Bar chartThe x – axis shows a variable and the y-axis a function of it. The variable could

be companies of different identities and the function could be the turnover of each, as below: -

Consider the following questions 2 to 5 based on the above data.

Q.1. What % of the average turnover of all the five Co’s, A to E, is that of C alone?(a) 40 (b) 72 (c) 86 (d) 90

Solution:

Average turnover = = 70(Rs.lakhs) Individual turnover of Co. C = 60 (Rs.lakhs) C is 60/70 of the average i.e. 6/7 6/7 = 85 5/7% (c)

Q.2: If the turnover of company C were to increase 10% every year, which of the following figures is closest to its turnover at the end of 3 years from the year shown in the chart?(a) Rs. 79.86 crore (b) 0.80 crore (c) Rs.80 lakhs (d) Rs.78 lakhs

Solution:Present turnover c 60 (Rs.lakhs)Add 10% 6Projected turnover at the end of one year from now 66Add 10% 6.6Projected turnover at the end of two year from now 72.6Add 10% 7.26Projected turnover at the end of 3 year from now 79.86. ………(c)

An alternative approach:

Turn-over in Rupees Hundred Lakhs in a certain year.

020406080100120

A B C D E

Names of Companies

As there is a rises in the turnover of 10% every year, we may say, every year’s turnover is 110% of the previous year’s, i.e. 1.1 times the previous year’s, and hence in 3 full year’s turnover will be (1.1) times the present year’s turnover.

(1.1) 3 = (1+0.1) 3 =1 + 3 x 0.1 + (by binomial expansion)= 1.3+ 0.03 + 0.001 = 1.331

Thus the 3 rd year’s turnover will be 1.331 times now = 1.331 x 60 (Rs. lakhs)= Rs.79.86 lakhs

Note: (1) The exact result above is closest to (c) as can seen by comparison

The true answer in Rs. lakhs Individual answers (Rs.)

79.864 79.86 cr. = 7, 986 lakhs0.80 cr. = 800 lakhs = 80 lakhs = 78 lakhs

(2) The answer (d) would be correct if the data has been “If the turnover of Co. C were to increase by an average of 10% every year …..”

The student must note that this is a case of simple rate of increase, when the same sum is added every year, whereas the actual problem expresses a compound rate of increase, where the rate of increase every year is the same. In other words the actual problem is one where geometric progression applies, with a mean ratio of 1.1 (corresponding to 10% increase) and the revised problem is one of arithmetic progression with a common difference of 0.1(of the present turnover every year) i.e.1.3 times in 3 years and works out to 1.3 x 60 =78

Q.3: If Co. E improves its turnover by 10% on an average every year and Co. B suffers a decrease at a 10% average every year, in how many years from now will C begin to be ahead of B in turnover?(a) 2 (b) 3 (c) 4 (d) 5

Solution: Present turnover of B = Rs.100 lakhs Present turnover of E = Rs.40 lakhs

Gap in turnoverBetween B & E = Rs. 60 lakhs

Annual average drop in B’sturnover = 10% of 100 = Rs. 10 lakhs

Annual average increase in E’s turnover = 10% of 40 = Rs. 4 lakhs

Thus the total or net effective change in the turnovers of B and E = 10 + 4 = Rs. 14 lakhs every year.

To bridge the gap of Rs. 60 lakhs between them it will take exactly years (d)

Note: 4 is arithmetically closer to 4 than to 5

It would, however, be incorrect to mark (C) as your response, because in 4 years, the turnover of E will not surpass that of B. Company turnover are taken only on a yearly basis. Hence, you have to mark only that year as your response, in which this would have happened; that is 5, and not 4.

Q.4: If in the year to which the bar chart relates, Co. A produced 20% fewer units of the same product X than Co. B and no other products were made by Co. B either, compare the units price of product X charged by company A had company B, in a ratio.(a) 1:1 (b) 10:11 (c) 11:12 (d) 6:5

Solution: unit price =

Shorter Approach:Form the chart it is seen A’s turnover = 80% of B’sBy the terms of this question, A’s sale = 80% of B’s Obviously A and B must be selling the product at the same price.