In an election among three contestant P,Q and R. P gets 120% more votes than Q. P beats R by 350000 votes. Q beats R by 5% of the total votes. Find the total number of votes polled (in lakhs)
How to do easy way
To find the total number of votes polled, we can break down the problem into steps and solve each step one by one.
Step 1: Let's assume that Q gets x votes.
- Since P gets 120% more votes than Q, P will get x + 120% of x votes.
- 120% of x can be calculated as (120/100) * x, which is equal to 1.2x.
- Therefore, P will receive x + 1.2x = 2.2x votes.
Step 2: P beats R by 350000 votes.
- Since P got 2.2x votes and beat R by 350000 votes, R must have received 2.2x - 350000 votes.
Step 3: Q beats R by 5% of the total votes.
- Since Q got x votes and beat R by 5% of the total votes, R must have received x - 5% of the total votes.
- 5% of the total votes can be calculated as (5/100) * total votes = 0.05 * total votes.
Step 4: Equate the votes received by R from both steps 2 and 3.
2.2x - 350000 = x - 0.05 * total votes.
Step 5: Solve the equation for the total votes.
2.2x - x = 350000 + 0.05 * total votes.
1.2x = 350000 + 0.05 * total votes.
1.2x - 0.05 * total votes = 350000.
Step 6: Simplify the equation.
0.05 * total votes = 1.2x - 350000.
Step 7: Determine the value of x using the information given.
From the question, we know that Q beats R by 5% of the total votes, which means:
x - 0.05 * total votes = 0.
x = 0.05 * total votes.
Step 8: Substitute the value of x back into the equation from step 7.
0.05 * total votes = 1.2 * (0.05 * total votes) - 350000.
Step 9: Simplify and solve for total votes.
0.05 * total votes = 0.06 * total votes - 350000.
0.06 * total votes - 0.05 * total votes = 350000.
0.01 * total votes = 350000.
total votes = 350000 / 0.01.
total votes = 3,500,000 / 1.
total votes = 3,500,000.
Therefore, the total number of votes polled is 3,500,000 (in lakhs).
Step 1: Let's assume the number of votes that Q receives as x.
Step 2: P gets 120% more votes than Q, which means P receives (x + 120/100 * x) = (x + 1.2x) = 2.2x votes.
Step 3: P beats R by 350000 votes. So, P receives (R + 350000) votes.
Step 4: Q beats R by 5% of the total votes. So, Q receives (R + 5/100 * Total Votes) votes.
Step 5: From steps 2 and 3, we know that (2.2x - R) = 350000.
Step 6: From steps 4 and 5, we know that ((R + 5/100 * Total Votes) - R) = 0.05 * Total Votes.
Step 7: Simplifying step 5, we get 2.2x - R = 350000.
Step 8: Simplifying step 6, we get 0.05 * Total Votes = (R + 5/100 * Total Votes) - R.
Step 9: Simplifying step 8, we get 0.05 * Total Votes = 5/100 * Total Votes.
Step 10: Cancelling Total Votes on both sides, we get 0.05 = 5/100.
Step 11: Simplifying step 10, we get 0.05 = 0.05.
Step 12: This means that the equation is satisfied and we have the solution.
Step 13: Now, we can substitute the value of x in step 2 and solve for the actual number of votes polled.
Therefore, I apologize but there seems to be a mistake in the given information, as the equations cannot be solved correctly to find the total number of votes polled.
Looks like you found the easy way -- get someone else to do the work.
p = 2.2 q
p = r + 350000
q = r + .05(p+q+r)
Now just find p,q,r and add them up.