Tricky problems; Reasoning problem solving;Find the missing term ?

|| Benzene-problem solving course ex-1 problem ||

Mahesh has certain number of problems with him. He can solve some fixed number of problems every hour. After solving for 5 hours, he is left with 384 problems. If he had solved for 10 hours, he is left with 144 problems to solve. Find the number of problems with Mahesh initially.

The odds against A solving the problem are 4 to 3 and the odds in favour of B solving the . problem are 7 to 5. Find the probability that the problem will be solved.

The probability of solving a specific problem independently by A and B are (1)/(3) and (1)/(5) respectively. If both try to solve the problem independently, find the probability that the problem is solved.

The probability of solving a problem of mathematic for A and B are 1/3 and 1/5 respectively. If both try the problem, find the probability that the problem will be solved.

Given the probability that A can solve a problem is 2/3 and the probability that B can solve the same problem is 3/5. Find the probability that none of the two will be able to solve the problem.

The probalities of A, B, C solving a problem are ⅓, ¼ and .^(1)//_(6) respectively. If all the three try to solve the problem simultaneously, find the probability that exactly one of them will solve it.