Question

$\frac{2}{7}\text{ths of a kingdom is a forest and}\frac{A}{B}\text{fraction}\text{of the forest is a grassland. If the grassland}\text{covers}\frac{1}{4}\text{th of the kingdom, choose the}\text{correct values of A and B}$

• A. A = 7 ; B = 9
• B. A = 7 ; B = 8
• C. A = 14 ; B = 9
• D. A = 14 ; B = 8

Answer 1

The correct option is B A = 7 ; B = 8

$\text{Fraction of the kingdom covered by the}\text{forest}=\frac{2}{7}$

$\text{Fraction of the forest that is a grassland}=\frac{A}{B}$

$⟹\text{Fraction of the kingdom that is a}\text{grassland}=\frac{2}{7}\times \frac{A}{B}=\frac{2\times A}{7\times B}$

$\text{Calculating}\frac{2\times A}{7\times B}\text{for each case, we find:}$

$Case1:A=7;B=9$

$\frac{2\times A}{7\times B}=\frac{2\times 7}{7\times 9}=\frac{2\times 7}{7\times 9}=\frac{2\times 1}{1\times 9}=\frac{2}{9}$

$\therefore \text{For A = 7 and B = 9, the fraction of}\text{the kingdom covered by grasslands is}\frac{2}{9}$

$Case2:A=7;B=8$

$\frac{2\times A}{7\times B}=\frac{2\times 7}{7\times 8}=\frac{2\times 7}{7\times 8}=\frac{1\times 1}{1\times 4}=\frac{1}{4}$

$\therefore \text{For A = 7 and B = 8, the fraction of}\text{the kingdom covered by grasslands is}\frac{1}{4}$

$Case3:A=14;B=9$

$\frac{2\times A}{7\times B}=\frac{2\times 14}{7\times 9}=\frac{2\times 14}{7\times 9}=\frac{2\times 2}{1\times 9}=\frac{4}{9}$

$\therefore \text{For A = 14 and B = 9, the fraction of}\text{the kingdom covered by grasslands is}\frac{4}{9}$

$Case4:A=14;B=8$

$\frac{2\times A}{7\times B}=\frac{2\times 14}{7\times 8}=\frac{2\times 14}{7\times 8}=\frac{1\times 1}{1\times 2}=\frac{1}{2}$

$\therefore \text{For A = 14 and B = 8, the fraction of}\text{the kingdom covered by grasslands is}\frac{1}{2}$

$\text{Hence, the values of A and B that gives}\text{the fraction of grasslands as}\frac{1}{4}\text{is:}$

$A=7;B=8$