Question

A basket has 30 items, find the number of items that two persons A and B get if the items are divided in the ratio of $2:3$.
A) 14 and 16
B) 12 and 18
C) 9 and 21
D) None of the above

Answer 1

Hint: Try to imagine the exact scenario in your head and expand that ratio ‘$2$ is to $3$’ of $30$ into a meaningful sentence. Figure out the way to distribute according to that ratio by visualizing.

Complete step by step answer:
Let us first look into the question and try to reframe it differently.
The total number of items is $30$. And you have to divide these $30$ items between two-person A and B in such a way that the items they get are in ratio $2:3$.
For the ease of calculation, we try to convert this ratio into fractions
We know that if $M:N \equiv x:y$ then $M$ and $N$ will divide the whole in fractions $\dfrac{x}{{x + y}}$ and $\dfrac{y}{{x + y}}$ respectively.
Similarly, for our case $A$ and $B$ will divide the whole, i.e. the total number of items present in the bag into fractions of $\dfrac{2}{{2 + 3}}$ and $\dfrac{3}{{2 + 3}}$ .
Therefore you can conclude,
The person $A$ will get $\dfrac{2}{5}$ of the total number of items
The person$B$will get $\dfrac{3}{5}$ of the total number of items
This implies that:
Number of items for person $A$ $ = \dfrac{2}{5} \times 30 = 2 \times 6 = 12$
Number of items for person $B$ $ = \dfrac{3}{5} \times 30 = 3 \times 6 = 18$

$\therefore$ Number of items A, B will get is 12, 18 respectively. So, Option B is correct.

Note:
The above problem can also be alternatively understood as that the ratio $2:3$ divides the whole into $2 + 3 = 5$ equal parts. And from those 5 equal parts, the person $A$ will get 2 parts and the person $B$ will get 3 parts. So, 5 equal parts mean $\dfrac{{30}}{5} = 6$ items in each part. Therefore, the person $A$ will get $2 \times 6 = 12$ items and the person$B$will get $3 \times 6 = 18$ items.