Question

The population of town $A$ is $96,000$ more than town $B$. If $62,000$ people move from town $B$ to town $A$, the ratio between the population of town $A$ and that of town $B$ will be $11:1$. Find the original population of the two towns.

• A. $A=3,20,000$ and $B=72,000$
• B. $A=2,90,000$ and $B=72,000$
• C. $A=1,80,000$ and $B=84,000$
• D. $A=1,60,000$ and $B=84,000$

Answer 1

Answer: (C)

$A=1,80,000$ and $B=84,000$

Let population of Town A be $x$ and of Town B be $y$
Given, $x=y+96000=>x-y=96000$ -- (1)
As per the statement, "If 62,000 people move from town B to town A, the ratio between the population of town A and that of town B will be 11:1 $=>x+62000:y-62000=11:1$
$=>\frac{x+62000}{y-62000}=\frac{11}{1}$
$=>x+62000=11y-682000$
$=>x-11y=-7,44,000$ --- (2)

Subtracting equation $\left(2\right)$ from $\left(1\right)$, we get $10y=8,40,000=>y=84,000$

Substituting $y=84,000$ in the equation $\left(1\right)$, we get $x-84000=96000=>x=1,80,000$

Hence, population of Town A $=1,80,000$ and population of Town B $=84000$