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Question

A and B each has some money. If A gives Rs. 30 to B, then B will have twice the money 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?

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Solution

Let A has money = Rs.x
& B has money = Rs.y
Case 1: 2x=(y+30)2x=y+302xy=30(i)

Case 2: (x+10)=3(y10)x3y=402x6y=80(ii)

On substracting (ii) from (i) we get ,
2xy(2x6y)=30(80)y+6y=30+805y=110y=22

On putting y in (i) we get ,
2xy=30
x=26
Hence , A has Rs.26 and B has Rs.22.

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