Doing this algebraically and since it is given \(p-q>\frac{pq}{100}\), I would expect this result to crop up during the calculation

Let rent collected in 2007 \(= 100\)

The rent collected in 2008 \(= 100 + 100 \times \dfrac{p}{100} = 100 + p\)

The rent collected in 2009= \((100 + p)[1 - \frac{q}{100}]\)

\(100-\dfrac{q100}{100}+p-\frac{pq}{100} \)

\(100-q+p-\dfrac{pq}{100}\)

\(100 +p-q-\dfrac{pq}{100}\)

Given \(p-q>\dfrac{pq}{100}\)

\(p-q-\dfrac{pq}{100} > 0 \text{ or a positive number}\)

Thus

1\(00 +p-q-\dfrac{pq}{100} = 100 + \text{a positive number}\)


Therefore,

\(\text{ rent collected in the year 2009 } > \text{ rent collected in the year 2007 }\)

Quantity A is greater than Quantity B