Data Interpretation QA || Bar Graphs || Aptitude

Bar Graph-Based Questions and Solutions

Directions (1-5):

The following bar graph represents the Income and Expenditure (in million US $) of five companies in the year 2001. The percentage profit or loss of a company is calculated using the formula:

\text{Percentage Profit/Loss} = \left( \frac{\text{Income} - \text{Expenditure}}{\text{Expenditure}} \right) \times 100

Question 1:

What was the combined percentage of profit or loss for companies M and N?

Options:
A) 12% Loss
B) 10% Loss
C) 10% Profit
D) No Profit, No Loss
E) None of these

Answer:

✅ D) No Profit, No Loss

Explanation:

Total Income of M and N = 35 + 50 = 85 million US $
Total Expenditure of M and N = 45 + 40 = 85 million US $
Percentage Profit/Loss:

\left( \frac{85 - 85}{85} \right) \times 100 = 0\%

Since income and expenditure are equal, there was neither profit nor loss for companies M and N together.

Question 2:

What was the approximate overall profit/loss percentage for all five companies combined in 2001?

Options:
A) 5% Profit
B) 6.5% Profit
C) 4% Loss
D) 7% Loss
E) None of these

Answer:

✅ A) 5% Profit

Explanation:

Total Income of all five companies = 35 + 50 + 40 + 40 + 50 = 215 million US $
Total Expenditure of all five companies = 45 + 40 + 45 + 30 + 45 = 205 million US $
Percentage Profit:

\left( \frac{215 - 205}{205} \right) \times 100 = 4.88\% \approx 5\%

Thus, all five companies together had an approximate 5% profit in 2001.

Question 3:

Which company earned the highest percentage profit in 2001?

Options:
A) M
B) N
C) P
D) Q
E) None of these

Answer:

✅ D) Q

Explanation:

The profit/loss percentages for each company are calculated as follows:

Company M:

\left( \frac{35 - 45}{45} \right) \times 100 = -22.22\% \quad \text{(Loss)}

Company N:

\left( \frac{50 - 40}{40} \right) \times 100 = 25\% \quad \text{(Profit)}

Company P:

\left( \frac{40 - 45}{45} \right) \times 100 = -11.11\% \quad \text{(Loss)}

Company Q:

\left( \frac{40 - 30}{30} \right) \times 100 = 33.33\% \quad \text{(Profit)}

Company R:

\left( \frac{50 - 45}{45} \right) \times 100 = 11.11\% \quad \text{(Profit)}

Since Company Q had the highest percentage profit of 33.33%, it was the most profitable company in 2001.

Question 4:
For Company R, if its expenditure in 2001 increased by 20% compared to the year 2000 and the company earned a 10% profit in 2000, what was its income in 2000 (in million US dollars)?

Options:
A) 35.75
B) 37.25
C) 38.5
D) 41.25
E) None of these

Answer: D) 41.25

Explanation:

Let the expenditure of Company R in 2000 be x million US $.

Since the expenditure increased by 20% in 2001, we can express it as:

$\text{Expenditure in 2001} = \left( \frac{120}{100} \times x \right)$

According to the given data, the expenditure in 2001 is 45 million US $:

$\frac{120}{100} \times x = 45$

Solving for x:

$x = 37.5$

Thus, the expenditure of Company R in 2000 was 37.5 million US $.

Now, let the income of Company R in 2000 be I million US $.

Since the company made a 10% profit in 2000, we apply the profit formula:

$10 = \left( \frac{I - 37.5}{37.5} \right) \times 100$ $I - 37.5 = 3.75$ $I = 41.25$

Thus, the income of Company R in 2000 was 41.25 million US $.

Question 5:

For Company Q, if its income in 2001 was 10% higher than its income in 2000 and the company earned a 20% profit in 2000, what was its expenditure in 2000 (in million US dollars)?

Options:
A) 28.28
B) 30.3
C) 32.32
D) 34.34
E) None of these

Answer: B) 30.3

Explanation:

Let the income of Company Q in 2000 be x million US $.

Since the income in 2001 was 10% more than in 2000, we write:

$\text{Income in 2001} = \left( \frac{110}{100} \times x \right)$

From the given data, the income in 2001 was 40 million US $:

$\frac{110}{100} \times x = 40$

Solving for x:

$x = \frac{400}{11}$

Thus, the income of Company Q in 2000 was $\frac{400}{11}$ million US $.

Let the expenditure of Company Q in 2000 be E million US $.

Since the company earned a 20% profit in 2000, we use the profit formula:

$20 = \left( \frac{\left( \frac{400}{11} \right) - E}{E} \right) \times 100$ $20 = \left( \frac{ \frac{400}{11} - E }{E} \right) \times 100$

Solving for E:

$E = \frac{400}{11} \times \frac{100}{120}$ $E = 30.3$

Thus, the expenditure of Company Q in 2000 was 30.3 million US $.

Directions (6-10):

The bar graph below presents the sales of books (in thousand numbers) from six branches of a publishing company during the years 2000 and 2001.

Sales of Books (in thousand numbers) from Six Branches - B1, B2, B3, B4, B5, and B6 in 2000 and 2001

Question 6:

What is 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
E) None of these

Answer: 7:9

Explanation:
The required ratio = (Sales of B2 in 2000 + Sales of B2 in 2001) / (Sales of B4 in 2000 + Sales of B4 in 2001)
= (75 + 65) / (85 + 95)
= 140 / 180
= 7:9

Question 7:

The total sales of branch B6 for both years is what percentage of the total sales of branch B3 for both years?

A) 68.54%
B) 71.11%
C) 73.17%
D) 75.55%
E) None of these

Answer: 73.17%

Explanation:
Required percentage = [(Sales of B6 in 2000 + Sales of B6 in 2001) / (Sales of B3 in 2000 + Sales of B3 in 2001)] × 100
= [(70 + 80) / (95 + 110)] × 100
= (150 / 205) × 100
= 73.17%

Question 8:

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) 77.5%
C) 82.5%
D) 87.5%
E) None of these

Answer: 87.5%

Explanation:
Average sales of B1, B3, and B6 in 2000 = (80 + 95 + 70) / 3 = 245 / 3
Average sales of B1, B2, and B3 in 2001 = (105 + 65 + 110) / 3 = 280 / 3

Required percentage = [(245 / 280) × 100]
= 87.5%

Question 9:

What are the average sales of all branches (in thousand numbers) for the year 2000?

A) 73
B) 80
C) 83
D) 88
E) None of these

Answer: 80

Explanation:
Average sales of all six branches in 2000 = (80 + 75 + 95 + 85 + 75 + 70) / 6
= 80

Question 10:

What are the total sales of branches B1, B3, and B5 together for both years (in thousand numbers)?

A) 250
B) 310
C) 435
D) 560
E) None of these

Answer: 560

Explanation:
Total sales of B1, B3, and B5 for both years =
(Sales of B1 in 2000 + Sales of B1 in 2001) + (Sales of B3 in 2000 + Sales of B3 in 2001) + (Sales of B5 in 2000 + Sales of B5 in 2001)
= (80 + 105) + (95 + 110) + (75 + 95)
= 560

Directions (11-15):

Study the bar graph carefully and answer the following questions. The given bar graph represents the marked prices of five different products available in a showroom.

Question 11:

If the marked price of a laptop is 20% higher than its cost price and the shopkeeper provides a 15% discount on the marked price, what is the profit percentage on the laptop?

Options:
(A) 1%
(B) 5%
(C) 3%
(D) 2%
(E) 4%

Correct Answer: (D) 2%

Explanation:

Marked Price (MP) = Rs. 15,000
Cost Price (CP) = $15000 \times \frac{100}{120} = Rs. 12,500$
Selling Price (SP) after a 15% discount = $15000 \times \frac{85}{100} = Rs. 12,750$
Profit % = $\frac{(12750 - 12500)}{12500} \times 100 = 2\%$

Question 12:

If the cost price to marked price ratio of a mobile is 3:4 and the shopkeeper earns a profit of Rs. 1200, what is the discount amount offered?

Options:
(A) Rs. 800
(B) Rs. 1000
(C) Rs. 900
(D) Rs. 600
(E) None of these

Correct Answer: (A) Rs. 800

Explanation:

CP of mobile = $\frac{3}{4} \times 8000 = Rs. 6000$
SP = CP + Profit = $6000 + 1200 = Rs. 7200$
Discount = MP - SP = $8000 - 7200 = Rs. 800$

Question 13:

Find the average of the marked prices of a table and a chair.

Options:
(A) Rs. 8000
(B) Rs. 8500
(C) Rs. 9000
(D) Rs. 7500
(E) None of these

Correct Answer: (B) Rs. 8500

Explanation:

Marked price of the table = Rs. 10,000
Marked price of the chair = Rs. 7,000
Average = $\frac{(10000 + 7000)}{2} = Rs. 8500$

Question 14:

The selling price of a watch and a chair is in a 4:5 ratio. If the cost price of the watch is Rs. 4800 and the shopkeeper earns a profit of 10% on the marked price, what is the discount offered on the chair?

Options:
(A) Rs. 100
(B) Rs. 150
(C) Rs. 200
(D) Rs. 250
(E) Rs. 300

Correct Answer: (D) Rs. 250

Explanation:

CP of the watch = Rs. 4800
Profit on watch = $6000 \times \frac{10}{100} = Rs. 600$
SP of the watch = $4800 + 600 = Rs. 5400$
SP of the chair = $5400 \times \frac{5}{4} = Rs. 6750$
Discount = MP - SP = $7000 - 6750 = Rs. 250$

Question 15:

The selling price to marked price ratio of a table is 4:5. If the shopkeeper earns a 25% profit, what is the cost price of the table?

Options:
(A) Rs. 6000
(B) Rs. 6200
(C) Rs. 6400
(D) Rs. 6500
(E) None of these

Correct Answer: (C) Rs. 6400

Explanation:

SP of the table = $\frac{4}{5} \times 10000 = Rs. 8000$
CP = $8000 \times \frac{100}{125} = Rs. 6400$

Directions (16-20):

Study the following information carefully and answer the question given below.

The bar graph represents the total number of 50 and 20-rupee note bundles printed in Mysore over four different days: Monday, Tuesday, Wednesday, and Thursday.

Note: Each 50 and 20-rupee bundle consists of 100 notes.

Question 16:

On Friday, the total number of 50-rupee note bundles printed was 50% more than those printed on Thursday, while the total number of 20-rupee note bundles was 25% more than those printed on Thursday. Find the ratio of 50-rupee bundles to 20-rupee bundles printed on Friday.

Options:
(A) 5:4
(B) 1:3
(C) 7:2
(D) 8:5
(E) None of these

Correct Answer: (B) 1:3

Explanation:

Total number of 50-rupee bundles printed on Friday:
- 50% more than Thursday’s 50-rupee bundles:
- $150\%$ of 10 (assumed) = 15
Total number of 20-rupee bundles printed on Friday:
- 25% more than Thursday’s 20-rupee bundles:
- $125\%$ of 36 (assumed) = $36 \times \frac{5}{4} = 45$
Required Ratio:
- $15:45 = 1:3$

✅ Final Answer: 1:3

Question 17:

Find the difference between the total number of 50-rupee notes printed on Tuesday and Wednesday together and the total number of 20-rupee notes printed on Tuesday and Wednesday together.

Options:
(A) 500
(B) 700
(C) 400
(D) 900
(E) None of these

Correct Answer: (C) 400

Explanation:

Total number of 50-rupee notes printed on Tuesday and Wednesday:
- Tuesday: 20 bundles × 100 = 2000 notes
- Wednesday: 32 bundles × 100 = 3200 notes
- Total: 2000 + 3200 = 5200
Total number of 20-rupee notes printed on Tuesday and Wednesday:
- Tuesday: 30 bundles × 100 = 3000 notes
- Wednesday: 18 bundles × 100 = 1800 notes
- Total: 3000 + 1800 = 4800
Required Difference:
- $5200 - 4800 = 400$

✅ Final Answer: 400

Question 18:

The total number of 20-rupee note bundles printed on Tuesday and Thursday together is what percentage more than the total number of 50 and 20-rupee note bundles printed on Monday?

Options:
(A) 10%
(B) 25%
(C) 40%
(D) 32%
(E) None of these

Correct Answer: (A) 10%

Explanation:

Total number of 20-rupee bundles printed on Tuesday and Thursday:
- Tuesday: 30 bundles
- Thursday: 36 bundles
- Total: $30 + 36 = 66$
Total number of 50 and 20-rupee bundles printed on Monday:
- 50-rupee bundles: 40
- 20-rupee bundles: 20
- Total: $40 + 20 = 60$
Percentage increase:
- $\frac{(66 - 60)}{60} \times 100 = \frac{6}{60} \times 100 = 10\%$

✅ Final Answer: 10%

Question 19:

Find the sum of the average number of 50-rupee note bundles printed on Monday and Thursday and the average number of 20-rupee note bundles printed on Monday and Tuesday.

Options:
(A) 70
(B) 30
(C) 80
(D) 50
(E) None of these

Correct Answer: (D) 50

Explanation:

Total number of 50-rupee bundles printed on Monday and Thursday:
- Monday: 40 bundles
- Thursday: 10 bundles
- Total: $40 + 10 = 50$
- Average: $\frac{50}{2} = 25$
Total number of 20-rupee bundles printed on Monday and Tuesday:
- Monday: 20 bundles
- Tuesday: 30 bundles
- Total: $20 + 30 = 50$
- Average: $\frac{50}{2} = 25$
Required Sum:
- $25 + 25 = 50$

✅ Final Answer: 50

Question 20:

The total number of 50 and 20-rupee notes printed in Mysore on Tuesday is 25% more than that of Nasik. If the ratio of the total number of 50 and 20-rupee notes printed in Nasik is 1:3, then find the total number of 50-rupee notes printed in Nasik on Thursday.

Options:
(A) 3000
(B) 1000
(C) 2000
(D) 4000
(E) None of these

Correct Answer: (B) 1000

Explanation:

Total number of 50 and 20-rupee notes printed in Mysore on Tuesday:
- 50-rupee notes: $20 \times 100 = 2000$
- 20-rupee notes: $30 \times 100 = 3000$
- Total: $2000 + 3000 = 5000$
Total number of 50 and 20-rupee notes printed in Nasik on Thursday:
- Since Mysore printed 25% more than Nasik:
- Let Nasik’s total be $x$
- $5000 = x + \frac{25}{100}x = 1.25x$
- $x = \frac{5000}{1.25} = 4000$
Total number of 50-rupee notes in Nasik:
- Given the ratio of 50 to 20-rupee notes is 1:3,
- 50-rupee notes: $\frac{1}{4} \times 4000 = 1000$

✅ Final Answer: 1000