Question

Mark the correct alternative in the following question:

$$\begin{gathered} \mathrm{If}p:q=2:5,\mathrm{then}\frac{25p+14q}{5p+7q}= \\ \left(\mathrm{a}\right)8:5\left(\mathrm{b}\right)5:8\left(\mathrm{c}\right)8:3\left(\mathrm{d}\right)3:8 \end{gathered}$$

Answer 1

$$\begin{gathered} \mathrm{As},p:q=2:5 \\ \Rightarrow \frac{p}{q}=\frac{2}{5} \\ \mathrm{Let}p=2x\mathrm{and}q=5x \\ \mathrm{Now},\frac{25p+14q}{5p+7q} \\ =\frac{25\times 2x+14\times 5x}{5\times 2x+7\times 5x} \\ =\frac{50x+70x}{10x+35x} \\ =\frac{120x}{45x} \\ =\frac{8}{3} \\ =8:3 \end{gathered}$$

Hence, the correct alternative is option (c).