MCQ
If $p : q = 2 : 5$, then $\frac{25\text{p}+14\text{q}}{5\text{p}+7\text{q}}=$
- A$8 : 5$
- B$5 : 8$
- ✓$8 : 3$
- D$3 : 8$
✓
Answer
Correct option: C.
$8 : 3$
As, $\text{p}:\text{q}=2:5$
$\Rightarrow\frac{\text{p}}{\text{q}}=\frac{2}{5}$
Let $\text{p}=\text{2x}$ and $\text{q}=5\text{x}$
Now, $\frac{25\text{p}+14\text{q}}{5\text{p}+\text{7q}}$
$=\frac{25\times2\text{x}+14\times5\text{x}}{5\times2\text{x}+7\times5\text{x}}$
$=\frac{50\text{x}+70\text{x}}{10\text{x}+35\text{x}}$
$=\frac{120\text{x}}{45\text{x}}$
$=\frac83$
$=8:3$
Hence, the correct alternative is option $(c).$
$\Rightarrow\frac{\text{p}}{\text{q}}=\frac{2}{5}$
Let $\text{p}=\text{2x}$ and $\text{q}=5\text{x}$
Now, $\frac{25\text{p}+14\text{q}}{5\text{p}+\text{7q}}$
$=\frac{25\times2\text{x}+14\times5\text{x}}{5\times2\text{x}+7\times5\text{x}}$
$=\frac{50\text{x}+70\text{x}}{10\text{x}+35\text{x}}$
$=\frac{120\text{x}}{45\text{x}}$
$=\frac83$
$=8:3$
Hence, the correct alternative is option $(c).$
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