Question

A and B each have some money. If A gives Rs. 30 to B, then B will have twice the money with A. But if B gives Rs. 10 to A, then A will have thrice as much as is left with B. How much money does each have?

Answer 1

Hint- Here we will proceed by assuming the money with A and B be x, y. Then we will convert the given cases in the form of linear equations in 2 variables such that we get the required values of variables i.e. x and y.

Complete step-by-step answer:
Let money with A = Rs. x
Let money with B = Rs. y
According to first case given in the question-
We get-
2x = (y + 30)
$\Rightarrow$ 2x = y + 30
$\Rightarrow$ 2x – y = 30……… (1)
Now using second case in the question,
We get-
(x + 10) = 3(y – 10)
$\Rightarrow$ x – 3y = -40
$\Rightarrow$ 2x – 6y = -80……………… (2)
On subtracting equation 2 from equation 1,
We get-
2x – y – (2x – 6y) = 30 – (-80)
$\Rightarrow$ –y + 6y = 30 + 80
$\Rightarrow$ 5y = 110
$\Rightarrow$ y = 22
Now substituting the value of y in equation 1 i.e. 2x – y = 30,
We get-
2x – 22 = 30
$\Rightarrow$ 2x = 52
$\Rightarrow$ x = 26
Hence, A has Rs. 26 and B has Rs. 22.

Note- While solving this question, we can assume any variables as here we assumed x and y. As here we used a substitution method, we can also solve the linear equations by any method like elimination method etc.