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.
Go on subtracting prime numbers 19, 17, 13, 11, 7, 5 from the number to get the next number. So, 88 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 multiplying the number by 2 and adding 1 to it to get the next number. So, 27 is wrong.
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.
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
A' s 1 day's work = 1/8
B' s 1 day's work = 1/10
? A' s share : B' s share
= 1/8 : 1/10 = 5/40 : 4/40 = 5 : 4
Let A' s share = 5k
and B' s share = 4k.
According to the question,
5k + 4k = 900
? 9k = 900
? k = 100
? A' s share = 5k = 5 x 100 = ? 500
and B' s share = 4k = 4 x 100 = ? 400.
A's 1 day's work = 1/3
B's 1 day's work = 1/2
A's share : B's share = 1/3 : 1/2 = 2/6 : 3/6
= 2 : 3
Share of A = (2/5) x 225 = ? 90
Work done by (P + Q) = 7/22
Work done by R = 1 - (7/ 22) = (22-7)/22 = 15/22
? (P + Q)'s share : R's share = (7/22) : (15/22) = 7 : 15
R's share = (15/22) x 1100 = 15 x 50 = ? 750
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