Study the table given below and answer the questions that follow :
The table below shows the cost price (in Rupees) and sale price (in Rupees) of four items for five years.
Year Item A Item B Item C Item D Cost Price Sale price Cost Price Sale Price Cost price Sale Price Cost Price Sale Price 2015 200000 230000 100000 110000 25000 28750 25000 28750 2016 140000 161000 150000 165000 27500 31625 27500 31900 2017 210000 241500 160000 176000 40000 44000 30000 35100 2018 185000 212750 190000 209000 33300 38295 40000 47200 2019 170000 195500 199500 221445 34000 39100 34000 40460
Understanding Profit and Profit Percentage Calculation
This question asks us to identify which item experiences a profit percentage that increases by exactly 1% each year. To find this, we need to calculate the profit and then the profit percentage for each item across the given years.
The fundamental formulas are:
- Profit Calculation: $\text{Profit} = \text{Sale Price (SP)} - \text{Cost Price (CP)}$
- Profit Percentage Calculation: $\text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100$
Analyzing Yearly Item Cost and Sale Prices
The provided table shows the Cost Price (CP) and Sale Price (SP) for four different items (A, B, C, and D) over a period of five years, from 2015 to 2019.
| Year | Item A | Item B | Item C | Item D | ||||
|---|---|---|---|---|---|---|---|---|
| Cost Price | Sale Price | Cost Price | Sale Price | Cost price | Sale Price | Cost Price | Sale Price | |
| 2015 | 200000 | 230000 | 100000 | 110000 | 25000 | 28750 | 25000 | 28750 |
| 2016 | 140000 | 161000 | 150000 | 165000 | 27500 | 31625 | 27500 | 31900 |
| 2017 | 210000 | 241500 | 160000 | 176000 | 40000 | 44000 | 30000 | 35100 |
| 2018 | 185000 | 212750 | 190000 | 209000 | 33300 | 38295 | 40000 | 47200 |
| 2019 | 170000 | 195500 | 199500 | 221445 | 34000 | 39100 | 34000 | 40460 |
Step-by-Step Profit Percentage Calculation for Each Item
Item A: Profit Percentage Analysis
Calculating profit percentage for Item A:
- 2015: Profit = 230000 - 200000 = 30000. Profit % = (30000 / 200000) * 100 = 15%
- 2016: Profit = 161000 - 140000 = 21000. Profit % = (21000 / 140000) * 100 = 15%
- 2017: Profit = 241500 - 210000 = 31500. Profit % = (31500 / 210000) * 100 = 15%
- 2018: Profit = 212750 - 185000 = 27750. Profit % = (27750 / 185000) * 100 = 15%
- 2019: Profit = 195500 - 170000 = 25500. Profit % = (25500 / 170000) * 100 = 15%
Item A's profit percentage is constant at 15%. It does not increase by 1% each year.
Item B: Profit Percentage Analysis
Calculating profit percentage for Item B:
- 2015: Profit = 110000 - 100000 = 10000. Profit % = (10000 / 100000) * 100 = 10%
- 2016: Profit = 165000 - 150000 = 15000. Profit % = (15000 / 150000) * 100 = 10%
- 2017: Profit = 176000 - 160000 = 16000. Profit % = (16000 / 160000) * 100 = 10%
- 2018: Profit = 209000 - 190000 = 19000. Profit % = (19000 / 190000) * 100 = 10%
- 2019: Profit = 221445 - 199500 = 21945. Profit % = (21945 / 199500) * 100 = 11%
Item B's profit percentage is mostly 10% but is not consistently increasing by 1% annually.
Item C: Profit Percentage Analysis
Calculating profit percentage for Item C:
- 2015: Profit = 28750 - 25000 = 3750. Profit % = (3750 / 25000) * 100 = 15%
- 2016: Profit = 31625 - 27500 = 4125. Profit % = (4125 / 27500) * 100 = 15%
- 2017: Profit = 44000 - 40000 = 4000. Profit % = (4000 / 40000) * 100 = 10%
Item C's profit percentage changes from 15% to 10% in 2017, so it does not meet the criteria.
Item D: Profit Percentage Analysis
Calculating profit percentage for Item D:
- 2015: Profit = 28750 - 25000 = 3750. Profit % = (3750 / 25000) * 100 = 15%
- 2016: Profit = 31900 - 27500 = 4400. Profit % = (4400 / 27500) * 100 = 16%
- 2017: Profit = 35100 - 30000 = 5100. Profit % = (5100 / 30000) * 100 = 17%
- 2018: Profit = 47200 - 40000 = 7200. Profit % = (7200 / 40000) * 100 = 18%
- 2019: Profit = 40460 - 34000 = 6460. Profit % = (6460 / 34000) * 100 = 19%
The profit percentages for Item D are 15%, 16%, 17%, 18%, and 19%. This sequence clearly shows a consistent increase of exactly 1% every year.
Final Conclusion
By analyzing the profit percentages calculated for each item year over year, we find that Item D is the only item whose profit percentage increases by one percent annually.
Important Questions from Data Interpretation
The table shows the monthly expenditure of Saumya. What percent of her monthly salary is she able to save?
Expense Amount Food 5,000 Rent 20,000 Travel 10,000 Clothing 3,000 Miscellaneous 15,000 Savings 7,500 What does the height of the rectangle in a histogram show?
Following table provides figures (in rupees) on annual expenditure of a firm for two years – 2010 and 2011.
Category
2010
2011
Raw material
5200
6240
Power & fuel
7000
9450
Salary & wages
9000
12600
Plant & machinery
20000
25000
Advertising
15000
19500
Research & Development
22000
26400
In 2011, which of the following two categories have registered increase by same percentage?
Read the following table giving sales data of five types of batteries for years 2006 to 2012
Year
Type I
Type II
Type III
Type IV
Type V
2006
75
144
114
102
108
2007
90
126
102
84
126
2008
96
114
75
105
135
2009
105
90
150
90
75
2010
90
75
135
75
90
2011
105
60
165
45
120
2012
115
85
160
100
145
Out of the following which type of battery achieved highest growth between the years 2006 and 2012?Each of the letters arranged as below represents a unique integer from 1 to 9. The letters are positioned in the figure such that (A × B × C), (B × G × E) and (D × E × F) are equal. Which integer among the following choices cannot be represented by the letters A, B, C, D, E, F and G?
A
D
B
G
E
C
F
