Question

There are some lotus flowers in a pond and some bees are hovering around. If one bee lands on each flower, one bee will be left; if two bees land on each flower, one flower will be left; then the number of flowers and bees respectively are
A. 3, 4
B. 4, 3
C. 2, 3
D. 3, 2

Answer 1

Hint: We will find the equation for the number of bees in two different conditions. We will first assume the number of flowers as x. Then we will take the first case, where one bee lands on one flower as, then the number of bees will be $\left( x+1 \right)$. We will take the second case where two bees land on one flower as, then the number of bees will be $\left( x-1 \right)\times 2=2x-2$. We will then equate these equations, $\left( x+1 \right)=\left( 2x-2 \right)$ to get the value of x and then we will find the required answer.

Complete step-by-step answer:
It is given in the question that there are some lotus flowers in a pond and some bees are hovering around. If one bee lands on each flower, one bee will be left; if two bees land on each flower, one flower will be left and we have to find the number of flowers and bees respectively. Let us assume the number of flowers as x. Now, let us take the first case, where one bee lands on each flower and one bee is left. So, we can represent the number of bees as,
$\begin{align}
  & =\left( \text{number of lotus flowers} \right)\times 1+1 \\
 & =\left( x \right)\left( 1 \right)+1 \\
 & =\left( x+1 \right)\ldots \ldots \ldots \left( i \right) \\
\end{align}$
Similarly, in the second case, where two bees land on one flower and one flower is left. So, we can represent the number of bees as,
$\begin{align}
  & =\left( \text{number of lotus fowers}-1 \right)\times 2 \\
 & =\left( x-1 \right)\left( 2 \right) \\
 & =\left( 2x-2 \right)\ldots \ldots \ldots \left( ii \right) \\
\end{align}$
Now, we know that the number of bees must be constant in both the cases, so it means that $\left( x+1 \right)$ must be equal to $\left( 2x-2 \right)$. So, we will equate these and get,
$\left( x+1 \right)=\left( 2x-2 \right)$
On transposing x from LHS or left hand side to the right hand side or the RHS, we get,
$\begin{align}
  & 1=2x-x-2 \\
 & \Rightarrow 1=x-2 \\
\end{align}$
We will now transpose -2 from RHS to LHS. So, we will get,
$\begin{align}
  & 1+2=x \\
 & \Rightarrow 3=x \\
 & \Rightarrow x=3 \\
\end{align}$
Hence, the number of lotus flowers is 3. The number of bees will be $\left( x+1 \right)=3+1=4$.
Therefore, the correct answer is option A, (3, 4).

Note: It is observed that most of the students make a mistake while forming the second equation. They may form the equation, when two bees land on one flower as $\left( x+1 \right)\left( 2 \right)$, but the condition in the question states that in that case, one flower will be left, so it should be $\left( x-1 \right)\left( 2 \right)$. Similarly, the number of bees can be calculated from any of the two equations formed for the number of the bees, $\left( x+1 \right)$ or $\left( 2x-2 \right)$. The answer will be the same, that is 4.