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.