Question

An enterprising businessman earns an income of Rs 1 on the first day of his business. On every subsequent day, he earns an income which is just double of that made on the previous day. On the 10^th day of business, his income is

• A. Rs 2⁹
• B. Rs 2¹⁰
• C. Rs 10²
• D. Rs 10

Answer 1

The Correct Option is A

The problem involves understanding an exponential growth where the income doubles each day starting from an initial amount on the first day. Given that the businessman earns Rs 1 on the first day, his income for each subsequent day is double that of the previous day. We need to calculate his income on the 10^th day.

Let's denote the income on the nth day by I_n. The sequence of incomes is as follows:

• First day: I₁ = Rs 1
• Second day: I₂ = 2 × I₁ = Rs 2
• Third day: I₃ = 2 × I₂ = Rs 4
• Fourth day: I₄ = 2 × I₃ = Rs 8

Following this pattern, the income on the nth day can be expressed as:

I_n = 2^(n-1)

For the 10^th day, we set n = 10:

I₁₀ = 2^(10-1) = 2⁹

Calculating 2⁹:

2⁹ = 512

Hence, the income on the 10^th day is Rs 512.

By converting 512 back to exponential form, it corresponds to the option Rs 2⁹.