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41. (1/4) : (1/8) :: (2/3) : ?

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Solution:
First term is double of the second term.
Hence, fourth term
= (1/2)*(2/3) = 1/3
42. 9 : 25 :: 49 : ?

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Solution:
First term = 32 = 9.
Second term = 52 = 25.
Third term = 72 = 49.
2 = 81.
43. 12 : 35 :: 16 : ?

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Solution:
First term = 6*2 = 12.
Second term = 62 - 1 = 35.
Third term = 8*2 = 16.
Fourth term = 82 - 1 = 63.
44. 1 : 8 :: 9 : ?

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Solution:
First term = 12 = 1.
Second term = 23 = 8.
Third term = 32 = 9.
Fourth term = 43 = 64.
45. Resignation : Office ::

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Solution:
As in Resignation the Office is to be left in the same manner when Abdication is done, Throne is to be left.
46. Bunch : Key ::

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Solution:
Bunch is collection of Keys and Bouquet is collection of Flowers.
47. Profit : Loss ::

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Solution:
Profit is antonym of Loss and Success is antonym of Failure.
48. Sapling : Tree ::

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Solution:
Sapling is young Tree and Bud is young Flower.
49. Supervisor : Worker ::

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Solution:
Supervisor supervises the Worker in the same way Officer supervises the Clerk.
50. Timid : Ass :: Cunning : ?

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Solution:
Ass is Timid and Fox is Cunning.