Question

Weight of one \[5Rs\] coin is \[9g\] . If a bag of \[5Rs\] coins weighs \[9Kg\] , then how many coins are present in the bag ?
A. \[100\]
B. \[500\]
C. \[10000\]
D. \[1000\]

Answer 1

Hint:We have to find the number of coins present in the bag of \[5Rs\] coins which weighs \[9Kg\] . We solve this question using the concept of fundamental solving the equations and we should also have the knowledge of the conversion of units from one unit to another . Using the data of weight of one coin , we can calculate the total number of coins in the bag of coins by dividing the weight of the bag by the weight of one coin . This will give us the total number of coins which are present in the bag of coins.

Complete step by step answer:
Given: \[Weight{\text{ }}of{\text{ }}one{\text{ }}5Rs{\text{ }}coin = 9g\]
We also know the conversion of units of weight in kilograms to grams is given as :
\[1Kg = 1000g\]
The relation we can also write it as :
\[1g = \dfrac{1}{{1000}}Kg\]
Using the relation we get the weight of one coin of 5 Rs as :
\[Weight{\text{ }}of{\text{ }}one{\text{ }}5Rs{\text{ }}coin = 9 \times \dfrac{1}{{1000}}Kg\]
Now , we also know that the weight of the bag is given as :
\[Weight{\text{ }}of{\text{ }}the{\text{ }}bag = 9Kg\]

Now , we can calculate the number of coins in the bag as :
\[Number{\text{ }}of{\text{ }}coins = \dfrac{{weight{\text{ }}of{\text{ }}the{\text{ }}bag}}{{weight{\text{ }}of{\text{ }}one{\text{ }}coin}}\]
Substituting the values , we get
\[Number{\text{ }}of{\text{ }}coins = \dfrac{9}{{9 \times \dfrac{1}{{1000}}}}\]
Simplifying the values , we get
\[Number{\text{ }}of{\text{ }}coins = \dfrac{{9 \times 1000}}{9}\]
Cancelling the terms , we get
\[Number{\text{ }}of{\text{ }}coins = 1000\]
Hence , the number of \[5Rs\] coins present in the bag are \[1000\] .

Thus , the correct option is D.

Note:The concept used to solve the question is known as direct proportion . The concept states that the relation between two variables whose ratio is equal to a constant value . In simple words , it states that changing the value of one of the two variables would affect the value of the other variable . As in the given question , if we decrease the value of the weight of the coins in the bag of coins then the number of coins would also decrease . As the value of weight of the coins in the bag of coins and the number of coins in the bag are directly proportional to each other . A change in any one affects the value of the other.