Question

In a college election there were two candidates Ramesh and Suresh. Voting being compulsory for every students, 30% voted for Ramesh and out of the remaining 60% voted for Suresh but the remaining votes were declared invalid. If the difference between the number of votes Ramesh gets and invalid votes is 48. Calculate the total number of students in the college.

1. 1600
2. 1400
3. 2400
4. 3000
5. 3800

Answer 1

Correct Answer - Option 3 : 2400

Given:

Ramesh gets 30% votes

Suresh gets 60% of remaining votes

40% of remaining votes are invalid

Difference between invalid votes and Ramesh’s votes is 48

Concept:

Total votes is 100%

Total number of votes is sum of votes each candidate gets and invalid votes.

Calculation:

Let total number of students be x

Total number of votes Ramesh gets = 30% of x

⇒ Ramesh gets = (30/100 × x) votes = (3/10x) votes

Remaining = (100 – 30)% of x

⇒ Remaining = (70% of x) votes

⇒ Remaining = 70/100 × x = (7/10x) votes

Invalid votes = 40% of (7/10x) votes

⇒ Invalid votes = 28/100x = (7/25x) votes

(3/10x) – (7/25x) = 48

⇒ (15x – 14x)/50 = 48

⇒ x/50 = 48

⇒ x = 48 × 50

⇒ x = 2400

∴ Number of students in the college is 2400.