Multiple choice

The population of City A increased by p% last year, and the number of employed residents increased by q%, where p > q. By what percentage did the ratio of total population to employed residents increase, in terms of p and q?

  1. p q %

  2. (p - q)%

  3. [ 100 ( p − q ) ( 100 + p ) ] %

  4. [ 100 ( p − q ) ( 100 + q ) ] %

  5. [ 100 ( p − q ) ( 100 + p + q ) ] %
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P be population and E be employed. Ratio R = P/E. New ratio R' = P(1+p/100) / E(1+q/100). The percentage increase is ((R'-R)/R) * 100, which simplifies to 100(p-q)/(100+q).

AI explanation

The initial ratio of total population to employed residents is P divided by E. After the increase, the new ratio is P multiplied by (1 plus p/100) divided by E multiplied by (1 plus q/100), which simplifies to the original ratio multiplied by (100 plus p) divided by (100 plus q). The percentage increase in this ratio is found by calculating the change over the new ratio, resulting in the formula 100 multiplied by (p minus q) divided by (100 plus q). Therefore, the ratio increased by [ 100 ( p − q ) ( 100 + q ) ] %.

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