In an election, 25% of the total votes are invalid. If the winning candidate got 60% of the valid votes and 15,000 valid votes more than the losing candidate, find the total number of valid votes.

Option 2 : 75,000

**Given:**

In an election, 25% of the total votes are invalid.

The winning candidate got 60% the valid votes and 15,000 valid votes more than the losing candidate.

**Concepts used:**

Total votes = Valid votes + invalid votes

Valid votes = Votes obtained by winning candidate + votes obtained by losing candidate

**Calculation:**

In an election, 25% of the total votes are invalid.

Let total votes cast be x.

⇒ Invalid votes = 0.25x

⇒ Valid votes = Total votes – Invalid votes

⇒ Valid votes = x – 0.25x = 0.75x

The winning candidate got 60% of the valid votes and 15,000 valid votes more than the losing candidate.

⇒ Votes obtained by winning candidate = 0.60 × 0.75x = 0.45x

⇒ Votes obtained by losing candidate = 0.40 × 0.75x = 0.30x

⇒ 0.45x – 0.30x = 15,000

⇒ x = 15,000/0.15 = 1,00,000

⇒ Number of valid votes = 0.75x = 0.75 × 1,00,000 = 75,000

**∴**** Number of valid votes is equal to 75,000 votes.**