Question

Lali wants to buy an equal number of oranges and apples. The oranges are packed in packets of $6$ and the apples are packed in packets of $10$. What is the least number of apples she can buy? How many packets of each fruit should she buy?

Answer 1

Hint: Let the total number of orange packets be $x$ and total number of apple packets be $y$. You can also find the $LCM\left( {6,10} \right)$ to find the least numbers of apples she can buy.

Complete step-by-step answer:
Given, Lali wants to buy an equal number of oranges and apples.
 The oranges are packed in packets of $6$ and the apples are packed in packets of $10$.
(1)Now, let us find how many packets of each fruit she should buy.
Let the total number of orange packets be $x$ and total number of apple packets be $y$.
According to given information, the number of oranges and apples are equal.
$\therefore 6 \times x = 10 \times y$
$ \Rightarrow 3x = 5y$
Here, $3x$ is a multiple of $3$ and $5y$ is a multiple of $5$.
We know that the least number which is common in the multiple of $3$ and $5$ is $15$.
So, $3x = 15$ and $5y = 15$$ \Rightarrow x = 5$ and $y = 3$
So, lali has to buy $5$ packets of oranges and $3$ packets of apples.
(2)Now, let us find the least number of apples she can buy.
From the above part, we know that she has to buy at least $3$ packets of apples.
So, \[the{\text{ }}least{\text{ }}number{\text{ }}of{\text{ }}apples = No.{\text{ }}of{\text{ }}packets{\text{ }}of{\text{ }}apples \times No.{\text{ }}of{\text{ }}apples{\text{ }}per{\text{ }}packet\]
$ = 3 \times 10$
$ = 30$ apples

Hence, lali has to buy $5$ packets of oranges and $3$ packets of apples with at least $30$ apples.

Note: An another short method to solve this question is described as below:
Number of oranges in each packet$ = 6$
Number of apples in each packet$ = 10$
To get the equal number of apples and oranges, we have to find $LCM\left( {6,10} \right)$.
$6 = 2 \times 3$
$10 = 2 \times 5$
$LCM\left( {6,10} \right) = 2 \times 3 \times 5 = 30$
Hence, lali should buy at least $30$ apples and $30$ oranges.
To find number of packets;
Number of packets of oranges$ = {{30}}{6} = 5$
Number of packets of apples$ = {{30}}{{10}} = 3$
Hence, lali has to buy $5$ packets of oranges and $3$ packets of apples with at least $30$ apples.