Given:We are given information about John investing his savings in investment X and Y such that he made 10% profit in investment X and 15% loss in investment Y. We are also told that John did not make any profit or loss on his total investment in X & Y. We are asked to find the ratio of his investment in X to his total investment.

Approach:We are told that John invested in investment X & Y only.Let's assume his investment in X to be \(x\) and investment in Y to be \(y\).

So, we need to find \(\frac{x}{x+y}\)

For finding the above ratio we need to find a relation between \(x\) and \(y\). Let's use the information given in the question to find out the same.

Profit made by John in investment X = 10% of amount invested in X = 10% of \(x\)

Loss made by John in investment Y = 15% of amount invested in Y = 15% of y

Since he did not make any profit or loss on his investments in X & Y that would mean his profit on investment X is equal to his loss in investment Y i.e. 10% of \(x\) = 15% of \(y\).

We now have a relation between \(x\) and \(y\). We will use this relation to find the ratio of his investment in X to his total investment.

Working OutWe know that 10% of \(x\) = 15% of \(y\)

\(0.1x = 0.15y\) i.e. \(x = \frac{3y}{2}\). From here, we can write \(y = \frac{2x}{3}\)

Hence \(\frac{x}{x+y}\) = \(\frac{x}{x+2x/3}\) = \(\frac{3x}{5x}\)

= \(\frac{3}{5}\) which is our answer

Hope its clear!

Regards

Harsh

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