Percentage Problems and Solutions

• 1. In an election between two candidates, 75 % of the voters cast their votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes.

  1. 16800
  2. 15800
  3. 16700
  4. 15700

  Answer :

  Option A

  Explanation:

  Let the total number of votes enrolled are x.
  Number of votes cast = 75% of x
  Valid votes = 98% of 75% of x
  
  Now, as 9261 is the 75% of valid casted votes so,
  
  75% of 98% of 75% of x = 9261 [imporant]
  
  \begin{align}
  => \frac{75 \times 98 \times 75 \times x}{100 \times 100 \times 100} = 9261 \\
  
  => x = 16800
  \end{align}
  

• 2. Rahul's Mathematics test had 75 problems, 10 arithmetic, 30 algebra, 35 geometry problems. Although he answered 70% of arithmetic, 40% of arithmetic and 60% of geometry problems correctly, still he got less than 60% problems right. How many more questions he would have to answer more to get passed

  1. 5
  2. 6
  3. 7
  4. 8

  Answer :

  Option A

  Explanation:

  Number of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35)
  = 7 + 12 + 21 = 40.
  
  Questions to be answered correctly for 60% = 60% of total quations
  = 60 % of 75 = 45.
  
  He would have to answer 45 - 40 = 5

• 3. If sales tax is reduced from 5% to 4%, then what difference it will make if you purchase an item of Rs. 1000

  1. 10
  2. 20
  3. 30
  4. 40

  Answer :

  Option A

  Explanation:

  Clue: Answer will be 5% of 1000 - 4% of 1000

• 4. What is 15 percent of 34

  1. 5.10
  2. 4.10
  3. 3.10
  4. 2.10

  Answer :

  Option A

  Explanation:

  It will be 15% of 34
  = (15/100) * 34 = 5.10

• 5. Due to an increase in 30% in the price of eggs, 3 eggs less are available for Rs. 7.80. Find the present rate of eggs per dozen.

  1. Rs. 9.36
  2. Rs. 10.36
  3. Rs. 11.36
  4. Rs. 12.36

  Answer :

  Option A

  Explanation:

  Let the original price per egg be Rs x
  Then increased price will be,
  \begin{aligned}
  \left(\frac{130}{100}x\right) \\
  => \frac{7.80}{x}-\frac{7.80}{\frac{130}{100}x} = 3\\
  => \frac{7.80}{x}-\frac{780}{130x} = 3 \\
  => 390x = 234 \\
  => x = 0.6 \\
  
  \text{Actual price was Rs 0.6} \\
  \text{Present price per dozen will be} \\
  Rs.\left(12*\frac{130}{100}*0.6 \right) \\
  = Rs. 9.36
  \end{aligned}

• 6. Half of 1 percent written as decimal is

  1. 5
  2. 0.5
  3. 0.05
  4. 0.005

  Answer :

  Option D

  Explanation:

  It will be 1/2(1%) = 1/2(1/100) = 1/200 = 0.005

• 7. Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate got

  1. 55%
  2. 56%
  3. 57%
  4. 58%

  Answer :

  Option C

  Explanation:

  Total number of votes polled = (1136 + 7636 + 11628) = 20400
  
  So, Required percentage = 11628/20400 * 100 = 57%