Which of the following statements is true ?

As, the denominators are 4, 6, 8, 9 in each option

take L.C.M. of 4, 6, 8, 9 = 72

Now, make all the denominators equal to 72.

Since 1 is common in each question, we can ignore it,

Option A: $$1\frac{1*18}{4*18}>1\frac{5*12}{6*12}>1\frac{7*9}{8*9}>1\frac{8*8}{9*8}$$

               $$1\frac{18}{72}>1\frac{60}{72}>1\frac{63}{72}>1\frac{64}{72}$$ 

               (condition does not satisfy)

Option B: $$1\frac{1*18}{4*18}>1\frac{7*9}{8*9}>1\frac{8*8}{9*8}>1\frac{5*12}{6*12}$$

              $$1\frac{18}{72}>1\frac{63}{72}>1\frac{64}{72}>1\frac{60}{72}$$ 

               (condition does not satisfy)

Option C: $$1\frac{8*8}{9*8}>1\frac{7*9}{8*9}>1\frac{5*12}{6*12}>1\frac{1*18}{4*18}$$

              $$1\frac{64}{72}>1\frac{63}{72}>1\frac{60}{72}>1\frac{18}{72}$$ 

               (condition satisfies)

Option D: $$1\frac{8*8}{9*8}>1\frac{5*12}{6*12}>1\frac{1*18}{4*18}>1\frac{7*9}{8*9}$$

              $$1\frac{64}{72}>1\frac{60}{72}>1\frac{4}{72}>1\frac{63}{72}$$ 

              (condition does not satisfy)

Hence, option C is correct.