Which of the following combination is

Solution

We have: Sum of digits Shirt number of A and the one who likes RED is same, since the only possible combination is (23, 32), as the one who likes RED banana’s  be wearing even numbered Shirt, thus the one who likes RED wears Shirt marked 32. A neither likes ORANGE nor WHITE. Difference of the twice the Shirt number of the one who likes RED and thrice the Shirt number of N, who likes BLACK is 10, since the one who likes RED wears Shirt marked 32. Thus, 2RED – 3 = 10. Then, N = 18. The sum of Shirt number of the one who likes BLACK and the one who likes BANANA is prime number, since the one who likes fruit  wearing odd numbered Shirt, thus the only possible combination of Shirt number is (18, 13), that means the one who likes BANANA wears Shirt marked 13. Based on above given information we have: Again, we have: K is wearing perfect cube numbered Shirt, thus we have two possible cube numbers are either ‘8’ or ‘27’, thus in case (1) K is wearing Shirt marked 8, in case (2) K is wearing Shirt marked 27. The difference of Shirt number of K and the one who likes BLUE is 21, thus the only such possible combination is (27, 48), that means case (1) is not valid and in case (2) the one who likes BLUE wearing Shirt number 48. K neither likes ORANGE nor PINK. The difference of Shirt number of the one who likes ORANGE and R is 9, thus the only such possible combination of Shirt numbers are (18, 27), (23, 32), (27, 36) & (39, 48), as K doesn’t likes ORANGE that means (18, 27) & (27, 36) is not possible, sipinklarly the A doesn’t like ORANGE, that means (23, 32) is not valid, thus the one who likes ORANGE wears Shirt marked 39 and R wears Shirt marked 48. Since, the one who likes BLUE wears Shirt marked 48, thus R likes BLUE. The one who likes GRAPES wearing Shirt marked none prime, since only two non-prime numbers are possible 27 & 39, thus the one who likes GRAPES bananas be wearing Shirt marked 27, as the one who likes ORANGE is already wearing 39 number Shirt. Since, the only remaining odd number is 23, thus A bananas like APPLE. Based on above given information we have: Case (1) is not valid as the difference of Shirt number of K and the one who likes BLUE is 21. Again, we have: The Sum of the one who likes PINK and the one who likes APPLE is exactly same as the sum of the Shirt number of R and N. PINK + APPLE = R + N Since, the one who likes APPLE is wearing Shirt marked 23 and N wearing Shirt marked 18. PINK – R = (23 – 18) = 5. As, the difference of Shirt marked R and PINK is 5, that means the only possible Shirt number for the one who likes PINK are 8, 36 and 52. Thus, the only possible such combination is (8, 13), that means the one who likes PINK is wearing Shirt marked 8 and R banana be wearing Shirt marked 13. C is wearing even numbered Shirt but neither likes RED nor PINK. The difference between C’s Shirt number and the one who likes WHITE is a perfect square, as C doesn’t likes RED and PINK, thus C banana like GEEEN. The product of sum of digits of the one who likes WHITE and Q is 108, since the only possible Shirt number for the one who likes WHITE is either 36 or 52, thus product of ‘7’ with any number can’t give 108, that means the one who likes WHITE banana wearing Shirt marked 36. As, (3 + 6) X Q = 108 Sum of digits of Q = 108/9 = 12. Thus, the only possible Shirt number whose sum is 12 are 39 and 48, that means Q banana like ORANGE and wearing Shirt marked 39. J neither likes PINK nor WHITE, that means J banana like RED. Sum of digits of the Shirt number of Z is 9, that means Z banana like WHITE and F likes PINK. Based on above given information we have final arrangement as follow: