In an election several candidates contested for a constituency. In any constituency, the winning candidate was the one who polled the highest number of votes, the first runner up was the one who polled the second highest number of votes, the second runner up was the one who polled the third highest number of votes, and so on. There were no ties (in terms of number of votes polled by the candidates) in any of the constituencies in this election.

In an electoral system, a securitydepositis the sum of money that acandidate is required to pay to the election commission before he or she is permitted to contest. Only the defeated candidates (i.e., one who is not the winning candidate) who fail to secure more than one sixth of the valid votes polled in the constituency, lose their security deposits.

The following table provides some incomplete information about votes polled in four constituencies: A, B, C and D, in this election.

Constituency | ||||

A | B | C | D | |

No. of candidates contesting | 10 | 12 | 5 | 8 |

Total No. of valid votes polled | 5,00,000 | 3,25,000 | 6,00,030 | |

No. of votes polled by the winning candidate | 2,75,000 | 48,750 | ||

No. of votes polled by the first runner up | 95,000 | 37,500 | ||

No. of votes polled by the second runner up | 30,000 | |||

% of valid votes polled by the third runner up | 10% |

The following additional facts are known:

- The first runner up polled 10,000 more votes than the second runner up in constituency A.
- None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled by any pair of candidates in this constituency was at least 10,000.
- The winning candidate in constituency D polled 5% of valid votes more than that of the first runner up. All the candidates who lost their security deposits while contesting for this constituency, put together, polled 35% of the valid votes.

**Question 1: **

What is the percentage of votes polled in total by all the candidates who lost their security deposits while contesting for constituency A?

**Show Answer**

**9**

**Question 2: **

How many candidates who contested in constituency B lost their security deposit?

**Show Answer**

**11**

**Question 3: **

What BEST can be concluded about the number of votes polled by the winning candidate in constituency C?

- 1,40,006
- less than 2,00,010
- 1,40,010
- between 1,40,005 and 1,40,010

**Show Answer**

**1**

**Question 4: **

What was the number of valid votes polled in constituency D?

- 1,75,000
- 1,50,000
- 1,25,000
- 62,500

**Show Answer**

**1**

**Question 5: **

The winning margin of a constituency is defined as the difference of votes polled by the winner and that of the first runner up. Which of the following CANNOT be the list of constituencies, in increasing order of winning margin?

- B, D, C, A
- D, B, C, A
- B, C, D, A
- D, C, B, A

**Show Answer**

**3**

**Question 6: **

For all the four constituencies taken together, what was the approximate number of votes polled by all the candidates who lost their security deposit expressed as a percentage of the total valid votes from these four constituencies?

- 23.91%
- 23.54%
- 32.00%
- 38.25%

**Show Answer**

**1**

**Question 1:**

Total valid votes in \(A =5,00,000\) Minimum no of valid votes required to save the security deposits \(=\frac{1}{6} \times 5,00,000=83,334\)

As per \(1^{\text {st }}\) additional information \(\Rightarrow\) the gap between \(1^{\text {st }}\) and \(2^{\text {nd }}\) runners up is 10,000 So the table for \(A \Rightarrow\) total \(\rightarrow 5,00,000\)

Winner \(\rightarrow 2,75,000\)

\(1^{\text {st }}\) runner up \(\rightarrow 55,000\)

2nd runner up \(\rightarrow 85,000\)

Total \(\rightarrow 4,55,000\)

The valid votes got by the other 7 candidates \(=5,00,000-4,55,000\)

\(=45,000\)

\(\therefore\) the \(\%\) of votes by the candidates who lost the security deposit is \(=\frac{45,000}{5,00,000} \times 100=9 \%\)

Answer: 9**Question 2:**

Total valid votes in A=3,25,000

Minimum no of valid votes required to save the security deposits \(=\frac{1}{6} \times 3,25,000=54,167\)

We can see the winner himself/herself has got 48,750 no of votes which is less than \(\frac{1}{6}\) th of the total votes.

\(\therefore\) all of the candidates got less than \(\frac{1}{6}\) th of the valid votes.

\(\therefore\) security deposits will be forfeited for all of the candidates as winner is exempted from this condition. (total no of such candidates \(=12-1=11)\)

Answer: 11**Question 3:**

As the additional information in condition (2)

The minimum difference in no of votes between any pair of candidates = 10,000 As there are 5 candidates in c, the possible distribution of valid is as follows.

Additional 30 votes can be distributed among them to maintain the gap at least 10,000. So the possible answer is 1,40,006

Option: 1**Question 4:**

Let the no of valid votes \(=100 x\)

The table looks like the following:

Total votes \(\rightarrow 100 x\)

Winner \(\rightarrow 39,375\)

\(1^{\text {st }} \rightarrow 37,500\)

\(2^{n d} \rightarrow 30,000\)

\(3^{\text {rd }} \rightarrow 10 x\)

Total \(\rightarrow 1,06,875\)

As the winner got 51 more than \(1^{\text {st }}\) runner up (as per 3 )

Total no of votes has to be more than

\(\frac{39,375+37,500+30,000}{0.9}\)

\(=1,10,208\)

\(\therefore\) option (62,500) is ruled out.

To eliminate two more options, lets consider 1,50,000 to be the correct one [as one option is less than \(\&\) the other one is the greater than this option]

\(\therefore 100 x=1,50,000\)

Total \(\rightarrow 1,50,000\)

Winner \(\rightarrow 45,000\)

\(1^{\text {st }} \rightarrow 37,500\)

\(2^{\text {nd }} \rightarrow 30,000\)

\(3^{\text {rd }} \rightarrow 15,000\)

Total \(\rightarrow 1,06,875\)

Minimum rates to save security deposits \(=\frac{1}{6} \times 1,50,000=25,000\)

So we can see except 3 candidates all others have lost their security deposits.

Candidates who saved their security deposits \(=(100-35) \%=65 \%\left[\right.\) as per \(3^{\text {rd }}\) additional inform]

\(\therefore 65 \%\) of \(1,50,000=97,500\)

\(\rightarrow\) which is less than 1,12,500

\(\therefore\) answer will be more than 1,50,000

Option: 1**Question 5:**

__Margins__

\(A \rightarrow 2,75,000-95,000=1,80,000\)

\(B \rightarrow\)

\(C \rightarrow 1,50,000-1,40,000=10,000\)

\(D \rightarrow 39,375-37,500=1,875\)

Clearly the margin in C is more than that of D. So clearly the sequence \(B , C , D , A\) is not possible.

Option: 3**Question 6:**

The no. of votes got by the candidates who has lost their security deposits is as follows

In A \(\rightarrow 45,000\)

In B \(\rightarrow 3,25,000-48,750=2,76,250\)

In C \(\rightarrow 0\)

In D \(\rightarrow 1,75,000-46,250-37,500-30,000=61250\)

Req %=\(\frac{3,82,500}{5,00,000+3,25,000+6,00,000+1,75,000} \times 100\)

\(=\frac{3,82,500}{16,00,000} \times 100=23.91 \%\)

Option: 1### CAT 2020 LRDI sets with Solutions

CAT 2020 LRDI set 1CAT 2020 LRDI set 2

CAT 2020 LRDI set 3

CAT 2020 LRDI set 4

CAT 2020 LRDI set 5

CAT 2020 LRDI set 6

CAT 2020 LRDI set 7

CAT 2020 LRDI set 8

CAT 2020 LRDI set 9

CAT 2020 LRDI set 10 [Current page]

CAT 2020 LRDI set 11

CAT 2020 LRDI set 12

CAT 2020 LRDI set 13

CAT 2020 LRDI set 14

CAT 2020 LRDI set 15