Question

A fifth part of a swarm of bees came to rest on a flower of Kadamba, a third on the flower of silinda. Three times the difference between these two numbers flew over the flower of kutaja, and one bee alone remained in the air, attracted by a perfume of jasmine in boom. Tell me, if you can, how many bees were in the swarm.

Answer 1

Hint: In this problem, make equations on the given information in the terms of variables and then by using the mathematical operations solve the equations to find the number of bees in the swarm.
Complete solution:
Word problems are mathematical exercises to represent the unknowns in the mathematical expression. It develops our skill and power of thinking.
Let the total number of bees in the swarm be $p$.
Given,
The number of swarms of bees that came to rest on the flower of the kadamba is $\dfrac{p}{5}$.
The number of swarms of bees that came to rest on the flower of silinda is $\dfrac{p}{3}$.
The number of bees flown over the flower of kutaja is $3\left( {\dfrac{p}{5} - \dfrac{p}{3}} \right)$.
The number of bees attracted by a perfume jasmine and remaining alone in the air is $1$.
The total number of bees is equal to the sum of all bees, so it is written as,
$ \Rightarrow p = \dfrac{p}{5} + \dfrac{p}{3} + 3\left( {\dfrac{p}{5} - \dfrac{p}{3}} \right) + 1$…….. (1)
Take L.C.M of $5$ and $3$, and solve the parenthesis in equation (1).
The L.C.M of $5$and $3$ is $15$ Hence, on solving equation (1) it can be written as,
$ \Rightarrow 3p + 5p + 15p - 9p + 15 = 15p$
Combining like terms,
$ \Rightarrow 3p + 5p + 15p - 9p - 15p = - 15$
After simplification, we get
$ \Rightarrow - p = - 15$
Now we get,
$\therefore p = 15$

Hence, the number of bees in the swarm was $15$.

Note: In this question, as we know that to solve the equation, we need to conduct operations such as addition and subtraction on the like terms. Like terms are those which have the same variables and those that are constants. These types of questions are always based on choosing any variable to represent the unknowns and carefully read the given problem and translate the unknowns in mathematical expression.