Three friends put ₹a, ₹b and ₹c into a common fund. Taken in pairs their contributions satisfy (a + b) : (b + c) : (c + a) = 5 : 7 : 8, and the three together put in ₹20000. The largest single contribution (in ₹) is:

The three pair-sums add up to $2(a+b+c)$ = ₹40000, and they are 5 + 7 + 8 = 20 parts, so one part is ₹2000: $a+b=10000,b+c=14000,c+a=16000$. Subtracting each from ₹20000 gives $c=10000,a=6000,b=4000$, so the largest contribution is ₹10000. Treating 5 : 7 : 8 as the ratio of the individual contributions gives $8/20\times 20000$ = ₹8000, but those parts belong to the PAIRS.