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from the answer choices we see that K is a positive integer

This can happen only if x+y which is the denominator is a factor of 10

Factors of 10 are 1,2,5

We cannot get 1 and 2 from x+y as x and y are +ve integers and x<y

so lets take 5 where x=2 and y = 3

we substitute these values we get

10(x+2y)/(x+y) = 10(2+6)/2+3 = 2(8) = 16 so answer is C

The other possible value of x and y is x=1 and y =4, we see that we wont get any of the given answers, this is not needed as we got the solution already but just gave as an extra step.

OA given is A i.e. 10.. i am not sure how.. Also, factors of 10 are 1, 2, 5, and 10. By the method explained above in a post answer comes to be 16 but OA is 10.. please lemme know, is there any other method to solve this question..

let's say c = [10x/(x+y)] +[20y/(x+y)] = (10x+20y)/(x+y) = 10 + {10y/(x+y)} = 10 + [10/((x/y)+1)] so ans should be > 10 now, x<y hence, x/Y <1 hence, (x/Y) + 1 <2 so, 10/ [(x/y)+ 1] >5 so, c> 15 now, since both x and y are positive and (1+(x/y)) > 1 therefore, 10 /(1+(x/y) must be <10

so, c < 10 + 10 c<20 so, 15<c<20 and only 16 satisfy this condition. hence ans is C.

How did you get this (10 + {10y/(x+y)})? Please explain

regards, hhk

hi HHk, sorry for the late reply. here is your explanation- (10x+20y)/(x+y) =(10x+10y +10y)/(x+y) =[(10x+10y)/(x+y)] + [10y/(x+y)] =[10(x+y)/(x+y)] + [10y/(x+y)] =10 + {10y/(x+y)}