Question

An enterprising businessman earns an income of Re. $1$ 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. One the 10th day of business, his income is

• A. Rs. $2^9$
• B. Rs. $2^{10}$
• C. Rs. $10$
• D. Rs. ${10}^2$

Answer 1

Answer: (A)

Rs. $2^9$

Income on the first day $=$ Re. $1$.
Income on the 2nd day $=$ Rs. $(1\times 2)=$ Rs. $2^1$.
Income on the 3rd day $=$ Rs. $(2^1\times 2)=$ Rs.$2^2$ and so on. Thus, Income on the $r$th day $=$ Rs. $2^{n-1}$.
Therefore Income on the 10th day $=$ Rs. $2^9$.