Question

Aahan and Arya have certain sums with them if Arya gives 50 rupees to a heart Aahan with have 5 times the sum left with Arya if ahaan gives 50 rupees to Arya both of them will have equal sum find the sum each of them have

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Answer 1

Answer:

The amount that Aahan has = Rs 200

The amount that Arya has = Rs 100

Step-by-step explanation:

Let the amount that Aahan has = Rs x

Let the amount that Arya has = Rs y

Case 1: If Arya gives 50 Rs to Aahan

Amount Aahan will have = (x + 50) Rs

Amount Arya will have = (y - 50) Rs

Aahan will have 5 times the sum left with Arya.

x + 50 = 5(y - 50)

x + 50 = 5y - 250

x - 5y + 300 = 0 ……. Eq (1)

Case 2: If Aahan gives 50 Rs to Arya

Amount Aahan will have = (x - 50) Rs

Amount Arya will have = (y + 50) Rs

Both of them will have equal sum.

x - 50 = y + 50

x - y - 100 = 0 ……. Eq (2)

Solving equations (1) & (2);

    x - 5y + 300 = 0

    x -   y - 100 = 0

  (-)  (+)  (+)

   ———————

      -4y = -400

    => y = 100

From Eq (2);

x - y - 100 = 0

x - 100 - 100 = 0

=> x = 200

Therefore,

the amount that Aahan has = Rs x = Rs 200

the amount that Arya has = Rs y = Rs 100