Three candidates P, Q and R participated in an election. P got 35% more votes than Q, and R got 15% more votes than Q. P overtook R by 2,412 votes. If 90% voters voted and no invalid or illegal votes were cast, then what was the number of voters in the voting list?

46,900

Let the votes of Q be 100x

P have 35% more votes than Q = 100x × 35% + 100x = 135x

R have 15% more votes than Q = 100x × 15% + 100x = 115x

P overtakes R by 2412 votes

135x - 115x = 2412

20x = 2412

x = 120.6

So, number of votes obtained by P = 135x = 135 × 120.6 = 16281

Number of votes obtained by Q = 100x = 100 ×120.6 = 12060

Number of votes obtained by R = 115x = 115 × 120.6 = 13869

Total votes obtained by all the 3 candidates = 16281 + 12060 + 13869 = 42210

Now, 90% of voters voted,

90% of x = 42210

x = 469

100x = 46900