Question

Ravi has ₹50 more than those with Kavita. If they both have ₹500 with them, make an algebraic statement and find the money with each.

Answer 1

Hint: Let amount with Ravi = y and amount with Kavita = x.
Express the given information in the form of linear equations and solve them simultaneously.
This will give the required answer.

Complete step by step solution: The question given to us has two parts to it.
First part is that we need to make an algebraic statement of the given question
The second part asks us to find the money with Ravi and Kavita each.
Let us begin with the first part.
We are given that Ravi has ₹50 more than that with Kavita.
But we do not know how much Kavita has.
So, let the amount with Kavita be x.
Also, let the amount with Ravi be y.
As there are only two people involved in the problem at hand, we can express the given conditions in the form of linear equations in two variables x and y.
According to the first part, we get an amount with Ravi =
y = x + 50.
Thus, our first algebraic statement would be
x - y = -50.
It is given that the amount with Ravi and Kavita together is ₹500.
Therefore, we get our second algebraic statement:
x + y = 500.
Thus, the required algebraic statement is the following system of linear equations:
\[x - y = - 50\] ………….equation (1)
\[x + y = 500\]………….equation (2)
Now, let’s find the values of x and y to answer the second part of the question.
We can do this by solving these equations simultaneously.
Adding (1) and (2), we get
\[ 2x = 450 \\
\Rightarrow x = 225 \\ \]
Substitute the value of x in equation (2)
Then,
$ y = 500 - 225 = 275 \\
\Rightarrow y = 275 \\ $
Hence the amount with Ravi is ₹ 275 and the amount with Kavita is ₹ 225.

Note: We can also solve this problem using a single variable in the following manner.
Let the amount with Kavita be x.
Then amount with Ravi = x + 50.
According to the given information, we have the following algebraic statement: x + (x + 50) = 500
This implies that 2x + 50 = 500.
Therefore, 2x = 500 - 50 = 450.
Divide both sides by 2.
Thus, x = 225
Then the amount with Kavita = ₹225 and the amount with Ravi = ₹225 + 50 = ₹275