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.

Step by Step Explanation:
  1. Let us assume A and B have $x and $y respectively.
  2. A gives $90 to B and then B will have twice the money left with A.

    Money with A = $ (x90)
    Money with B = $ (y+90)  2(x90)=(y+90)2x180=y+902xy=270(1)
  3. 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 = $ (y30)  x+30=3(y30)x+30=3y90x3y=120(2)
  4. On multiplying (1) by 3 we get 6x3y=810(3)Now, subtracting (2) from (3), we get 5x=930x=186
  5. Now, substituting x=186 in (1), we get2(186)y=270y=372270=102
  6. Hence, A has $186 and B has $102.

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