Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
What should be the maximum value of $Q$ in the following equation? $5 P 9-7 Q 2+9 R 6=823$
(a)5
(b)6
(c)7
(d)9
(e)None of these
Answer
Answer (as printed): C
Explanation
$5 P 9-7 Q 2+9 R 6=823$ $$\begin{aligned} & \Rightarrow(500+10 P+9)-(700+10 Q+2)+ \\ & (900+10 R+6)=823 \\ & \Rightarrow(500+900-700)+10(P+R-Q)+(9+6-2)=823 \\ & \Rightarrow 700+10(P+R-Q)=810=700+110 \\ & \Rightarrow 10(P+R-Q)=110 \\ & \Rightarrow P+R-Q=11 \\ & \Rightarrow Q=(P+R-11) . \end{aligned}$$ To get maximum value of $Q$ we take $P=9$ and $R=9$. This gives $Q=(9+9-11)=7$. Hence, the maximum value of $Q$ is 7.
Explanation as extracted from the printed page; notation may be imperfect.