The ratio of P's and Q's ages is 5 : 7. If the difference between the present age of Q and the age of P six years hence is 2 then what is the total of present ages of P and Q?  Choose the correct choice from the following answers:
A) 52 years  B) 48 years  C) 56 years  D) Data inadequate  E) None of these
P⁄Q = 5⁄7   or, Q = 7⁄5P   Case I : Q – (P + 6) = 2   or, Q = P + 8   ∴ 7⁄5P = P + 8   or, 7P = 5P + 40   ∴ P = 40⁄2 = 20 and Q = 7⁄5 × 20 = 28   P + Q = 20 + 28= 
<gadget id="calculator">20 + 28</gadget>
<output>48</output>
48   Case II : (P + 6) – Q= 2   or, P + 6 – 7⁄5P = 2   or, P = –10 and Q = 14   ∴ P + Q = 10 + 14= 
<gadget id="calculator">10 + 14</gadget>
<output>24</output>
24 years   Answer Data inadequate
<result>D</result>
The ratio of P's and Q's ages is 5 : 7. If the difference between the present age of Q and the age of P six years hence is 2 then what is the total of present ages of P and Q?