Question

Rohit says to Ajay,"Give me a hundred,I shall then become twice as rich as you."Ajay replies ,"If you give me ten,I shall be six times as rich as you."How much does each have originally?

Answer 1

Let money with Rohit be x and money with Ajay be y.

Then according to question,

x + 100 = 2(y - 100)

x + 100 = 2 y - 200

  x - 2 y = -300                        ................(1)
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Also, 

6(x - 10) = y + 10

 6 x - 60  = y + 10

     6 x - y = 70                        .............(2)
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From (1) and (2)

(1) × 1 ⇒      x - 2 y = -300

(2) × 2 ⇒ 12 x - 2 y = 140
                (-)     (+)       (-)
                ______________

                     -11 x = -440
                ______________

Then x = 40 and so y = 170
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