2880, 480, 92, 24, 8, 4, 2?

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.

Second number is one more than twice the first third number is one less than twice the second, fourth number is one more than twice the third, fifth number is one less than the fourth. Therefore, the sixth number is one more than twice the fifth. So, the missing number is 75.

Go on multiplying the number by 2 and adding 1 to it to get the next number. So, 27 is wrong.

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