The odds against ram solving the problem are 4 to 3 and the

'They both try' means that they both try independently. It doesn't mean that they both are working together on the problem.
The intent of the problem is quite clear: The probability of A succeeding is 'a'; the probability of B succeeding is 'b'. What is the probability that at least one of them succeeds?

Thanks for making it clear

Hi Karishma,

How did you assume, 3 is the failure rate of Ram and 7 is success rate of Krishna.

I don't think I've ever seen "odds" mentioned in a real GMAT question, so this probably isn't important to know, but odds are just a ratio of good outcomes to bad outcomes (and 'odds against' are the ratio of bad to good). So if the odds in favour of something happening are 3 to 1, then for every 3 times it happens, there is 1 time it does not happen, and the probability it happens is thus 3/4.

If the odds against Ram solving are 4 to 3, then 4/7 of the time Ram will not solve the problem. If the odds in favour of Krishna solving are 7 to 5, then 5/12 of the time Krishna will not solve the problem. If they both attempt the problem independently, they will both not solve the problem (4/7)(5/12) = 5/21 of the time. The rest of the time, or 1 - 5/21 = 16/21 of the time, at least one of them will solve it.

The chance that one of them will solve it = 1 - (odds that neither will solve it)
The chance that neither will solve it = odds that Krishna won't solve it * the odds that Ram won't solve it
Odds that Ram won't solve it = 4/7
Odds that Krishna won't solve it = 5/12
Odds that neither will solve it is 4/7*5/12 = 20/84
Odds that one of them will solve it is 1-20/84 = 64/84
Simplified, answer is (C)

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