GATE DS&AI 2024 | GA Question: 5

Question

​​​​​​In an election, the share of valid votes received by the four candidates $\text{A, B, C}$, and $\mathrm{D}$ is represented by the pie chart shown. The total number of votes cast in the election were $1,15,000$, out of which $5,000$ were invalid.

Based on the data provided, the total number of valid votes received by the candidates $\mathrm{B}$ and $\mathrm{C}$ is

• A. $45,000$
• B. $49,500$
• C. $51,750$
• D. $54,000$

Answer 1

To find the total number of valid votes received by candidates B and C, we need to first calculate the number of valid votes represented by each percentage, then sum up the valid votes for candidates B and C.

Given:

Total valid votes = 115,000 - 5,000 (invalid votes) = 110,000

Candidate A: 40% of 110,000 = 0.4 * 110,000 = 44,000 votes

Candidate B: 25% of 110,000 = 0.25 * 110,000 = 27,500 votes

Candidate C: 20% of 110,000 = 0.2 * 110,000 = 22,000 votes

Candidate D: 15% of 110,000 = 0.15 * 110,000 = 16,500 votes

Now, the total number of valid votes received by candidates B and C:

B + C = 27,500 (votes for B) + 22,000 (votes for C) = 49,500 votes.

So, the total number of valid votes received by candidates B and C is 49,500.

Answer 2

Total Votes = 115000
Total Valid Votes  = 115000 - 5000 = 110000

Valid votes received by B and C combined = (20+25)/100 * (110000) = 49500

Answer 3

The total number of votes that are cast is $1,15,000$, out of which $5,000$ are invalid.

$\therefore \text{ Number of valid votes=Total votes-invalid votes}$

$\text{ Number of valid votes=1,15,000-5000=1,10,000}$

Let's calculate the total number of votes received by each candidate:

$$\small \begin{array}{|c|c|c|} \hline \textbf{Candidate} & \textbf{Votes %}& \textbf{Total number of votes received by candidates}  \\\hline \text{A} & 40 \%& \frac{1,10,000*40}{100}=44,000  \\\  \text{B} & 25\% &\frac{1,10,000*25}{100}=27,500 \\ \text{C} & 20 \% & \frac{1,10,000*20}{100}=22,000 \\ \text{D} & 15 \% & \frac{1,10,000*15}{100}=16,500\\\hline  \end{array}$$

From the above table, we can calculate the total number of votes received by candidate $B,C=27,500+22,000=49,500$

Option $(B)$ is correct.

Answer 4

B. 49500

Total no. of valid votes = total no. of votes cast - total no. of invalid votes = 1,15,000 - 5,000=1,10,000

Total no. of valid votes received by B and C is 45% of 1,10,000 = 45*1100=49500