Question

If in the year 1998, there was an increase of 10% in the population of U.P. and 12% in the population of M.P. compared to the previous year, then what was the ratio of populations of U.P. and M.P. in 1997?

• A. 42 : 55
• B. 48 : 55
• C. 7 : 11
• D. 4 : 5

Answer 1

The correct option is A 42 : 55

Let x be the population of U.P. in 1997. Then,
Population of U.P. in 1998 = 110% of $x=\frac{110}{100}\times x$
Also, let y be the population of M.P. in 1997. Then,
Population of M.P. in 1998 = 112% of $y=\frac{112}{100}\times y$
Ratio of populations of U.P. and M.P. in 1998 $=\frac{(\frac{100}{100}\times x)}{(\frac{112}{100}\times y)}=\frac{100x}{112y}$
From the pie-chart, this ratio is $\frac{15}{20}$
$\therefore \frac{110x}{112y}=\frac{15}{20}\Rightarrow \frac{x}{y}=\frac{15}{20}\times \frac{112}{110}=\frac{42}{55}$
Thus, ratio of populations of U.P. and M.P. in 1997 = x : y = 42 : 55.