Have You Figured It Out? understanding graphs and relationships


by R. Sreenivasan (Co-founder CL); Article appeared in The Hindustan Times   www.sreeni.org

In the last edition you had a look at certain methods and techniques to be efficient in Data Interpretation (DI).  In this edition you will discover some more tools and techniques which if made part of your armory could make all the difference to cracking the banking exams conducted by IBPS, SBI or RBI.

The two principles which you came across were –

Principle No. 1.   Understand the graph thoroughly

You should understand the relationships between various entities in the given pictorial representation. Unless you are sure of the representation, you should not proceed to answer the questions.

Principle No. 2.   Build your speed

Data interpretation is nothing but reciprocals, multiplications and computation of percentages; inculcate the habit of calculating mentally; hence master tables upto 30 X 30, reciprocals upto 30; use approximations;

Let us now discuss some of the questions on typical graphical representations that we had raised in the last edition.

 Graph 1 – Pie Charts


Two wheeler industry prices and costs
Two wheeler industry prices and costs


Fig. 1


The price of a two-wheeler is Rs. 20,000.



Before we proceed we should understand the relationship between these two pi-charts. The second pi-chart explodes the sector ‘transmission’ of the first pi-chart. If you haven’t figured that out, you would not have been able solve any of the questions.


  1. What is the profit % ?

Looking at the first pi-chart, we can say that the profit is 10% of the selling price and cost price is 90% of the selling price. Hence profit % will be percentage equivalent of 10/90 or 1/9; which is 11.11.

  1. If the price of the tyres goes up by 25%, by what amount should be the sale price be increased to maintain the amount of profit margin ?

Tyres constitute 15% of transmission and transmission constitutes 20% of the selling price. Hence transmission is .15 X .20 or .03% of  selling price, 20,000. Hence Rs 600. If the price of the tyre goes up by 25% on Rs 600, it would amount to Rs. 150. Hence the seller should increase the price of the two-wheeler by 150 so as to retain the same margin of 2000.

  1. If the price of the tyres goes up to 25% of transmission cost, by what amount should be the sale price be increased to maintain the amount of margin ?

Here we have to pay attention to the phrase ‘up to 25% of transmission cost’. To start with the cost of the tyre is 15% of the transmission cost and therefore the rest of the transmission components constitute 85% of the cost. In value terms tyres cost Rs 600 and the rest of the components together cost Rs 3400, since total transmission is 20% of the price of the two-wheeler, Rs 20000. As the price of the tyre increases naturally the transmission cost increases. The price increase will be such that at some point of time, the cost of the tyre will reach 25% of the total transmission cost.  It means the other components which constituted 85% earlier will now constitute 75% of the transmission cost. Therefore Rs 3400 is 75% of transmission cost and total transmission cost will be one-third more or 4/3 * 3400 or Rs 4533. Hence the increase of Rs 533 should be the amount by which the price of the two-wheeler should go up by so as to retain the same margin of Rs. 2000.



Indexing - understanding the basics
Indexing – understanding the basics



Fig. 2.


Selling price and Cost price of a product have been indexed at 100 for 1990.


Before answering questions let us understand indexing. If you have been reading newspapers regularly you will know what is ‘wholesale price index’. Its base year is 1980-81, indexed at 100. Whatever be the value of the commodities, the value is depicted as 100. In 1998, it is hovering at 352. What does this mean ? In these seventeen years, the prices have gone up by 252%.


Let us consider another example. Mitu Berry is a designer. One of her creations is priced at 40,000 while it would have costed her only 1000. I can index these two to 100 each in 1990. Look at the graph now. Selling price in ’91 is 130. It means the price has gone up by 30% over ’90. Similarly in 1995, 55%.  Cost price in ’93 is 50% more over that of ’90. By now you should realise that the line graphs here are not absolute values but relative to whatever value existed in ’90. Therefore you can comment on the profits in terms of exact numbers only when you know how far apart are these two figures – selling price and cost price to begin with in 1990. For instance in ’93, the graph is showing cost price more than the selling price. You cannot say that loss has been incurred, because these figures are indexed on ’90. In this example on hand, selling price 40000 and cost price 1000, you can clearly see that the cost price even if goes up by 2000% it will reach only 21000 and in order to incur loss the selling price has to fall by 50% and reach 20000.


Now let us go and answer the questions on the given graph –




  1. If % profit in 1990 was 20%, what was the % profit in 1995 ?
  2. Which year had the maximum change in the profit ?
  3. In which year did the company make a loss ?
  4. Which year had the maximum change in cost price ?




  1. If CP in ’90 is 100, SP is 120. In ’95 CP is 140, a growth of 40% over ’90 and SP is 120 * 1.55 = 1.86 a growth of 55% over ’90. Profit is 46 over 140 or 46/140 * 100 = 32.14%.

( calculate 120 * 1.55 mentally – 120 * 1 + 120 * .5 + 120 * .05 = 120 + 60 + 6 = 186 )

  1. By observation you can see that in ‘93-’94, the cost price is decreasing and selling price is increasing, hence the profit would have changed the maximum between these two years, irrespective of the values in the base year ’90.
  2. Can you answer this question ? No, You cannot answer this question until you know the values in the base year ’90.
  3. Obviously ‘90-91,  20%.


Graph 3 – Percentages

Percentage Change in the bottom-line of  five companies


1992-93 1993-94
A 10 -10
B -20 9
C 5 12
D -7 -15
E 17 -8

Fig. 3.

Here only percentage changes have been provided, therefore you will not be able to calculate or comment on the actual values until you know the values in ‘91-92.


Questions –


  1. Which company had the highest sales in 1993 ?
  2. If sales of company A in 1992 is 1,00,000 then what was its sale in 1994 ?
  3. Which company had the maximum decrease in sales from 1992 to 1994 ?
  4. Which company had the maximum % decrease in sales from 1992 to 1994 ?


Answers –


  1. You cannot answer until you know the value in the base year. Cannot be determined
  2. You can answer, since the base value is given. 99,000.
  3. You can comment on percentage decrease, but not in value terms. Cannot be determined.
  4. Obviously D, since both years negative growth recorded.


Tips for faster calculations –

  • Always look at the choices before answering the questions.
  • Try and eliminate at least two choices which is possible, always
  • Wherever possible make approximations. More so when the choices are not close
  • Finally whatever calculations you do, do it fast. Make use of your knowledge of reciprocals, tables, squares, cubes….. etc. which you must have mastered by now.
eg. Find out 64.41% of 12275 ?  How to calculate mentally and faster –
64.41% is close to 66.67% or 2/3rd  of 12275. Therefore calculate 2/3 of  (12000 + 275); which is 8000 + 180. But what we need is 2.2% less than 2/3rd.  1% of 12275 is 123, therefore 2% is 246 and .2% is 25.  Now subtract the sum 246 + 25 = 271 from 8180.        8190 – 300 + 29 = 7909.

If you have observed this calculation carefully, you can do any calculation faster. Any given decimal value could be approximated to the nearest decimal value which can be easily calculated. Say 1.79%, is nothing but 1% + .75% or ¾ + .01% * 4.


Unless you consciously keep practising and innovating, finding ways and means to do faster calculations, you will not improve. Many of you must have already been taking tests you have subscribed to from various coaching institutes. You have to analyse each test subjecting each question to close scrutiny in terms of the techniques we have discussed above. Only by doing so you will become faster.


Happy figuring. See you next week with some DI and test taking techniques.





  1. Dear Sir
    I am CL student , I am giving regular PO Speed test , I am Getting Average marks in QT 35 and Reasoning 32 .
    My week area is Logical reasoning (Statement and assumption / Statement and Argument / Course of Action ) where I am doing 10 questions but hardly correct 2 only and got 8 wrong .
    I read your DI and other article which is really very helpful .
    Is there any way to improve my Logical reasoning part? I am searching blog or article related to LR but not getting any valuable.
    Looking forward your consideration.

    • Dear Ajay,

      The key to doing well in any of the exam is not only taking the practice tests seriously, but also analyzing every test thoroughly. Kindly sit with every question that you encounter and figure out how to solve it better.

      – conceptual clarity is important; Keep visiting the fundamental booklets, revise them time and again
      – If you have conceptual clarity, then you will not depend on the formulae; most of the times you do not need any formula to solve the questions
      – The questions and choices are designed in such a way that you can eliminate choices if you have clarity of the concepts
      – In review kindly focus on solving every problem without putting pencil on paper.
      – Coming to reasoning, look at the logical flow – ask why? is there an assumption, is it a fact…
      – The more you read, the more you will understand the structure of sentences, the arguments, suppositions based.. etc.
      – Whatever you learn, kindly write on flash cards and keep it handy for revision
      – Keep analyzing, reviewing and in the process improving..

      Best wishes.