In this task, you need to provide the correct option for a given problem from the provided options.

[Q]: Problem: the least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21 , is 
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
[A]: a


[Q]: Problem: two numbers are in the ratio of 5 : 8 . if 30 be subtracted from each , they are in the ratio of 5 : 9 . find the numbers ? 
Options: a ) 122,195 , b ) 121,199 , c ) 120,192 , d ) 102,192 , e ) 126,109
[A]: c


[Q]: Problem: if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 126 , what is the common ratio of the g . p ? 
Options: a ) 3 , b ) 1 / 3 , c ) 2 , d ) 5 , e ) 1 / 5
[A]:
d