Quantity of copper in 17.5kg of alloy \begin{align} & = \left( {17.5 \times \frac{5}{7}} \right){\text{kg}} \cr & = 12.5{\text{kg}}. \cr\end{align} Quantity of zinc in 17.5kg of alloy \begin{align} & = \left( {17.5 \times \frac{2}{7}} \right){\text{kg}} \cr & = 5{\text{kg}}. \cr & \therefore {\text{Required ratio}} \cr & = 12.5:\left( {5 + 1.25} \right) \cr & = 12.5:6.25 \cr & = 2:1. \cr\end{align}

If we go through normal method, It will be quite cumbersome, so,

We will solve this question through options.

Taking option a: It has P+Q = 3. The possible value of P/Q is 1/2 or 2/1.

Using 1/2, we see that on adding 2 in both the numerator and denominator we get 3/4 (not required value).

Similarly we check for 2/1, this will also not give the required value.

OPTION b:

We have 1/3 possible ratio.

Then, we get the final value as 3/5 (not = to 1/2)

Hence, rejected.

Option c:

Here we have 1/4 or 2/3.

Checking for 1/4 we get 3/6 = 1/2. Hence, the option is correct.

\begin{align} & {\text{A}}:{\text{B}}:{\text{C}} \cr & {\text{ }}8:9 \cr & \, \, \, \, \, \, \, \, \, 3:4 \cr & \boxed{8:9:12} \cr & 8x:9x:12x \cr & \therefore 8x \times 12x = 2400 \cr & \Rightarrow {x^2} = \frac{{2400}}{{12 \times 8}} \cr & \Rightarrow x = 5 \cr & \therefore {\text{B}} = 9 \times 5 = 45 \cr\end{align}

(a+b+c) = 3+4+7 = 14 and

c = 7 Then, (a+b+c):c = 2:1.

$\frac{{3x + 5}}{{5x - 2}} = \frac{2}{3}$ ⇒ Cross multiply the equation \begin{align} & 9x + 15 = 10x - 4 \cr & x = 19 \cr\end{align}