options.
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