# A has Rs9 & B has Rs4 and 20p.After B has won from A a certain sum in a board game, A has then five-sixth of what B has. How much did B gain

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B has gained Rs 3.

Here is how to figure this out:

What you are saying is that A has lost an amount and B has gained that same amount. We should call that amount x.

So after the game, A has 9-x and B has 4.2+x

We also know that A ends up with 5/6 of what B has. That tells us that

9-x = 5/6(4.2+x)

5/6, made into decimals is .8333333333 so we can say that

9-x = .833333333(4.2 +x)

So now we must do the math on the right side.

That gets us

9-x = 3.5+.833333333x

So now we move the numbers to one side and the xs to the other and get

1.83333333x = 5.5

We then divide both sides by 1.83333333 and get

x = 3

This means that the amount won and lost was Rs 3

We can check this by adding that amount to B's money and subtracting it from A's. When we do, we see that B has Rs 7.2 and A has Rs 6.

If we divide 6 by 7.2, we find that it equals .8333333, which is equivalent to 5/6

The total amount between A and B is Rs9 of A+Rs 4.2 of B = Rs 13.20 which remains same irrespective of who of the two wins.

After the game, A has five sixth amount of B implies,A and B has the amount in 5:6 ratio . So now after the game also the total amount between A and B remains the same Rs 13.20 but amount with A and B is in 5:6 ratio.

Therefore, we make Rs 13.20 into 5+6=11 equal parts, i.e, Rs 13.20/11 = Rs 1.20 each. Now 5 equal parts = 5*(Rs1.2)= Rs 6.00 would be with A and 6 equal parts =6*(Rs1.20) = Rs7.20 would be with B. So B gained Rs 7.20 - Rs4.20 = Rs 3.00.