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: Let the number of flowers and bees be x and y, respectively. It is given that if one bee lands on each flower, one bee will be left, so we can deduce that the number of bees is one more than the number of flowers, and this can be mathematically represented as y-x=1 . Similarly use the other statement given to get another relation between x and y. Finally solve the equations to get the answer to the above question.

Complete step-by-step answer:
Let us start the solution to the above question by letting the number of flowers and bees be x and y, respectively.
Now, it is given that if one bee lands on each flower, one bee will be left, so we can deduce that the number of bees is one more than the number of flowers, i.e. x is one more than y. So, if we represent this in form of equation, we get
$y-x=1......(i)$
Also, it is given that if two bees land on each flower, one flower will be left, which means that the number of flowers is 1 more than half the number of bees. This can be mathematically represented in terms of x and y as:
 $x-\dfrac{y}{2}=1......(ii)$
Now we will add equation (i) and equation (ii). On doing so, we get
$y-x+x-\dfrac{y}{2}=1+1$
Cancelling x in the LHS and adding the other terms, we get
$y-\dfrac{y}{2}=2$
Now we will take LCM of LHS to be 2. On doing so, we get
$\dfrac{2y-y}{2}=2$
$\Rightarrow \dfrac{y}{2}=2$
Now we will multiply both the sides of the equation by 2.
$y=2\times 2$
$\Rightarrow y=4$
Now we will substitute the value of y in equation (i). On doing so, we get
$\begin{align}
  & 4-x=1 \\
 & \Rightarrow x=3 \\
\end{align}$
Hence, the answer to the above question is option (a).

Note: If you want you can solve the above question by option elimination as well. First thing to note is that the number of bees is even, as it is given that when each flower has two bees on it, one flower is left free. So, using this two options are eliminated. Now use the options left one by one and check which satisfy the given condition to get the correct answer out of the two left out options.