Question

Given that a (a+b) = 36 and b(a+b) = 64 where a and b are positive (a-b) equals

• A. 2.8
• B. 3.2
• C. -2.8
• D. -2.5

Answer 1

Answer: (C)

-2.8

$a(a+b)=36$ $...\left(i\right)$
$b(a+b)=64$ $...\left(ii\right)$
$\text{On dividing (i) by (ii), we get}$
$\frac{a}{b}=\frac{9}{16}$
$\Rightarrow b=\frac{16}{9}a$ $...\left(iii\right)$
$\therefore \left(i\right)becomes$
$a^2+ab-36=0\Rightarrow a^2+a\left(\frac{16}{9}a\right)-36=0$
$\Rightarrow \frac{25a^2}{9}=36$
$\Rightarrow a^2=\frac{324}{25}$
$\Rightarrow a=\frac{18}{5}$ $(\because \text{a is positive.})$
From (iii)
$b=\frac{16}{9}\times \frac{18}{5}$
$\Rightarrow b=\frac{32}{5}$
$a-b=\frac{18}{5}-\frac{32}{5}=-\frac{14}{5}=-2.8$
Option C is correct.