Let the original fraction be p/q
Then, (p + 2) / (q + 1) = 5/8
? 8p - 5q = 11 .....(i)
Again (p + 3) / (q + 1) = 3/4
? 4p - 3q = 9 ...(ii)
Solving equations , (i) and (ii), we get ,
p = 3 and q = 7
? Fraction = 3/7
Prime number 2, 3, 5, 7, 11, 13 are to be added successively. So, 165 is wrong.
Go on dividing by 4 to get the next number. So, 200 is wrong.
Go on multiplying with 1, 2, 3, 4, 5, 6 to get the next number. So, 96 is wrong.
The pattern is x2 + 1, where x = 1, 2, 3, 4, 5, 6, 7, 8 etc. But 64 is out of pattern
The number are square of odd natural numbers, starting from 5 up to 15. So, 36 is wrong.
The number are 7 x 8, 8 x 9, 9 x 10, 10 x 11, 11 x 12, 12 x 13 . So, 150 is wrong.
The terms are alternately multiples by 1.5 and divided by 3. However 18.5 does not satisfy it.
Sum of the digits in each number, except 324 is 10.
The number are cubes of primes i.e., 23, 33, 53, 73, 113. Clearly, none is wrong.
Alternetly, we add 4 and double the next. So, 132 is wrong. It must be (68 x 2) i.e., 136.
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