Question

Divide $1400$ into three parts such that the 1st part is $\dfrac{2}{3}$ of the 2nd part and the ratio between the 2nd and 3rd part is $4:5$. Find the value of each part.

Answer 1

Hint: We have to find the value of each part and for that we will let the 3 parts as x, y and z respectively. Then we will convert them into a common term which will be put in an equation to get the answer of one part, then similarly, we will find the other two parts.

Complete step by step answer:
Let the 1st part = x
Let the 2nd part = y
Let the 3rd part = z
According to the question,
Given: $x = \dfrac{2}{3}y$
$\dfrac{y}{z} = \dfrac{4}{5}$
$x + y + z = 1400$-------(1)
Now we will convert x and z in terms of y,
$x = \dfrac{2}{3}y$--------(2)
$\dfrac{y}{z} = \dfrac{4}{5}$
$5y = 4z$
$z = \dfrac{5}{4}y$---------(3)
Now we will put value of x from (2) and z from (3) in equation (1)
$x + y + z = 1400$
$\dfrac{2}{3}y + y + \dfrac{5}{4}y = 1400$
$\dfrac{{8y + 12y + 15y}}{{12}} = 1400$
$\dfrac{{35y}}{{12}} = 1400$
$y = 480$
Now we will put value of y in equation (2)
$x = \dfrac{2}{3}y$
$x = \dfrac{2}{3} \times 480$
$x = 320$
Now we will put value of y in equation (3)
$z = \dfrac{5}{4}y$
$z = \dfrac{5}{4} \times 480$
$z = 600$
Therefore, the value of $x$ is $320$, $y$ is $480$ and $z$ is $600$.

Note:
In these types of questions it is necessary to let what we have to find (like in this question we leave the parts as x, y and z) this makes the approach to answer the question very easy. In this question we have found the answers and there is a way to check whether our answer is correct or not, we can do that by putting all the values we have found in the equation we made from the question and with LHS matches with RHS our answer is absolutely correct.