Hello Friends, Today we are sharing some important Line Graphs - Data Interpretation Questions with Answers, helpful for SBI and IBPS PO and Clerk exams. These Line Graphs - Data Interpretation Questions are very important for SBI po exam and IBPS PO & other upcoming bank exam. in IBPS PO, SBI PO, SSC, CAT, XAT, NMAT, MAT& other exams 2015.
Line graphs:
A line graph is a way of visually representing related data where individual items of data are plotted and joined by a line. They are useful for presenting data over time to compare changes to a variable over set period. Joining up the points gives an instant picture of past trends (increases or decreases) and can be used to extrapolate those trends to make predictions for future.
- The variable represented is continuous.
- A graph is set within 2 axes: x and y.
The axes will not always start measuring from zero. If they don’t this is called the suppression of zero. This will affect the appearance of the line(s) on the graph making them steeper than they would be if the scale started at zero and occupied the same space as the scale would be smaller.
Questions of Line Graphs - Data Interpretation
Ques 1-5: Two different finance companies declare fixed annual rate of interest on the amounts invested with them by investors. The rate of interest offered by these companies may differ from year to year depending on the variation in the economy of the country and the banks rate of interest. The annual rate of interest offered by the two Companies P and Q over the years is shown by the line graph provided below.
Annual Rate of Interest Offered by Two Finance Companies Over the Years.
1. A sum of Rs. 4.75 lakhs was invested in Company Q in 1999 for one year. How much more interest would have been earned if the sum was invested in Company P?
A. Rs 19,000
B. Rs.14, 250
C. Rs.11, 750
D. Rs. 9,500
2. If two different amounts in the ratio 8:9 are invested in Companies P and Q respectively in 2002, then the amounts received after one year as interests from Companies P and Q are respectively in the ratio?
A. 2:3
B. 3:4
C. 6:7
D. 4:3
3. In 2000, a part of Rs. 30 lakhs was invested in Company P and the rest was invested in Company Q for one year. The total interest received was Rs. 2.43 lakhs. What was the amount invested in Company P?
A. Rs.9 lakh
B. Rs.11 lakh
C. Rs.12 lakh
D.Rs.18 lakh
4. An investor invested a sum of Rs. 12 lakhs in Company P in 1998. The total amount received after one year was re-invested in the same Company for one more year. The total appreciation received by the investor on his investment was?
A. Rs. 2, 96,200
B. Rs. 2, 42,200
C. Rs. 2, 25,600
D. Rs. 2, 16,000
5. An investor invested Rs. 5 lakhs in Company Q in 1996. After one year, the entire amount along with the interest was transferred as investment to Company P in 1997 for one year. What amount will be received from Company P, by the investor?
A. Rs. 5, 94,550
B. Rs. 5, 80,425
C. Rs. 5, 77,800
D. Rs. 5, 77,500
Ques : 6-10 : The following line graph gives the annual percent profit earned by a Company during the period 1995 - 2000.
Percent Profit Earned by a Company over the Years.
6. If the expenditures in 1996 and 1999 are equal, then the approximate ratio of the income in 1996 and 1999 respectively is?
A.1:1
B. 2:3
C.13:14
D. 9:10
7. If the income in 1998 was Rs. 264 crores, what was the expenditure in 1998?
A. Rs. 104 crores
B. Rs. 145 crores
C. Rs. 160 crores
D. Rs. 185 crores
8. In which year is the expenditure minimum?
A. 2000
B. 1997
C. 1996
D. Cannot be determined
9. If the profit in 1999 was Rs. 4 crores, what was the profit in 2000?
A. Rs. 4.2 crores
B. Rs. 6.2 crores
C. Rs. 6.8 crores
D. Cannot be determined
10. What is the average profit earned for the given years?
A. 50 2/3
B. 55 5/6
C. 60 1/6
D. 33 5/3
Ques 11-15: Study the following line graph and answer the questions.
Exports from Three Companies over the Years (in Rs. crore)
11. For which of the following pairs of years the total exports from the three Companies together are equal?
A. 1995 and 1998
B. 1996 and 1998
C. 1997 and 1998
D. 1995 and 1996
12. Average annual exports during the given period for Company Y is approximately what percent of the average annual exports for Company Z?
A. 87.12 %
B. 89.64 %
C.91.21 %
D. 93.33 %
13. In which year was the difference between the exports from Companies X and Y the minimum?
A. 1994
B. 1995
C. 1996
D. 1997
14. What was the difference between the average exports of the three Companies in 1993 and the average exports in 1998?
A. Rs. 15.33 crores
B. Rs. 18.67 crores
C. Rs. 20 crores
D. Rs. 22.17 crores
15. In how many of the given years, were the exports from Company Z more than the average annual exports over the given years?
A. 2
B. 3
C. 4
D. 5
Ques 16-20 : The following line graph gives the ratio of the amounts of imports by a company to the amount of exports from that company over the period from 1995 to 2001.
Ratio of Value of Imports to Exports by a Company over the Years.
16. If the imports in 1998 were Rs. 250 crores and the total exports in the years 1998 and 1999 together was Rs. 500 crores, then the imports in 1999 was?
A. Rs. 250 crores
B. Rs. 300 crores
C. Rs. 357 crores
D. Rs. 420 crores
17. The imports were minimum proportionate to the exports of the company in the year ?
A. 1995
B. 1996
C. 1997
D. 2000
18. What was the percentage increase in imports from 1997 to 1998?
A. 72
B. 56
C. 28
D. Data inadequate
19. If the imports of the company in 1996 was Rs. 272 crores, the exports from the company in 1996 was?
A. Rs. 370 crores
B. Rs. 320 crores
C. Rs. 280 crores
D. Rs. 275 crores
20. In how many of the given years were the exports more than the imports?
A. 1
B. 2
C. 3
D. 4
Ques 21-25: Study the following line graph and answer the questions based on it.
Number of Vehicles Manufactured by Two companies over the Years (Number in Thousands)
21. What is the difference between the number of vehicles manufactured by Company Y in 2000 and 2001?
A. 50, 000
B. 42, 000
C. 33, 000
D. 21, 000
22. What is the difference between the total productions of the two Companies in the given years ?
A. 19, 000
B. 22, 000
C. 26, 000
D. 28, 000
23. What is the average numbers of vehicles manufactured by Company X over the given period? (Rounded off to nearest integer)
A. 1,19,333
B. 1,13,666
C. 1,12,778
D. 1,11,223
24. In which of the following years, the difference between the productions of Companies X and Y was the maximum among the given years?
A. 1997
B. 1998
C. 1999
D. 2000
25. The production of Company Y in 2000 was approximately what percent of the production of Company X in the same year?
A. 173
B. 164
C. 132
D. 97
Answers
Ans 1. (D)
Difference = Rs. [(10% of 4.75) - (8% of 4.75)]
= Rs. (2% of 4.75) lakhs
= Rs. 0.095 lakhs
= Rs. 9500
Ans 2 : (D)
Let the amounts invested in 2002 in Companies P and Q be Rs 8x and Rs 9x respectively.
Then, interest received after one year from Company P = Rs (6% of 8x) or Rs 48x/100
Interest received after one year from Company Q = Rs. (4% of 9x)
or Rs 36x/100
Required ratio = (48x/100) / (36x/100) = 4/3 or 4:3
Let Rs. x lakhs be invested in Company P in 2000, the amount invested in Company Q in
2000 = Rs. (30 - x) lakhs.
Total interest received from the two Companies after 1 year
= Rs. [(7.5% of x) + {9% of (30 - x)}] lakhs
= Rs. {2.7 -(1.5x/100)}lakhs.
2.7 - 1.5x/100 = 2.43
x = 18.
Ans 4 : (C)
Amount received from Company P after one year (i.e., in 1999) on investing Rs. 12 lakhs in it = Rs. [12 + (8% of 12)] lakhs
= Rs. 12.96 lakhs.
Appreciation received on investment during the period of two years
= Rs. (14.256 - 12) lakhs
= Rs. 2.256 lakhs = Rs. 2, 25,600.
Ans 5 : (B)
Amount received from Company Q after one year on investment of Rs. 5 lakhs in the year 1996 = Rs. [5 + (6.5% of 5)] lakhs
= Rs. 5.325 lakhs.
Amount received from Company P after one year on investment of Rs. 5.325 lakhs in the year 1997 = Rs. [5.325 + (9% of 5.325)] lakhs = Rs. 5.80425 lakhs
Ans 6 : (D)
Let the expenditure in 1996 = x.
Also, let the incomes in 1996 and 1999 be I1 and I2 respectively.
Then, for the year 1996, we have:
55 = ( I1 – x)/(x)*100
I1= 155x/100 --- (1)
70 = ( I2 – x )/(x) * 100
I2 = 170x/100 ----- (2)
From (i) and (ii), we get:
I1 /I2 = 155/170 = 0.91/1 or 9/10
Ans 7 : (C)
Let the expenditure is 1998 be Rs. x crores.
Then, [65 =( 264 –x)/ x] * 100
x = 160
Expenditure in 1998 = Rs. 160 crores
Ans 8 : (D)
The line-graph gives the comparison of percent profit for different years.
But the comparison of the expenditures is not possible without more data.
Therefore, the year with minimum expenditure cannot be determined
Ans 9 : (D)
From the line-graph we obtain information about the percentage profit only. To find the profit in 2000 we must have the data for the income or expenditure in 2000.
Therefore the profit for 2000 cannot be determined.
Ans 10 : (B)
Average percent profit earned for the given years
= (1/6) x [40 + 55 + 45 + 65 + 70 + 60] = 55 5/6
Ans 11 : (D)
Total exports of the three Companies X, Y and Z together, during various years are:
In 1993 = Rs. (30 + 80 + 60) crores = Rs. 170 crores.
In 1994 = Rs. (60 + 40 + 90) crores = Rs. 190 crores.
In 1995 = Rs. (40 + 60 + 120) crores = Rs. 220 crores.
In 1996 = Rs. (70 + 60 + 90) crores = Rs. 220 crores.
In 1997 = Rs. (100 + 80 + 60) crores = Rs. 240 crores.
In 1998 = Rs. (50 + 100 + 80) crores = Rs. 230 crores.
In 1999 = Rs. (120 + 140 + 100) crores = Rs. 360 crores.
Clearly, the total exports of the three Companies X, Y and Z together are same during the years 1995 and 1996
Ans 12 : (D)
Analysis of the graph: From the graph it is clear that
The amount of exports of Company X (in crore Rs.) in the years 1993, 1994, 1995, 1996, 1997, 1998 and 1999 are 30, 60, 40, 70, 100, 50 and 120 respectively.
The amount of exports of Company Y (in crore Rs.) in the years 1993, 1994, 1995, 1996, 1997, 1998 and 1999 are 80, 40, 60, 60, 80, 100 and 140 respectively.
The amount of exports of Company Z (in crore Rs.) in the years 1993, 1994, 1995, 1996, 1997, 1998 and 1999 are 60, 90,, 120, 90, 60, 80 and 100 respectively.
Average annual exports (in Rs. crore) of Company Y during the given period.
= 1/7 x (80 + 40 + 60 + 60 + 80 + 100 + 140) = 560/7 = 80
Average annual exports (in Rs. crore) of Company Z during the given period
= 1/7 x (60 + 90 + 120 + 90 + 60 + 80 + 100) = 600/7
Required percentage = [80/(600/7) x 100]% = 93.33%
Ans 13 : (C)
The difference between the exports from the Companies X and Y during the various years are:
In 1993 = Rs. (80 - 30) crores = Rs. 50 crores.
In 1994 = Rs. (60 - 40) crores = Rs. 20 crores.
In 1995 = Rs. (60 - 40) crores = Rs. 20 crores.
In 1996 = Rs. (70 - 60) crores = Rs. 10 crores.
In 1997 = Rs. (100 - 80) crores = Rs. 20 crores.
In 1998 = Rs. (100 - 50) crores = Rs. 50 crores.
In 1999 = Rs. (140 - 120) crores = Rs. 20 crores.
Clearly, the difference is minimum in the year 1996.
Ans 14 : (C)
Ans 15 : (C)
Average annual exports of Company Z during the given period
= 1/7 x (60 + 90 + 120 + 90 + 60 + 80 + 100) = 600/7
= Rs. 85.71 crores.
From the analysis of graph the exports of Company Z are more than the average annual exports of Company Z (i.e., Rs. 85.71 crores) during the years 1994, 1995, 1996 and 1999, i.e., during 4 of the given years.
Ans 16 : (D)
The ratio of imports to exports for the years 1998 and 1999 are 1.25 and 1.40 respectively.
Let the exports in the year 1998 = Rs. x crores.
Then, the exports in the year 1999 = Rs. (500 - x) crores.
1.25 = 250/x
x = 250/1.25 = 200 [ Using ratio for 1998 ]
Thus, the exports in the year 1999 = Rs. (500 - 200) crores = Rs. 300 crores.
Let the imports in the year 1999 = Rs. y crores.
Then, 40 = y/300
y = (300 * 1.40) = 420
Imports in the year 1999 = Rs. 420 crores.
Ans 17 : (C)
The imports are minimum proportionate to the exports implies that the ratio of the value of imports to exports has the minimum value.
Now, this ratio has a minimum value 0.35 in 1997, i.e., the imports are minimum proportionate to the exports in 1997.
Ans 18 : (D)
The graph gives only the ratio of imports to exports for different years. To find the percentage increase in imports from 1997 to 1998, we require more details such as the value of imports or exports during these years.
Hence, the data is inadequate to answer this question.
Ans 19 : (B)
Ratio of imports to exports in the year 1996 = 0.85.Let the exports in 1996 = Rs. x crores.
Then , 272/x = 0.85
x = 272/0.85 = 320
Exports in 1996 = Rs. 320 crores.
Ans 20 : (D)
The exports are more than the imports imply that the ratio of value of imports to exports is less than 1.Now, this ratio is less than 1 in years 1995, 1996, 1997 and 2000.
Thus, there are four such years.
Ans 21 : (D)
Required difference = (128000 - 107000) = 21000.
Ans 22 : (C)
From the line-graph it is clear that the productions of Company X in the years 1997, 1998, 1999, 2000, 2001 and 2002 are 119000, 99000, 141000, 78000, 120000 and 159000 and those of Company Y are 139000, 120000,100000, 128000, 107000 and 148000 respectively.Total production of Company X from 1997 to 2002
= 119000 + 99000 + 141000 + 78000 + 120000 + 159000
= 716000.
and total production of Company Y from 1997 to 2002
= 139000 + 120000 + 100000 + 128000 + 107000 + 148000
= 742000.
Difference = (742000 - 716000) = 26000.
Ans 23 : (A)
Average number of vehicles manufactured by Company X
= 119333.
Ans 24 : (D)
The difference between the productions of Companies X and Y in various years are:
For 1997 (139000 - 119000) = 20000.
For 1998 (120000 - 99000) = 21000.
For 1999 (141000 - 100000) = 41000.
For 2000 (128000 - 78000) = 50000.
For 2001 (120000 - 107000) = 13000.
For 2002 (159000 - 148000) = 11000.
Clearly, maximum difference was in 2000.
Ans 25 : (B)
Explanation - Required percentage= 128/78 * 100 = 164% = 164%