MCQ
If $\text{a}:\text{b}=2:5,$ then $\frac{3\text{a}+2\text{b}}{4\text{a}+\text{b}}=$
- ✓$\frac{16}{13}$
- B$\frac{13}{16}$
- C$\frac{25}{22}$
- D$\frac{20}{21}$
✓
Answer
Correct option: A.
$\frac{16}{13}$
As, $\text{a}:\text{b}=2:5$
$\Rightarrow\frac{\text{a}}{\text{b}}=\frac{2}{5}$
Let $\text{a}=\text{2x}$ and $\text{b}=5\text{5x}.$
Then,
$\frac{3\text{a}+\text{2b}}{4\text{a}+\text{b}}$
$=\frac{3\times2\text{x}+2\times\text{5x}}{4\times2\text{x}+5\text{x}}$
$=\frac{6\text{x}+10\text{x}}{8\text{x}+5\text{x}}$
$=\frac{16\text{x}}{13\text{x}}$
$=\frac{16}{13}$
Hence, the correct alternative is option $(a).$
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