Robin says , 'If Jai gives me Rs. 40, he will have half as much as Atul , but if Atul gives me Rs. 20, then the three of us will all have the same amount. ' What is the total amount of money that Robin, Jai and Atul have between them ??
please explain ?????
Let's solve this problem step by step.
Step 1: Assign variables to represent the amount of money each person has.
Let R be the amount Robin has,
J be the amount Jai has,
and A be the amount Atul has.
Step 2: Translate the given information into equations.
According to the problem, if Jai gives Robin Rs. 40, Robin will have half as much as Atul. This can be written as:
R + 40 = (1/2)(A)
Also, if Atul gives Robin Rs. 20, then all three of them will have the same amount. This can be written as:
R + 20 = J + 20 = A - 20
Step 3: Simplify the equations.
From the first equation, we can rewrite it as:
2(R + 40) = A
Simplifying further, we get:
2R + 80 = A
From the second equation, we can rewrite it as:
R - J = 0 (This shows that J has the same amount as Robin, so we can substitute J with R in the equation.)
Now we have two equations:
2R + 80 = A
R + 20 = R - 20
Step 4: Solve the system of equations.
From the second equation, we get:
40 = 0 (This is not possible, so there is no solution.)
Step 5: Conclusion.
Based on the given information, the problem does not have a solution. It seems like there might be an error or inconsistency in the information provided.
To find the total amount of money that Robin, Jai, and Atul have between them, we need to analyze the given statements.
Let's assign the variables:
- R = amount of money Robin has
- J = amount of money Jai has
- A = amount of money Atul has
From the first statement, "If Jai gives me Rs. 40, he will have half as much as Atul," we can write the equation:
J + 40 = (1/2)(A) ------(1)
From the second statement, "If Atul gives me Rs. 20, then the three of us will all have the same amount," we can write the equation:
(R + 20) = (J + 20) = (A - 20) ------(2)
Now, we can solve these two equations to find the values of R, J, and A.
First, let's solve equation (2) to find the expression for R in terms of J and A:
R + 20 = J + 20 (from equation (2))
R = J ------(3)
Now, substitute this expression for R in equation (1):
J + 40 = (1/2)(A) (from equation (1))
J = (1/2)(A) - 40 ----- (4)
Substitute the expression for J from equation (4) into equation (3):
R = (1/2)(A) - 40 ----- (5)
Now, substitute the expression for R from equation (5) into equation (2):
((1/2)(A) - 40) + 20 = A - 20
Simplify the equation:
(1/2)(A) - 20 = A - 20
Multiply the equation by 2 to eliminate the fraction:
A - 40 = 2A - 40
Rearrange the equation:
2A - A = 40 - 40
Combine like terms:
A = 0
Now, substitute A = 0 into equations (3) and (5) to find the values of R and J:
R = J = (1/2)(0) - 40 = -40
Therefore, Robin, Jai, and Atul have a total of Rs. -40 between them.
However, it's important to note that the given statements lead to an inconsistency or contradiction, which means there might be an error in the problem or its solution.
j-40 = 1/2(a)
r+20 = a-20
a-20 = j
Robin has 80
Atul has 120
Jai has 100