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Percentage Test - 2

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Percentage Test - 2
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Weekly Quiz Competition
  • Question 1
    2 / -0.83

    In an election contested by two parties A and B, party A secured 25 percent of the total votes more than Party B. If party B gets 15000 votes. By how much votes does party B loses the election?

    Solution

    Let total votes = T and party B gets 15000 votes then party A will get T -15000 votes
    T –15000 –15000 = 25T/100
    T = 40000, so A get 25000 and B gets 15000 votes, so difference = 10000

  • Question 2
    2 / -0.83

    A vendor sells 50 percent of apples he had and throws away 20 percent of the remainder. Next day he sells 60 percent of the remainder and throws away the rest. What percent of his apples does the vendor throw?

    Solution

    Let total apples be 100
    first day he throws = 50*20/100 = 10 apples
    next day he throws = 40*40/100 = 16 apples
    so total = 26

  • Question 3
    2 / -0.83

    40% of the women are above 30 years of age and 80 percent of the women are less than or equal to 50 years of age. 20 percent of all women play basketball. If 30 percent of the women above the age of 50 plays basketball, what percent of players are less than or equal to 50 years?

    Solution

    take total women =100
    Women less than or equal to 50 years = 80 and women above 50 years = 20
    20 = women plays basketball
    30% of the women above 50 plays basketball = 6
    So remaining 14 women who plays basketball are less than or equal to 50 years
    So (14/20)*100 = 70%

  • Question 4
    2 / -0.83

    Alisha goes to a supermarket and bought things worth rupees 60, out of which 40 paise went on sales tax. If the tax rate is 10 percent, then what was the cost of tax free items?

    Solution

    tax = 40/100 = (10/100)*T, T = 4
    so cost of tax free items = 60 –4 –0.40 = 55.60

  • Question 5
    2 / -0.83

    60 percent of the employees of a company are women and 75% of the women earn 20000 or more in a month. Total number of employees who earns more than 20000 per month in the company is 60 percent of the total employees. What fraction of men earns less than 20000 per month?

    Solution

    let total employees are 100
    males = 40 and females = 60 (45 women earns more than 20000)
    total 60 employee earns more than 20000 per month, so number of males earns more than 20000 is 15
    so fraction = 25/40 = 5/8

  • Question 6
    2 / -0.83

    In a library, 30% of the books are in History. 50% of the remaining are in English and  40% of the remaining are in German. The remaining  4200 books are in regional languages. What is the total number of books in library?

    Solution

    Step 1: Let ’s Define the Total Number of Books

    Let  T  represent the total number of books in the library.

    Step 2: Calculate the Number of History Books

    30% of the total books are in History.

    Number of History books = 30% of T = 0.30 ×T

    Step 3: Calculate the Remaining Books After History

    Remaining books after History = T - 0.30T = 0.70T

    Step 4: Calculate the Number of English Books

    50% of the remaining books are in English.

    Number of English books = 50% of 0.70T = 0.50 ×0.70T = 0.35T

    Step 5: Calculate the Remaining Books After English

    Remaining books after English = 0.70T - 0.35T = 0.35T

    Step 6: Calculate the Number of German Books

    40% of the subsequent remaining books are in German.

    Number of German books = 40% of 0.35T = 0.40 ×0.35T = 0.14T

    Step 7: Calculate the Remaining Books After German

    Remaining books after German = 0.35T - 0.14T = 0.21T

    Step 8: Set Up the Equation for Regional Languages

    The remaining books are in regional languages, and it is given that:

    0.21T = 4200

    Step 9: Solve for T (Total Number of Books)

    T = 4200 / 0.21 = 20,000

     

  • Question 7
    2 / -0.83

    A got  30% of the maximum marks in an examination and failed by 10 marks. However, B who took the same examination got  40% of the total marks and got 15 marks more than the passing marks. What were the passing marks in the examination?

    Solution

    (30/100)*T = P -10
    (40/100)*T = P + 15
    U will get P = 85

  • Question 8
    2 / -0.83

    The population of a town is 15000. It increases by 10 percent in the first year and 20 percent in the second year. But in the third year it decreases by 10 percent. What will be the population after 3 years.

    Solution

    15000*(11/10)*(12/10)*(9/10) = 17820

  • Question 9
    2 / -0.83

    30 litre of solution contains alcohol and water in the ratio 2:3. How much alcohol must be added to the solution to make a solution containing 60% of alcohol?

    Solution

    alcohol = 30*2/5 = 12 and water = 18 litres 
    (12 + x)/(30 +x) = 60/100, we will get x = 15

  • Question 10
    2 / -0.83

    2000 sweets need to be distributed equally among the school students in such a way that each student gets sweet equal to 20% of total students. Then the number of sweets, each student gets.

    Solution

    Let nnn be the total number of students. According to the problem, each student receives sweets equal to 20% of the total number of students, which can be expressed as 0.2n.

  • Question 11
    2 / -0.83

    A reduction of 20% percent in the price of rice enables a housewife to buy 5 kg more for rupees 1200. The reduced price per kg of rice.

    Solution

    let original price is x rupees per kg
    1200/(4x/5) –1200/x = 5
    We will get x = 60, so reduced price = (4*60)/5 = 48

  • Question 12
    2 / -0.83

    The population of a village has increased annually at the rate of 20%. If at the end of 3 years it is 21600, the population in the beginning of the first year?

    Solution

    • The population increases by 20% annually, meaning it multiplies by 1.20 each year.
    • After 3 years, the population is 21600.
    • Using the compound growth formula P=P0 (1+r)t , where P = 21600, r = 0.20, and t = 3, we calculate the initial population P0 .
    • Solving 21600=P0   x (1.20)3 , we find P0   = 12500.
    • The initial population is therefore 12500 .

  • Question 13
    2 / -0.83

    12 percent of the voters in an election did not cast their votes. In this election there are only two candidates. The winner by obtaining 45% of the total votes and defeated his rival by 2000 votes. The total number of votes in the election.

    Solution

    12% percent didn ’t cast their vote. 45% of total votes get by the winning candidates, so remaining 43% will be scored by his rival. So,
    (45/100 -43/100)*P = 2000
    P = 100000

  • Question 14
    2 / -0.83

    A number is first decreased by 25%. The decreased number is then increased by 20%. The resulting number is less than the original number by 40. Then the original number is –

    Solution

    Let the number is a
    a –(75/100)*a*(120/100) = 40
    we will get a = 400

  • Question 15
    2 / -0.83

    The number of seats in a cinema hall is decreased by 8% and also the price of the ticket is increased by 4 percent. What is the effect on the revenue collected?

    Solution

    Let initially seats are 100 and price of each seat is 100, so total initial revenue = 10000
    now, seats are 92 and price of each seat = 104, so total revenue = 92*104 = 9568
    so percent change in revenue = (432/10000)*100 = 4.32 decrease

  • Question 16
    2 / -0.83

    A man spends 60% of his income. His income is increased by 20% and his expenditure also increases by 10%. Find the percentage decrease/increase in his savings?

    Solution

  • Question 17
    2 / -0.83

    Weights of two friends A and B are in the ratio of 1:2. A ’s weight increases by 20% and the total weight of A and B together becomes 60 kg, with an increase of 30%. By what percent the weight of B increase?

    Solution

    weight of A is x and weight of B is 2x
    given that 60 kg weight is the 30% percent increase of the original weight, so
    (130/100)*W = 60, W = 600/13 kg (W = original weight)
    X + 2x = 600/13, x = 200/13
    So weight of A = 200/13 and of B = 400/13
    (120/100)*(200/13) + [(100 + a)/100]*(400/13) = 60
    Solve for a. We will get a = 35%

  • Question 18
    2 / -0.83

    The marked price of an article is 20% higher than the cost price. A discount of 20% is given on the marked price. In this transaction the seller.

    Solution

    let cost price = 100 so, marked price = 120
    now discount of 20% is given, so sp = 120*80/100 = 96
    so % loss = (4/100)*100 = 4 percent

  • Question 19
    2 / -0.83

    When the price of rice is increased by 30 percent, a family reduces its consumption such that the expenditure is only 20 percent more than before. If 50 kg of rice is consumed by family before, then find the new consumption of family (approx.)

    Solution

    Suppose initially price per kg of rice is 100 then their expenditure is 5000.
    Now their expenditure is only increased by only 20% i.e –6000.
    Increased price of rice = 130.
    So new consumption = 6000/130 = 46

  • Question 20
    2 / -0.83

    A man has 4000 rupees in his account two years ago. In the first year he deposited 20 percent of the amount in his account. In the next year he deposited 10 percent of the increased amount in the account. Find the total amount in the account of the person after 2 years.

    Solution

    4000 + 800 + 480 = 5280

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