Shopkeeper solds goods worth rupees 3 million during 2008 if he is able to increase a sale by 15% annually and which year he would achieve annual sale of rupees 25 million
To find out in which year the shopkeeper would achieve an annual sale of 25 million rupees, we can start by calculating the growth rate per year. The shopkeeper is increasing the sale by 15% annually.
1. Calculate the growth rate per year:
Annual Growth Rate = 15% = 0.15 (expressed as a decimal)
2. Calculate the total growth factor:
Total Growth Factor = 1 + Annual Growth Rate
= 1 + 0.15
= 1.15
3. Calculate the number of years required to achieve a sale of 25 million rupees:
Target Sale / Initial Sale = Total Growth Factor ^ Number of Years
Rearranging the formula:
Number of Years = log(Target Sale / Initial Sale) / log(Total Growth Factor)
Substituting the values:
Number of Years = log(25,000,000 / 3,000,000) / log(1.15)
Using a logarithmic calculator, we can solve for the number of years:
Number of Years ≈ log(8.33) / log(1.15) ≈ 5.12
Rounded up, it would take approximately 6 years for the shopkeeper to achieve an annual sale of 25 million rupees. Therefore, the shopkeeper would achieve this goal in the year 2014 (2008 + 6 years).
Let's break down the problem step by step:
1) Calculate the annual increase in sales:
15% of 3 million = 0.15 * 3,000,000 = 450,000
2) Determine how many years it would take to reach a sales target of 25 million:
25,000,000 - 3,000,000 = 22,000,000 (the difference between the desired sales and the initial sales)
22,000,000 / 450,000 = 48.89 (the number of years needed to achieve the desired sales)
Since we cannot have a fraction of a year, we round up to the nearest whole number. Therefore, it would take 49 years to reach an annual sales of 25 million.
Thus, the shopkeeper would achieve an annual sale of rupees 25 million in the year 2008 + 49 = <<2008+49=2057>>2057.