In a constituency, 85% of the total number of people on the electoral roll cast their votes during an election. 10% of the votes cast were declared invalid. If there were 3,00,000 people on the electoral roll, and Dharam secured 1,37,700 valid votes, what percentage of the total number of valid votes did Dharam secure?

Correct option is D

Given:

Total number of people on the electoral roll = 3,00,000

85% of people cast their votes.

10% of the votes cast were declared invalid.

Dharam secured 1,37,700 valid votes.

Formula Used:

The total number of valid votes can be calculated by finding 85% of 3,00,000 and then subtracting the invalid votes (10% of votes cast).

The percentage of valid votes secured by Dharam = (Votes secured by Dharam / Total valid votes) × 100.

Solution:

The total number of votes cast:

Total votes cast = 85% of 3,00,000

​$$\text{Total votes cast} = \frac{85}{100} \times 3,00,000 = 2,55,000$$​​

The number of invalid votes:

Invalid votes = 10% of 2,55,000

​$$\text{Invalid votes} = \frac{10}{100} \times 2,55,000 = 25,500$$​​

The total number of valid votes:

Valid votes = Total votes cast - Invalid votes

​$$\text{Valid votes} = 2,55,000 - 25,500 = 2,29,500$$​​

The percentage of valid votes secured by Dharam:

Percentage secured by Dharam = $$\frac{1,37,700}{2,29,500} \times 100 = 60\%$$​​