# 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?

Question:

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?

Solution:

Let the money with A be Rs x and the money with B be Rs y.

If A gives Rs 30 to B, Then B will have twice the money left with A, According to the condition we have,

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

$y+30=2 x-60$

$0=2 x-y-60-30$

$0=2 x-y-90 \cdots(i)$

If B gives Rs 10 to A, then A will have thrice as much as is left with B,

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

$x+10=3 y-30$

$x-3 y+10+30=0$

$x-3 y+40=0 \cdots(i i)$By multiplying equation (ii) with 2 we get, $2 x-6 y+80=0$

By subtracting $(i i)$ from $(i)$ we get,

By substituting $y=34$ in equation $(i)$ we get

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

$x=62$

Hence the money with $\mathrm{A}$ be $R s .62$ and the money with $\mathrm{B}$ be $R s .34$