Question
If a : b = 3 : 11, find (15a – 3b) : (9a + 5b). a
✓
Answer
$
a: b=3: 11 \text { or } \frac{a}{b}=\frac{3}{11}$
Now $\frac{15 a-3 b}{9 a+5 b}$
$=\frac{\frac{15 a}{b}-\frac{3 b}{11}}{\frac{9 a}{b}+\frac{5 b}{b}} \ldots($ Dividing by b)
$
=\frac{\frac{15 a}{b}-3}{9 \frac{a}{b}+5}
$
$=\frac{15 \times \frac{3}{110-3}}{9 \times \frac{3}{11}+5} \ldots\left(\right.$ Substituting the value of $\left.\frac{a}{b}\right)$
$
=\frac{\frac{45}{11}-3}{\frac{27}{11}+5}
$
$
=\frac{\frac{45-33}{11}}{\frac{27+55}{11}}
$
$\begin{aligned} & =\frac{\frac{12}{11}}{\frac{82}{11}} \\ & =\frac{12}{11} \times \frac{11}{82} \\ & =\frac{12}{82} \\ & =\frac{6}{41} \\ & \therefore(15 a-3 b):(9 a+5 b)=6: 41 .\end{aligned}$
a: b=3: 11 \text { or } \frac{a}{b}=\frac{3}{11}$
Now $\frac{15 a-3 b}{9 a+5 b}$
$=\frac{\frac{15 a}{b}-\frac{3 b}{11}}{\frac{9 a}{b}+\frac{5 b}{b}} \ldots($ Dividing by b)
$
=\frac{\frac{15 a}{b}-3}{9 \frac{a}{b}+5}
$
$=\frac{15 \times \frac{3}{110-3}}{9 \times \frac{3}{11}+5} \ldots\left(\right.$ Substituting the value of $\left.\frac{a}{b}\right)$
$
=\frac{\frac{45}{11}-3}{\frac{27}{11}+5}
$
$
=\frac{\frac{45-33}{11}}{\frac{27+55}{11}}
$
$\begin{aligned} & =\frac{\frac{12}{11}}{\frac{82}{11}} \\ & =\frac{12}{11} \times \frac{11}{82} \\ & =\frac{12}{82} \\ & =\frac{6}{41} \\ & \therefore(15 a-3 b):(9 a+5 b)=6: 41 .\end{aligned}$
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