Arithmetic

Ratio, Proportion & Variation

Easy

In an election, there were four candidates and $80\%$ of the registered voters casted their votes. One of the candidates received $30 \%$ of the casted votes while the other three candidates received the remaining casted votes in the proportion $1: 2: 3$ . If the winner of the election received $2512$ votes more than the candidate with the second highest votes, then the number of registered voters was

$40192$

$62800$

$50240$

$60288$

✅ Correct Option: 2

We need to track multiple candidates and their vote counts.

Let us call the total number of registered voters = $N$

Since 80% of registered voters cast their votes:

Total votes cast = $0.8N$

One candidate received 30% of the cast votes:

Candidate A's votes = $30\% \times 0.8N = 0.3 \times 0.8N = 0.24N$

The remaining three candidates shared the leftover votes in the ratio 1:2:3:

Remaining votes = $0.8N - 0.24N = 0.56N$

When we have a ratio 1:2:3, the total parts = 1+2+3 = 6 parts

Candidate B gets $\tfrac{1}{6}$ of remaining votes = $\tfrac{1}{6} \times 0.56N = \tfrac{0.56N}{6}$

Candidate C gets $\tfrac{2}{6}$ of remaining votes = $\tfrac{2}{6} \times 0.56N = \tfrac{1.12N}{6}$

Candidate D gets $\tfrac{3}{6}$ of remaining votes = $\tfrac{3}{6} \times 0.56N = \tfrac{1.68N}{6}$

Simplifying these:

Candidate B: $\tfrac{0.56N}{6} = 0.0933N$

Candidate C: $\tfrac{1.12N}{6} = 0.1867N$

Candidate D: $\tfrac{1.68N}{6} = 0.28N$

Comparing all vote counts:

Candidate A: $0.24N$

Candidate B: $0.0933N$

Candidate C: $0.1867N$

Candidate D: $0.28N$

Winner: Candidate D with $0.28N$ votes

Second highest: Candidate A with $0.24N$ votes

The winner received 2512 votes more than the second-highest candidate:

$0.28N - 0.24N = 2512$

$0.04N = 2512$

$N = \dfrac{2512}{0.04} = 62800$

Therefore, the number of registered voters was 62800.

When dealing with ratio problems involving percentages, always convert everything to the same base (total registered voters in this case) to make comparisons easier.

CAT 2024 Slot 3

Rajesh and Vimal own $20$ hectares and $30$ hectares of agricultural land, respectively, which are entirely covered by wheat and mustard crops. The cultivation area of wheat and mustard in the land owned by Vimal are in the ratio of $5 : 3$ . If the total cultivation area of wheat and mustard are in the ratio $11: 9$ , then the ratio of cultivation area of wheat and mustard in the land owned by Rajesh is

CAT 2021 Slot 2

Anil, Bobby and Chintu jointly invest in a business and agree to share the overall profit in proportion to their investments. Anil's share of investment is $70\%$ . His share of profit decreases by Rs. $420$ if the overall profit goes down from $18\%$ to $15\%$ . Chintu's share of profit increases by Rs. $80$ if the overall profit goes up from $15\%$ to $17\%$ . The amount, in INR, invested by Bobby is

CAT 2022 Slot 1

In a village, the ratio of number of males to females is $5: 4$ . The ratio of number of literate males to literate females is $2 : 3$ . The ratio of the number of illiterate males to illiterate females is $4: 3$ . If $3600$ males in the village are literate, then the total number of females in the village is

CAT 2021 Slot 1

The amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days. The amount Sita and Neeta together earn in a day equals what Geeta alone earns in 2 days. The ratio of the daily earnings of the one who earns the most to that of the one who earns the least is

CAT 2018 Slot 2

The scores of Amal and Bimal in an examination are in the ratio $11:14$ . After an appeal, their scores increase by the same amount and their new scores are in the ratio $47 : 56$ . The ratio of Bimal's new score to that of his original score is

CAT 2020 Slot 1

An alloy is prepared by mixing three metals $A, B$ and $C$ in the proportion $3 : 4 :7$ by volume. Weights of the same volume of the metals $A, B$ and $C$ are in the ratio $5:2: 6.$ In $130$ kg of the alloy, the weight, in kg, of the metal $C$ is

Solution

Related questions:

Keyboard Shortcuts

CAT Past Year Questions (Topic-Wise)