Q. Study the following line graph which gives the percentage profit earned by the three companies A, B and C during the period from 2011 to 2016 and answer the questions given below:
Ans:
Percenatage-profit in different years by company A,B and C:
| Years | Company A | Company B | Company C |
| 2011 | 15 | 30 | 40 |
| 2012 | 30 | 10 | 20 |
| 2013 | 20 | 40 | 30 |
| 2014 | 40 | 60 | 70 |
| 2015 | 70 | 60 | 40 |
| 2016 | 45 | 30 | 60 |
(a) The income of company B in 2012 was ₹ 60 lakhs, which increased by 30% in the year 2013. Find the expenditure of company B in the year 2013.
Ans:
Income of company B in 2013 = 60 + 30% of 60 = 60+18 = 78 lakhs
Percentage profit of company B in 2013 = 40%
Let, expenditure in 2013 = x rs.
x + 40 % of x = 78 lakhs
140x/100 = 78
Therefore, x = 100*78/ 140 = 55.71 lakhs
(b) If the expenditures of companies A, B and C in the year 2016 were equal and their total income in that year was ₹ 870 lakhs, find the profit of each company in that year.
Ans:
Let, the expenditure of each company in 2016 = x rs.
The income of company A in 2016 = x + 45% of x = 145x/100
The income of company B in 2016 = x + 30% of x = 130x/100
The income of company C in 2016 = x + 60% of x = 160x/100
Given,
145x/100 + 130x/100 + 160x/100 = 870 lakhs
- 435x = 870*100
- x = 870*100/435 = 200 lakhs
Therefore,
Profit of company A in 2016 = 200*45/100 = 90 lakhs
Profit of company B in 2016 = 200*30/100 = 60 lakhs
Profit of company C in 2016 = 200*60/100 = 120 lakhs
(c) If the companies A, B and C had an expenditure of ₹ 200 lakhs, ₹ 300 lakhs and ₹ 400 lakhs respectively in the year 2014, find the ratio of their profits in 2014.
Ans:
Profit of A in 2014 = 200*40/100 = 80 lakhs
Profit of B in 2014 = 300*60/100 = 180 lakhs
Profit of C in 2014 = 400*70/100 = 280 lakhs
The ratio of profit of A, B and C = 80:180:280 = > 4:9:14 ans.
(d) If the incomes of companies A, B and C in the year 2015 were equal and their total expenditure in that year was ₹ 1,835 lakhs, find the profit of each company in that year.
Ans:
Let, the income of each companies in 2015 = x rs.
Expenditure of company A in 2015 = x*100/170 = 10x/17
Expenditure of company A in 2015 = x*100/160 = 10x/16
Expenditure of company A in 2015 = x*100/140 = 10x/14
From question,
- 10x/17 + 10x/16 + 10x/14 = 1835 lakhs
- 7340x/3808 = 1835 lakhs
- x = 952 lakhs
Therefore in 2015,
The profit of A = 952*100/ 170 = 392 lakhs
The profit of B = 952*100/160 = 357 lakhs
The profit of C = 952*100/140 = 272 lakhs
