Question

There are 49 children. A certain amount of money is distributed among them and each one of them got Rs. 20. Now the same amount of money is distributed among a certain number of children so that each child gets Rs. 3.5. Find out the number of children.

Answer 1

Hint: We have been provided with two different situations. In the first case the number of children and amount of money of each student has been provided. Using multiplication, we find out the total amount of money. In the second case we have total money and amount of money each student got. Using division, we find out the number of children.

Complete step-by-step answer:
There are 49 children in the first case. After distribution each on of them got Rs. 20.
So, 1 child got Rs. 20 which means 49 children in total got Rs. $\left( 49\times 20 \right)$.
The total amount of money is $\left( 49\times 20 \right)=980$.
Now we divide all the money among a certain number of children so that each one of them gets Rs. 3.5.
Let’s the number of children be x. each one got Rs. 3.5.
Total amount of money will be $\left( 3.5\times x \right)=3.5x$ which should be equal to the total amount of Rs. 980.
So, $3.5x=980$
We have a linear equation of x. We solve it to get the value of x.
So, $3.5x=980\Rightarrow x=\dfrac{980}{3.5}=280$
The total number of children is 280.

Note: In the second case we have used an algebraic equation to find out the solution. Instead we can also only use the method of division without taking any kind of variable to solve it.
As the total amount of money was Rs. 980 and each child gets Rs. 3.5.
So, we can say Rs. 3.5 is for 1 child. Then Rs. 980 will be for $\dfrac{980}{3.5}=280$ children.
The process is the same just without using the variable.