Answer : Option A

Explanation :

Let x be the population of U.P. in 1997. Then,

Population of U.P. in 1998 = 110% of x = \(\frac { 110 } { 100 } \) x x.

Also, let y be the population of M.P. in 1997. Then,

Population of M.P. in 1998 = 112% of y = \(\frac { 112 } { 100 } \) xy 

Ratio of populations of U.P. and M.P. in 1998 = \(\frac { (110/100 X X) } {( 112 /100 X Y )} \) = \(\frac { 110 X } {11 2 Y } \)

From the pie-chart, this ratio is \( \frac { 15 } { 2 0} \)

\(\frac { 110 X } {11 2 Y } \) = \( \frac { 15 } { 2 0} \)   \(\frac { X } { Y }\) =  \( \frac { 15 } { 2 0} \)x  \(\frac { 112 } { 100 } \)= \( \frac { 42 } { 55 } \)

Thus, ratio of populations of U.P. and M.P. in 1997 = x : y = 42 : 55.