Quantitative Techniques: Questions and Explanations on Bar Graph
Question 1: The bar graph represents the tax collection by the Indian government over a period of 7 years(in Rs. Trillion). Solve the following questions according to the given data.
Which year exhibited the second-highest growth percentage in tax collection over the given period?
2001 (b) 2003 (c) 2004 (d) 2007
The approximate ratio of tax collected in 2003 by average tax collection is
11/8 (b) 8/9 (c) 11/3 (d) 9/11
In which two consecutive years the tax collected growth percentage wrt the previous year is more than 25%?
2002&2003 (b)2005&2006 (c) 2003&2004 (d) 2006&2007
Question 2: In the given bar graph Total sales and Total cost of 5 companies for 2015 are given (in lakhs). Answer the following questions based on the data.
2.1 Which company earned the maximum profit(percentage) in the year 2010?
B (b) C (c) D (d) E
If the cost incurred by company C is decreased by 15% and Sales increased by 5% then what will be the profit per cent of company C?
12% (b) 18% (c) 15% (d) 22%
Which two Companies together incur the loss equivalent in numeric terms to the profit percentage of Company B?
A & D (b) A & E (c) C & D (d) A &C
Question 3: A deviated bar graph is representing the data for the year 2010 trade deficit/surplus of different countries. Read carefully to answer the questions following the graph.
3.1 Net trade deficit/surplus of all countries is (approx.) equal to:
(a) 10500 (b)123050 (c)5684400 (d) 47300
3.2 The country whose trade deficit is nearly equal to the average of all trade deficit countries is:
(a) Argentina (b) Turkey (c)Norway (d) Egypt
3.3 The ratio between the difference of highest and lowest surplus country to the difference of highest and lowest deficit countries:
(a) 7/2 (b)2/7 (c) 3/2 (d) 2/3
3.4 Sum of middle 4 countries trade surplus/deficit is(approx.) equal to trade deficit/surplus of which country?
(a) Ethiopia (b) Romania (c) Switzerland (d) South Africa
Answers And Solutions:
Ans: (b) 2003
Solution: As in the graph all the data labels are given you only have to calculate the percentage increase for consecutive years and mark the answer where you get the second-highest percentage increase.
Tax collected ( Rs. In trillion)
I the given table you can see after 130 % the second-highest growth in percentage is seen in 2003 hence (b) will be your answer.
Ans: (b) 8/9
Solution: the average you can find by directly applying the formula i.e.
avg = SUM/ No. of observations = 6.12
Now, you need to find the ratio of 2003 tax collection and avg tax collection i.e. = 5.4/6.12
Further solving the ratio = 54/61 = (by adding 2 in both numerator and denominator)= 56/63
= 8/9 (option (b))
Ans: (c) 2003 & 2004
Solution: If you look at the table you can clearly see the consecutive years growth percentage in 2003 and 2004 is above 25%, hence option(c) is your answer.
TIP: In such questions, you can do approximate calculation instead of tedious decimal calculation and as you have pen paper-based exam write the percentages alongside bars so that all the questions become handy.
2.1 Ans: (d) E
Solution: As the question talks about profit and if you read all the questions, all of them are based on that only we have to use the concept of profit/loss in this whole set.
Here you have been given total sales and the total cost incurred by the companies hence as we usually find profit/loss by finding the difference between Selling Price and Cost price or Expenditure and Revenue, here also we will find the difference between total sales and the total cost to find profit and loss.
For the percentage related questions, we will use toral cost as a base to calculate the percentage.
Here the values have to be estimated as the bars do not have labels hence be careful with that. You can make a table or side at the side of the bars only. You can refer to the table for exact calculations.
Total cost incurred(approx.)
Hence as you can see E has earned the highest profit hence option (d) will be your answer.
2.2 Ans: (b) 18%
Solution: Decrease in the total cost of Company C by 15% = 42*(1-15/100)
= 42*0.85 = 35.7
Increase in the total sales of company C by 5% = 40*(1+5/100)
= 40*1.05 = 42
Profit = Total sales – Total Cost incurred
= 42 – 35.7 = 6.30
Profit Percentage = 6.30 / 35.7 = 17.65% (18% approx.)
Ans: (d) A &C
Solution: This question can be marked with the help of your previous calculation of the first part. Company B profit % = 30%, 22+ 4 is approx. equal to 26% hence answer is A & C
Loss is only incurred by A & C and question clearly says loss equivalent to a profit of B hence directly mark (d) as your answer.
3.1 Ans: (b)123050
Solution: As the question asks the net trade deficit/surplus, we will simply add all the values of trade deficit/surplus to get the net value.
But, the values of the bars are not given so you have to estimate the values first and then add them and mark the approximate value. Also, the values below x-axis are always negative so take them negative while doing the calculations.
Estimate trade deficit/surplus value
As the values are estimated, we will be using the approximate value to mark the answer and closest value to 125500 is 123050
3.2 Ans: (a) Argentina
Solution: Now this can be a tricky question hence read it carefully: trade deficit country to be compared with the average of all trade deficit values.
So first, we will find out the average of all trade deficit countries i.e. UK, Turkey, Argentina, Egypt, South Africa, Romania, Ethiopia
Avg = -(105000+49000+30100+15000+8000+7000+6000) / 7 = -31442
Now the comparison has to be done: Closest value to 31442 is 30100 hence answer will be Argentina.
3.3 Ans: (c) 3/2
Solution: Before finding the ratio we need to find the difference in highest and lowest values of trade surplus as well as the deficit.
Difference between highest and lowest trade surplus value = 168000-15000 = 153000
Difference between highest and lowest trade deficit value = 105000-6000 = 99000
Ratio = 153000/99000 = 153/99 ≈ 150/100 = 3/2
Here be carefull while doing the approximation as in adding and subtracting value from numerator denominator together can cause error.
3.4Ans: (a) Ethiopia
Solution: We need the sum of the middle 4 country trade deficit/surplus values of the chart which are: South Africa; Romania; Ethiopia & UAE
Sum = -8000+(-7000)+(-6000)+15000 = -6000
Now, the question asked is which country’s Trade deficit/surplus is equivalent to the above sum; hence the value of Ethiopia is the desired value.
Shortcut: If you would have observed the value then in the bar itself it is visible that -8000 and -7000 would make be equal to -15000 that cancels 15000 of UAE; therefore, Ethiopia would be the right answer because it is the only left value.