Question

A sum of Rs. $1,60,000$ is divided in the ratio of $3:5.$ what is the smaller share?

Answer 1

Hint: Here we will assume one reference value for the given ratio and its common factor and will frame the mathematical expression to get the value of the common term and accordingly will find the smaller share. Apply the concepts of multiplication and division.

Complete step by step answer:
Given that a sum of Rs. $1,60,000$ is divided in the ratio of $3:5.$
Let us assume that the common factor in the given ratio is “x”.
The smaller part of the number will be $3x$. …. (A)
The larger part of the number will be $5x$ ….. (B)
Now frame the given ratio in the form of the mathematical expression –
$3x + 5x = 160000$
Simplify the above expression finding the sum of the terms on the left hand side of the equation,
$8x = 160000$

Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
$ \Rightarrow x = \dfrac{{160000}}{8}$
Find the factors of the terms for the numerator on the left hand side of the equation.
$ \Rightarrow x = \dfrac{{8 \times 20000}}{8}$
Common multiples from the numerator and the denominator cancels each other.
$ \Rightarrow x = 20000$
Now, by using the equation (A)
The smaller part of the number will be $ = 3x$.
Place the value of “x” in the above expression –
The smaller part of the number will be $ = 3(20000)$
The smaller part of the number will be $ = 60000$Rs.
This is the required solution.

Hence, the smallest part of the share is 60000 Rs.

Note: Ratio is the term expressed for comparing two physical quantities and it is unitless. Ratio can be calculated using any multiple and then getting its equivalent value. Be good in multiples and remember that the common factors from the numerator and the denominator cancels each other.