Operations on Ratios

For a ratio X/Y where X>Y>5, (X-5):(Y-5) > X:Y. Hence, the ratio of their ages 5 years earlier should be greater than 9:7. Among the options given, only 17:13 is greater than 9:7

For X/Y where X>Y, (X+5):(Y+5)<X:Y. Hence, the ratio of their ages 5 years from today would be lesser than than 9:7. Among the options given, only 16:13 is lesser than 9:7

a/d = a/b * b/c * c/d = 1/3 * 2 * 1/2 = 1/3

Similarly, b/e and c/f are 3 and 3/8 respectively.

b/e = b/c*c/d*d/e = 3

c/f = c/d*d/e*e/f = 3/8

=> Value of abc/def = 1/3 * 3 * 3/8 = 3/8