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If a, b, c and d are four different positive integers selected from 1 to 25, then the highest possible value of ((a + b) + (c +d ))/((a + b) + (c - d)) would be:
Expression : $$\frac{a + b + c + d}{a + b + c - d}$$
To maximize the above expression, we have to minimize the denominator
Minimum value of the denominator = 1
So we can make $$a + b + c = 26$$ and $$d = 25$$ (as maximizing d will give denominator the least value).
So required maximum value = $$\frac{a + b + c + d}{a + b + c - d}$$
= $$\frac{26 + 25}{26 - 25} = 51$$
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