Study the following information carefully to answer these questions: A young girl Roopa leaves home with $x$ flowers and goes to the bank of a nearby river. On the bank of the river, there are four places of worship, standing in a row. She dips all the $x$ flowers into the river, the number of flowers doubles. Then, she enters the first place of worship and offers $y$ flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the second place of worship and offers $y$ flowers to the deity. She dips the remaining flowers into the river and again the number of flowers doubles. She goes to the third place of worship and offers $y$ flowers to the deity. She dips the remaining flowers into the river and again the number of flowers doubles. She goes to the fourth place of worship and offers $y$ flowers to the deity. Now she is left with no flowers in hand. The minimum number of flowers that could be offered to each deity is

### Concept & Logic This question relies on the algebraic relationship established from the sequence of doubling and subtracting. The key constraint is that the number of flowers $x$ (initial) and $y$ (offered) must be positive integers, as you cannot realistically leave home with fractional flowers or offer fractions of a flower in this logical context. By finding the simplest integer ratio between $x$ and $y$, we can determine the absolute minimum positive values for both variables. ### Step-by-Step Solution * **Given:** * We derived the relationship between $x$ (initial flowers) and $y$ (offered flowers) in the general setup: * After 4 iterations of (doubling then subtracting $y$), the final remaining amount is $16x - 15y = 0$. * **Calculation:** 1. Express the equation as a ratio: $$16x = 15y$$ $$\frac{x}{y} = \frac{15}{16}$$ 2. Because 15 and 16 are coprime (they share no common positive factors other than 1), the fraction $\frac{15}{16}$ is in its simplest form. 3. For $x$ and $y$ to be integers, $x$ must be a multiple of 15, and $y$ must be a multiple of 16. $$x = 15k$$ $$y = 16k$$ *(where $k$ is an integer greater than 0)* 4. To find the minimum possible number of flowers offered to each deity ($y$), we take the smallest positive integer value for $k$, which is 1. 5. Therefore, the minimum value for $y$ is $16(1) = 16$. ### Exam Strategy & Shortcut When you arrive at an equation like $16x = 15y$, swap the coefficients to find the minimum integer values. The minimum positive integer value for $x$ is always the coefficient of $y$ (which is 15), and the minimum positive integer value for $y$ is always the coefficient of $x$ (which is 16), provided the coefficients are coprime. ### Common Pitfall Choosing option (a) 0. While mathematically $x = 0$ and $y = 0$ perfectly satisfy $16x = 15y$, logical word problems describing physical scenarios ("leaves home with $x$ flowers", implying she actually brought something) inherently require non-zero positive integers. Zero is a trivial solution that invalidates the premise of the puzzle. ### Final Answer Therefore, the correct answer is 16.