Each one of A and B has some money. If A gives $90 to B then B will have twice the money left with A. But, if B gives $30 to A then A will have thrice as much as is left with B. How much money does each have?
Answer:
A has $186 and B has $102.
- Let us assume A and B have $x and $y respectively.
- A gives $90 to B and then B will have twice the money left with A.
Money with A = $ (x−90)
Money with B = $ (y+90) ∴ 2(x−90)=(y+90)⟹2x−180=y+90⟹2x−y=270…(1) - B gives $30 to A and then A will have thrice as much as is left with B.
Money with A = $ (x+30)
Money with B = $ (y−30) ∴ x+30=3(y−30)⟹x+30=3y−90⟹x−3y=−120…(2) - On multiplying (1) by 3 we get 6x−3y=810…(3)Now, subtracting (2) from (3), we get 5x=930⟹x=186
- Now, substituting x=186 in (1), we get2(186)−y=270⟹y=372−270=102
- Hence, A has $186 and B has $102.