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.
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