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 given below shows the earnings of two persons on five different days.
What is the ratio of total earnings of P to the total earnings of Q?Earnings Days P Q Monday 105 150 Tuesday 96 110 Wednesday 65 122 Thursday 115 106 Friday 130 68 The table below shows the number of toys of 6 different colours sold from a shop during a given period. The table also shows the percentage of toys of each colour which are cars.
Colour Total toys Percentage of cars C1 500 12 C2 600 15 C3 400 12.5 C4 550 10 C5 650 20 C6 450 10 What is the total number of car toys of C2 and C3 taken together?
Study the given graph carefully and answer the question that follows. The graph shows the demand and production of different companies.
The ratio between the companies having more production than demand and more demand than production is:
Study the given table and answer the question that follows. The given table shows the number of new employees added to different categories of employees in a company for four years and the number of employees from these categories who left the company every year.
During the period between 2001 and 2004, the total number of Technicians who left the Company is what percentage (rounded off to the nearest integer) of the total number of Technicians who joined the Company?
The given pie-chart shows the percentage distribution of 20,000 employees in a company. Study the given chart and answer the question that follows. If 30% of the employees in department D are females, then how many male employees are there in that department?
