Question

Class - 8 th
When a certain sum of money is divided equally among 25 people each receives ₹ 42 ; how much would each person receive if the same sum had been equally divided among 30 people ?
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Answer 1

$\large\underline{\sf{Solution-}}$

Given that, a certain sum of money is divided equally among 25 people, each receives ₹ 42.

Now, we have to find how much would each person receive, if the same sum had been equally divided among 30 people.

As more peoples are there, so share of each is less.

It means, number of person and money distribution in each are in inverse variation.

So, Let assume that each person receive ₹ x, if the same sum had been equally divided among 30 people.

So,

$\begin{array}{|c|c|c|c} \hline \rm Number \: of \: persons&\rm 25&\rm 30 \\ \hline\rm Amount \: received \: &\rm 42&\rm x \\ \hline \end{array}$

Now, using Law of inverse Variation, we have

$\rm \: 25 \times 42 = 30 \times x$

$\rm \: x = \dfrac{25 \times 42}{30}$

$\rm \: \rm\implies \:x = 35$

So, each person receive ₹ 35, if the same sum had been equally divided among 30 people.

$\rule{190pt}{2pt}$

Basic Concept Used :-

Inverse Variation :- Two quantities x and y are said to be in inverse variation if x increases then y decreases or if x decreases then y increases. If x varies inversely with y that xy = k where k is constant of proportionality.

Answer 2

Answer:

Amount of received by each person = 35

Step-by-step explanation:

Given:-

Number of people = 25

Amount of money received by each person = ₹42

To Find:-

How much would each person receive if the same sum had been equally divided among 30 people?

Solution:-

Total amount of money =Amount of money received x Number of people

                                       = 42 x 25

                                       = ₹1050

Before the number of people = 25 but now the number of people = 30

Number of people increased = 30 - 25 = 5

Money received by each person = 1050/30

                                                       = 105/3

                                                       = 35

$\boxed{\therefore\bold{Amount\:of\:received \:by\:each\:person = 35}}$