oracle Company Numerical Ability Ratio and Proportion

There are two numbers in the ratio 8:9. If smaller of the two numbers is
increased by 12 and the larger number is reduced by 19 then the ratio of
the two numbers is 5:9. Find the larger number

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In a class of 10 students, the teacher writes a number on the board. The first student tells that number is divisible by 1, the second student tells that the number is divisible by 2, the third by 3, the forth by 4 and so on till 10. If the statement of one of the students is wrong then what is the least number possible.