In a election among $3$ candidates P,Q and R.P gets $120$% more votes than Q.P beats R by 3,50,000 votes.Q beats R by 5% of the total votes.Find the total no of votes polled in lakhs.
MyApproach
P gets $120$% more votes than Q.
=>P gets $11$/$5$ ....1
=>P beats R by 3,50,000 votes. .....2
Unlike,First Eqn,the value is directly given.
Q beats R by 5% of the total votes.
=>Q gets $21$/$20$ x=The votes by which Q beat ....3
Let,Total number of votes polled be x.
I am not able to form any relation.
Can anyone guide me how to solve the problem?
The three equation are
$P=Q+1.2Q \Rightarrow P=2.2Q \Rightarrow \frac{P}{2.2}=Q\quad \color{blue}{(1)}$.
$1.2Q$ are $120\%$ of the votes of $Q$
$P=R+350,000 \quad \color{blue}{(2)}$
$Q=R+0.05\cdot (P+Q+R) \quad \color{blue}{(3)}$
P+Q+R are the total votes and $0.05\cdot (P+Q+R)$ are $5\%$ of it.
The third equation can be simplified. We can first collect the Q´s by substracting $0.05Q$ on both sides. And also collect the R´s.
$0.95Q=1.05R+0.05\cdot P$
Then solving (2) for $R$ gives $R=P-350,000 \quad \color{blue}{(4)}$
Inserting the expression for Q (1) and for R (4) in (3):
$0.95\cdot \frac{P}{2.2}=1.05\cdot (P-350,000)+0.05\cdot P$
Solve this equation for P. By using (1) and (4) you can calculate $Q$ and $R$, respectively.
Hint: $P=550,000$