Multiple Bar Graph Problems And Solutions

In this post, we will be learning about Bar graph problems and answers. We will see many situations where Bar graph can be used with tricks/shortcut to make and solve them. Bar graphs are used to compare things between different groups or to track changes over time. However, when trying to measure change over time, bar graphs are best when the changes are larger.

So, let us start the learning now on basically how to frame a bar graph with the figures provided and how to solve problems in identifying the figures with the help of Bar graph.

Related article: Pie Chart Questions And Answers With Examples

Getting Started

This post contains three sections –

Section A – This section contains important formulas, short tricks, concepts on Bar graphs
Section B – This section contains some examples that demonstrates how to build and solve questions on Bar graphs using short tricks, formulas shown in section A.
Section C – This is an exercise section that contains some Bar graph problems and solutions.

Now,

Where to start from?

We recommend to go through section A, then section B, then section C. Even if you are familiar with this topic, do not just skip section A and section B.

Section A (Terms & Definition)

The data collected in a particular category are represented in the form of vertical or horizontal bars drawn by selecting a particular scale. One of the parameters is plotted on the horizontal axis and the other on the vertical axis. The Student is required to understand the given information and then answer the given questions based on data analysis.

$Tutorialwing Math Bag Graph Chart Title example$

Thus,

A bar graph is useful for comparing facts. It provides a visual display for comparing different quantities. Another name for bar graph is bar chart.

Section B (Examples)

Now, we will see an example on bar graph and how to solve it.

I. The bar graph below shows the data about the foreign exchange reserves of a country (in million US $) from 1991-92 to 1998-99. Answer the questions based on this graph.

$Tutorialwing Math Graph Problems With Solutions Foreign Exchange$

Example 1

How many times was the foreign exchange reserves in 1997-98 that in 1994-95?

Solution:

Required ratio = 5040 / 3360

= 1.5

Example 2

What was the percentage increase in foreign exchange reserves in the year 1997-98 over 1993-94?

Solution:

Foreign exchange reserves in 1997-98 = 5040

Foreign exchange reserves in 1993-94 = 2520

So, Increase = 5040 – 2520

= 2520

Hence, Percentage increase = ((2520 / 2520) × 100) %

= 100 %

Example 3

During which year, the percentage increase of foreign exchange reserves over the previous year, is the highest?

Solution:

There is an increase in foreign exchange reserves in the following years 1992-93, 1994-95,1996-97 and 1997-98 as compared to previous year (as shown in bar graph).

The percentage increase in the reserves during these years compared to previous year is:

For 1992-93 = [ (3720-2640)/2640× 100] % = 40.91%
For 1994-95 = [ (3360-2520)/2520 × 100] % = 33.33%
For 1996-97 = [(4320-3120)/3120× 100] % = 38.46%
For 1997-98 = [(5040-4320)/4320× 100] % = 16.67%

Clearly, the percent increase of foreign exchange reserves over the previous year is the highest for 1992-93.

Thus, we just went through different bar graph problems and solutions.

Section C (Exercises)

In this section, we will see different questions and answers on bar graph ( or bar chart).

At first try to solve questions on your own. Then see the solution.

II. Study the following bar graph and answer the questions given below:

$Tutorialwing Math Bar Graph Example$

2.1 The production of fertilizers more than the average production of the given years in how many years?

a. 1
b. 2
c. 3
d. 4

Solution: (d)

Explanation

Average production of the given years

= (1/8) * (25 + 40 + 60 + 45 + 65 + 50 + 75 + 80)

= 55

So, the productions during the years 1997, 1999, 2001 and 2002 are more than the average production.

Hence, no. of years is 4.

2.2 Which of the following pairs of years was exactly equal to the average production of the years 1996 and 1997?

a. 2000 and 2001
b. 1999 and 2000
c. 1998 and 2000
d. 1995 and 2001

Solution: (d)

Explanation

Average production of 1996 and 1997 = (40 + 60) / 2 = 50

We shall find the average production for each of the given alternative pairs:
2000 and 2001 = (50+75) / 2 = 62.5
1999 and 2000 = (65+50) / 2 = 57.5
1998 and 2000 = (45+50) / 2 = 47.5
1995 and 2001 = (25+75) / 2 = 50

Hence, the average production of 1996 and 1997 was exactly equal to the average production of 1995 and 2001.

2.3 What was the percentage decrease in the production of fertilizers from 1997 to 1998?

a. 33 1/3 %
b. 30 %
c. 25 %
d. 21 %

Solution: (c)

Explanation

Required percentage = [((45 – 60) / 60) × 100] %

= -25%

Hence, there is a decrease of 25% in the production of fertilizers from 1997 to 1998.

2.4 As compared to the previous year, in which year was the percentage increase in production the maximum?

a. 2002
b. 2001
c. 1999
d. 1996

Solution: (d)

Explanation

The percentage increase in production as compared to the previous year for different years are:

In 1996 = [((40 – 25) / 25) × 100] % = 60%

In 1997 = [((60 – 40) / 40) × 100] % = 50%

In 1998 there is a decrease in production.

In 1999 = [((65 – 45) / 45) × 100] % = 44.44%

In 2000 there is a decrease in production.

In 2001 = [((75 – 50) / 50) × 100] % = 50%

In 2002 = [((80 – 75) / 75 × 100] % = 6.67%

Clearly, there is a maximum percentage increase in production in 1996.

2.5 How much was the percentage increase in production of fertilizers in 2002 compared to 1995?

a. 320 %
b. 300 %
c. 220 %
d. 200 %

Solution: (c)

Explanation

Required percentage = [((80 – 25) / 25) × 100] % = 220 %

Now, we will move to our next exercise on bar graph problems and solutions chapter. This is related to sales of different product in a cosmetic companies. Please read the data carefully and solve the questions.

III. A cosmetic company produces five different products. The sales of these five products (in lakh number of packs) during 1995 and 2000 are shown in the following graph. Answer the questions below based on this graph.

$Tutorialwing Math Bag Graph Example Sales$

3.1. The sales of which product has increased by nearly 55% from 1995 to 2000 in the case of:

a. Lipsticks
b. Nail enamels
c. Talcum powder
d. Shampoos

Solution: (d)

Explanation

The percentage increase from the year 1995 to 2000 for various products is:

Lipsticks = [((48.17 – 20.15) / 20.15) × 100] % = 139.06 %

Nail Enamels = [((37.76 – 5.93) / 5.93) × 100] % = 536.76 %

Talcum powder = [((29.14 – 14.97) / 14.97) × 100] % = 94.66 %

Shampoos = [((12.21 – 7.88) / 7.88) × 100] % = 54.95% = 55 %

3.2. What is the minimum rate of increase in sales during the period 1995-2000?

a. Lipsticks
b. Nail enamels
c. Talcum powder
d. Shampoos

Solution: (d)

Explanation

As calculated in the solution of Q.6 above, the minimum rate of increase in sales from 1995-2000 is in the case of Shampoos.

3.3. By what percent was the sales of lipsticks in 2000 was more than the sales of nail enamels in 2000?(rounded off to the nearest integer)

a. 33%
b. 31%
c. 28%
d. 22%

Solution: (c)

Explanation

Required Percentage = [(48.17- 37.76)/37.76 × 100] %

= 27.57%

= 28%

3.4. By what percent was the sales of conditioners in 1995 was less than the sales of shampoos in 1995? (rounded off to the nearest integer)

a. 57 %
b. 36 %
c. 29 %
d. 25 %

Solution: (b)

Explanation

Required Percentage = [((7.88 – 5.01) / 7.88) × 100] %

= 36.42 %

= 36 %

3.5. What is the ratio of the sales of nail enamels in 2000 to the sales of Talcum powders in 1995?

a. 7:2
b. 5:2
c. 4:3
d. 2:1

Solution: (b)

Explanation

Required ratio = 37.76 / 14.97

= 2.5

= 5/2

So, 5:2 is the answer.

That’s end of our questions on sales in different product.

Now, we will move to our next exercise on bar graph problems and solutions – production of different cars in a company. Read the questions carefully and answer questions.

IV. Study the bar graph and answer the questions that follow. The figure shows the percentage distribution production of 6 different cars by a car manufacturing company into various models over two years.

$Tutorialwing Math Bar Graph Problems and Solution$

Total number of cars produced in 2000 = 3, 75,000

Total number of cars produced in 2001 = 4, 70,000

4.1. What are total number of cars of models P, Q and T manufactured in 2000?

a. 2,45,000
b. 2,27,500
c. 2,25,000
d. 1,92,500

Solution: (c)

Explanation

We shall first find the number of cars of each model produced by the company during the two years:

Total number of cars produced in 2000= 3, 75,000

P = (30 – 0) % of 3, 75,000 = 30% of 3, 75,000 = 1, 12,500

Q = (45 – 30) % of 3, 75,000 =15% of 3, 75,000 =56,250

R = (65 – 45) % of 3, 75,000= 20% of 3, 75,000 =75,000

S = (75 – 65) % of 3, 75,000 = 10% of 3, 75,000 =37,500

T = (90 – 75) % of 3, 75,000 = 15% of 3, 75,000 = 56250

U = (100 – 90) % of 3, 75,000 = 10% of 3, 75,000 = 37,500

Total number of cars produced in 2001 = 4, 70,000

P = (40 – 0) % of 4, 70,000 = 40% of 4, 70,000 = 188,000

Q = (60 – 40) % of 4, 70,000 = 20% of 4, 70,000 = 94,000

R = (75 – 60) % of 4, 70,000 = 15% of 4, 70,000 = 70,500

S = (85 – 75) % of 4, 70,000 = 10% of 4, 70,000 = 47,000

T = (95 – 85) % of 4, 70,000 = 10% of 4, 70,000 = 47,000

U = (100 – 95) % of 4, 70,000 = 5% of 4, 70,000 = 23,500

Now we shall solve the question:

Hence, Total number of cars of models P, Q and T manufactured in 2000 = 1, 12,500 + 56,250 + 56250 = 2, 25,000

4.2. For which model the percentage rise/fall in production from 2000 to 2001 was minimum?

a. Q
b. R
c. S
d. T

Solution: (b)

Explanation

Using the above calculation, the percentage rise/fall in production from 2000 to 2001 for various models is:

For P = [((188,000 – 1,12,500) / 1, 12,500) × 100] % = 67.11 % rise

For Q = [((94,000 – 56,250) / 56,250) × 100] % = 67.11 % rise

For R = [((70,500 – 75,000) / 75,000) × 100] % = 6.00 % fall

For S = [((47,000 – 37,500) / 37,500) × 100] % = 25.33 % rise

For T = [((47,000 – 56250) / 56250) × 100] % = 16.44 % fall

For U = [((23,500 – 37,500) / 37,500) × 100] % = 37.33 % fall

Hence, Minimum percentage rise/fall in production is in the case of model R.

4.3 What was the difference in the number of Q type cars produced in 2000 and that produced in 2001?

a. 37,750
b. 27,000
c. 22,500
d. 17,500

Solution: (a)

Explanation

Please refer to the solution in Q 11.

Required difference = 94,000 – 56,250 = 37750

4.4 What is the number of P type cars produced in 2001 if the percentage production of P type cars in 2001 was the same as that in 2000?

a. 1,41,000
b. 1,32,000
c. 1,17,000
d. 1,05,000

Solution: (a)

Explanation

In 2001, Percentage production of P type cars = In 2000, Percentage production of P type cars = 30%

Then, percentage production of P type cars in 2001 = 30% of 4, 70,000 = 141000

4.5 If 85% of the S type cars produced in each year were sold by the company, how many S type cars remained unsold?

a. 7650
b. 9350
c. 12675
d. 12250

Solution: (c)

Explanation

Number of S type cars that remained unsold in 2000 = 15% of 37,500

Number of S type cars which remained unsold in 2001 = 15% of 47,000

So, total number of S type cars which remained unsold =

15% of (37,500 + 47,000)

15% of 84500 = 12675

That’s end of questions on production of cars in manufacturing company.

Now, we will move to our next exercise on bar graph problems and solutions chapter. This exercise is related to book sales in two years in a publishing company.

V. Study the bar graph that shows the books sales (in thousand numbers) from different branches of a publishing company during two consecutive years 2000 and 2001.Answer the questions based on this bar graph.

$Tutorialwing Bar Graph Problems And Solutions Math Best Math Aptitude Questions$

5.1 Total sales of branches B1,B3,B5 together for both years (in thousand numbers) is:

a. 250
b. 310
c. 435
d. 560

Solution: (d)

Explanation

Total sales of branches B1, B3, B5 together for both years (in thousand numbers) = (80 + 105) + (95 + 110) + (75 + 95)

= 560

5.2 What percentage of total sales of branch B6 for both the years is the total sales of branch B3 for both the years?

a. 68.54 %
b. 71.11 %
c. 73.17 %
d. 75.55 %

Solution: (c)

Explanation

Required Percentage = [(70 + 80) / (95 + 110) × 100] %

= 150 / 205 × 100 %

= 73.17%

5.3 What is the average sale of all branches (in thousand numbers) for the year 2000?

a. 73
b. 80
c. 83
d. 88

Solution: (b)

Explanation

Average sale of all branches (in thousand numbers) for the year 2000 = 1 / 6 × [80 + 75 + 95 + 85 + 75 + 70]

= 80

5.4 Find the ratio of the total sales of branch B2 for both years to the total sales of branch B4 for both years?

a. 2:3
b. 3:5
c. 4:5
d. 7:9

Solution: (d)

Explanation

Required ratio = (75 + 65) / (85 + 95)

= 140 / 180

= 7 / 9

5.5 What percentage of the average sales of branches B1, B2 and B3 in 2001 is the average sales of branches B1, B3 and B6 in 2000?

a. 75%
b. 5%
c. 5%
d. 85%

Solution: (c)

Explanation

Average sales of branches B1, B3 and B6 in 2000 = (1/3) × (80 + 95 + 70) = 245/3

Average sales of branches B1, B2 and B3 in 2001 = (1/3) × (105 + 65 + 110) = 280/3

So, required percentage = [(245/3)/ (280/3) × 100] %

= ((245/280) × 100) %

= 87.5%

Now, we will move to our next exercise on bar graph problems and solutions chapter. This is related to percentage distribution of total expenditure of a company.

VI. Read the bar graph that shows the percentage distribution of total expenditure of a company under various expense heads during 2003 and answer the questions that follow:

$Tutorialwing Math Bar Graph Problems And Solutions Percentage Distribution$

6.1 The expenditures on the interest on loans is by what percent more than the expenditures on transport?

a. 5 %
b. 10 %
c. 20 %
d. 40 %

Solution: (d)

Explanation

Let the total amount of expenditure be Rs.x

So, the expenditure on interest on loans = Rs. (17.5% of x)

= Rs. (17.5 / 100x)

Expenditure on transport = Rs. (12.5% of x)

= Rs. (12.5 / 100x)

So, Difference between 2 expenditures = Rs.((17.5 / 100x) – (12.5 / 100x))

= Rs. 5x/100

So, required percentage = [(5x/100) / (12.5x/100)] %

= 40%

6.2 Find the ratio of the total expenditure on infrastructure and transport to the total expenditure on taxes and interest on loans?

a. 5:4
b. 8:7
c. 9:7
d. 13:11

Solution: (d)

Explanation

Let the total amount of expenditure be Rs.x

Total expenditure on infrastructure and transport is = Rs.[(20 + 12.5)% of x] = Rs. (32.5% of x)

= Rs. (32.5x/100)

Total expenditure on taxes and interest on loans is

= Rs. [(10 + 17.5)% of x] = Rs. (27.5% of x)

= Rs. (27.5x/100)

So, required ratio = (32.5x/100) / (27.5x/100)

= 13:11

6.3 Find the difference between the expenditures on transport and taxes, If the expenditure on advertisement is Rs.2.10 crores.

a. 1.25 crores
b. 95 lakhs
c. 65 lakhs
d. 35 lakhs

Solution: (d)

Explanation

Let the total expenditure be Rs.x crores

Then, 15% of x = 2.10

x = ((2.10 × 100) / 15)

= 14

So, total expenditure = Rs.14 crores

Hence, the difference between the expenditures on transport and taxes = Rs. [(12.5 – 10)% of 14] crores

= Rs. (2.5% of 14) crores

= Rs. 0.35 crores

= Rs.35 lakhs

That’s end of exercise on Bar graph problems and solutions. Let me know in comment section if you find anything wrong in this article.

Getting Started

Section A (Terms & Definition)

Section B (Examples)

Example 1

Example 2

Example 3

Section C (Exercises)

2.1 The production of fertilizers more than the average production of the given years in how many years?

2.2 Which of the following pairs of years was exactly equal to the average production of the years 1996 and 1997?

2.3 What was the percentage decrease in the production of fertilizers from 1997 to 1998?

2.4 As compared to the previous year, in which year was the percentage increase in production the maximum?

2.5 How much was the percentage increase in production of fertilizers in 2002 compared to 1995?

3.1. The sales of which product has increased by nearly 55% from 1995 to 2000 in the case of:

3.2. What is the minimum rate of increase in sales during the period 1995-2000?

3.3. By what percent was the sales of lipsticks in 2000 was more than the sales of nail enamels in 2000?(rounded off to the nearest integer)

3.4. By what percent was the sales of conditioners in 1995 was less than the sales of shampoos in 1995? (rounded off to the nearest integer)

3.5. What is the ratio of the sales of nail enamels in 2000 to the sales of Talcum powders in 1995?

4.1. What are total number of cars of models P, Q and T manufactured in 2000?

4.2. For which model the percentage rise/fall in production from 2000 to 2001 was minimum?

4.3 What was the difference in the number of Q type cars produced in 2000 and that produced in 2001?

4.4 What is the number of P type cars produced in 2001 if the percentage production of P type cars in 2001 was the same as that in 2000?

4.5 If 85% of the S type cars produced in each year were sold by the company, how many S type cars remained unsold?

5.1 Total sales of branches B1,B3,B5 together for both years (in thousand numbers) is:

5.2 What percentage of total sales of branch B6 for both the years is the total sales of branch B3 for both the years?

5.3 What is the average sale of all branches (in thousand numbers) for the year 2000?

5.4 Find the ratio of the total sales of branch B2 for both years to the total sales of branch B4 for both years?

5.5 What percentage of the average sales of branches B1, B2 and B3 in 2001 is the average sales of branches B1, B3 and B6 in 2000?

6.1 The expenditures on the interest on loans is by what percent more than the expenditures on transport?

6.2 Find the ratio of the total expenditure on infrastructure and transport to the total expenditure on taxes and interest on loans?

6.3 Find the difference between the expenditures on transport and taxes, If the expenditure on advertisement is Rs.2.10 crores.

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