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Quiz: Ratio and Proportion

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Number of Questions: 25

Question: 11 -

A person covers the different distances by train, bus, and car in the ratio of 4: 3: 2. The ratio of the fair is 1: 2: 4 per km. The total expenditure as a fair is Rs 720. Find the total expenditure as fair on the train.

Options:

  1. 150

  2. 170

  3. 160

  4. 140

    5. Answer:

    160
    Solution:

    Distance covered in the ratio T: B: C = 4: 3: 2
    Fair ratio per km. T: B: C = 1: 2: 4
    So, the ratio of total fair T: B: C = 4: 6: 8

    Sum of the ratio of total fair = 18
    But ATQ, it is 720, so multiply 18 by 40.
    Now, multiply each and every ratio with 40.
    The total expenditure as fair on a train = 4*40=160

Question: 12 -

The ratio of income in two consecutive years is 2: 3 respectively. The ratio of their expenditure is 5: 9. Income of second-year is Rs 45000 and Expenditure of first-year is Rs 25000. Find the Savings in both years together.

Options:

  1. 8025

  2. 6075

  3. 7000

  4. 5000

    5. Answer:

    5000
    Solution:

    Let the First-year income = 2x
    And, Second-year income = 3x
    But ATQ, the second-year income = 45000
    So, x = 45000/3 = 15000
    Then, first-year income = 2*15000=30000

    Similarly,
    Let the first-year expenditure = 5y
    But ATQ, the first-year expenditure =25000
    So, y = 25000/5 = 5000
    Second-year expenditure = 9y= 9* 5000 = 45000

    Apply formula:

    Income = expenditure + savings
    Or, savings = income - expenditure
    Or, first-year savings = 30000- 25000 = 5000
    Similarly,
    Second-year savings = 45000- 45000 = 0

    Now, total saving in two years = first-year savings + second-year savings
    Or, Total saving = 5000+0 = 5000.

Question: 13 -

The price of silver-biscuit is directly proportional to the square of its weight. A person broke down the silver-biscuit in the ratio of 3: 2: 1, and faces a loss of Rs 4620. Find the initial price of silver-biscuit.

Options:

  1. 7520

  2. 7560

  3. 7540

  4. 7580

    5. Answer:

    7560
    Solution:

    Given ratio = 3: 2: 1
    Or, 3x: 2x: x
    The initial price= (6x)2 = 36x2
    After broke down the price = (3x)2: (2x)2: x2 = 9x2: 4x2: x2 = 14x2
    After breakdown, a loss of Rs. 4620 occurs.
    i.e., loss = initial price - final price
    Loss = 36x2 - 14x2 = 22x2
    22x2 = 4620
    Or, x2 =4620/22 = 210
    The initial price of silver-biscuit = 36*210 = 7560

Question: 14 -

The ratio of income of Pervez, Sunny, and Ashu is 3: 7: 4 and the ratio of their expenditure is 4: 3: 5 respectively. If Pervez saves Rs 300 out of 2400, find the savings of Ashu.

Options:

  1. 575

  2. 560

  3. 570

  4. 565

    5. Answer:

    575
    Solution:

    ATQ, income ratio of Pervez: Sunny: Ashu = 3: 7: 4
    Let the income of Pervez: Sunny: Ashu = 3x, 7x, 4x
    The income of Pervez = 3x = 2400 (given in the question)
    That means x = 2400/3 = 800
    Now, the income of Sunny = 7x = 7*800 = 5600
    Similarly the income of Ashu = 4x = 4*800 = 3200

    Now,
    Their expenditure is in the ratio of 4: 3: 5
    So, let their expenditure is 4y, 3y, 5y
    The expenditure of Pervez = income of Pervez - saving of Pervez
    Or, expenditure of Pervez = 4y = 2400-300 = 2100
    Or, y = 2100/4 = 525
    Here 4y comes from expenditure's ratio
    Similarly, the expenditure of Sunny = 3y = 3* 525 = 1575
    The expenditure of Ashu = 5y = 5*525 = 2625

    Saving's of Ashu = Income of Ashu - Expenditure of Ashu
    Saving's of Ashu = 3200- 2625 = 575

Question: 15 -

Pervez, Sunny, and Ashu Bhati alone can complete a piece of work in 30, 50, and 40 days. The ratio of their salaries of each day is 4: 3: 2 respectively. The total income of Parvez is Rs 144. Find the total income of Sunny.

Options:

  1. 195

  2. 190

  3. 185

  4. 180

    5. Answer:

    180
    Solution:

    Note: Total income = total days * per day salary

    Let per day salary of Pervez = 4
    Pervez can complete a piece of work in 30 days and his per day salary is 4
    So, the total income of Pervez = 30* 4 = 120

    Let per day salary of Sunny = 3

    Similarly, Sunny can complete the same work in 50 days and his per day salary is 3
    So, the total income of Sunny = 50 * 3 = 150

    Let per day salary of Ashu Bhati = 2
    Ashu Bhati can complete the same work in 40 days and his per day salary is 2
    So, the total income of Ashu Bhati = 40* 2 = 80

    Or, the ratio of total income of Pervez: Sunny: Ashu Bhati = 120: 150: 80                                            = 12: 15: 8
    That means total income of Pervez = 12, but according to the question it is 144.
    On multiplying 12 by 12, we get the original value.
    So, multiply each by 12.
    Hence, the total income of Pervez = 144
    Total income of Sunny = 15*12 = 180
    Total income of Ashu Bhati = 8*12 = 96