A and B each has some money. If A gives Rs. 30 to B, then B will have twice the money left 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?

Given:

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

To do:

We have to find the money each has.

Solution:

Let the money with A and B be $x$ and $y$ respectively.

In the first case, when A gives Rs. 30 to B, then B will have twice the money left with A.

According to the question,

$2(x-30)=(y+30)$

$2x-60=y+30$

$2x-y=60+30$

$2x-y=90$....(i)

In the second case, when B gives Rs. 10 to A, then A will have thrice as much as is left with B. 

According to the question,

$(x+10)=3(y-10)$

$x+10=3y-30$

$x-3y=-30-10$

$x-3y=-40$....(ii)

Multiplying (ii) by 2 we get,

$2(x-3y)=2(-40)$

$2x-6y=-80$...(iii)

Subtracting (iii) from (i), we get,

$2x-y-(2x-6y)=90-(-80)$

$2x-2x-y+6y=90+80$

$5y=170$

$y=\frac{170}{5}$

$y=34$

$2x-34=90$   (From (i))

$2x=90+34$

$2x=124$

$x=\frac{124}{2}$

$x=62$

Therefore, the amount of money with A and B is Rs. 62 and Rs. 34 respectively.