3, 7, 15, 27, 63, 127, 255?

Go on dividing by 6, 5, 4, 3, 2, 1 respectively to obtain the next number. Clearly, 92 is wrong.

Each number is 15 multiplied by a prime number i.e., 15 x 11, 15 x 13, 15 x 17, 15 x 19, 15 x 23. So, the next number is 15 x 29 = 435.

There are two series (10, 13, 16, 19) and (5, 10, 20, 40)one increasing by 3 and another multiplied by 2.

Each previous number is multiplied by 2.

Alternately, we add 5 and subtract 7.

Let the given number be A, B, C, D, E, F, G. Then A x 1 + 1, B x 2 + 2, C x 3 + 3, D x 4 + 4, E x 5 + 5, F x 6 + 6 are the required number . Clearly, 228 is wrong.

Go on subtracting prime numbers 19, 17, 13, 11, 7, 5 from the number to get the next number. So, 88 is wrong.

The pattern is
1² ,
1² + 2²,
1² + 2² + 3²,
1² + 2² + 3² + 4²,
1² + 2² + 3² + 4² + 5²,
1² + 2² + 3² + 4² + 5² + 6² .
But 50 is not of this pattern.

Shantanu's 1 day's work = 1/2
Manu's 1 day's work =1/10
Shantanu's share : Manu's share =(1/12) : (1/10)
= (5/60) : (6/60)
= 5 : 6

A's 1 day's work = 1/9
B's 1 day's work = 1/15
A's share : B's share = (1/9) : (1/15)
= (5/45) : (3/45)
= 5 : 3