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Quiz: Ratio and Proportion

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Number of Questions: 25

Question: 16 -

A bag contains Rs 410 in the form of Rs 5, Rs 2, and Rs 1 coins. The number of coins is in the ratio 4: 6: 9. So, find the number of 2 Rupees coins.

Options:

  1. 70

  2. 60

  3. 50

  4. 40

    5. Answer:

    60
    Solution:

    ATQ, if the ratio of coins = 4: 6: 9
    That means if Rs 5 coins are 4, Rs 2 coins are 6, and then Rs 1 coins are 9.

    According to the given ratio, the ratio of amounts = 5*4: 6*2: 9*1 = 20: 12: 9
    The sum of the ratios of the amounts = 20+12+9 = Rs 41
    But ATQ, it is Rs 410, which means multiply each ratio by 10
    i.e., new ratio = 40: 60: 90
    Now, 40*5: 60*2: 90*1 = 200: 120: 90

    The total amount in the form of two rupees coins = 120
    So, the two rupees coins = 120/2= 60

Question: 17 -

The ratio of land and water on earth is 1: 2. In the northern hemisphere, the ratio is 2: 3. What is the ratio in the southern hemisphere?

Options:

  1. 3:11

  2. 2:11

  3. 1:11

  4. 4:11

    5. Answer:

    4:11
    Solution:

    The ratio of land: water = 1: 2
    In the northern hemisphere the ration of land: water = 2: 3

    Note: Earth is divided equally into two hemispheres called northern hemisphere and southern hemisphere.

    i.e., the northern hemisphere is 50% of the total earth.

    We can say southern hemisphere = total area- northern hemisphere.

    To make the northern hemisphere 50% of the total area
    Multiply the ratio of the earth by 10 and northern hemisphere by 3
    Now, earth's ratio Land: water = 1*10: 2*10 = 10: 20............... (i)
    Northern hemisphere's ratio = 2*3: 3*3 = 6: 9...................... (ii)

    Subtract equation i by ii

    Hence, southern hemisphere = 10- 6: 20-9 = 4: 11

Question: 18 -

Rs 7800 are distributed among A, B, and C. The share of "A" is the ¾ of the share of B, and the share of B is the 2/3 of the share of C. Find the difference between the share of B and C.

Options:

  1. 1200

  2. 1250

  3. 800

  4. 1300

    5. Answer:

    1200
    Solution:

    The share of A: B is 3: 4
    The share of B: C is 2: 3

    Note: Whenever such form is given, multiply a to b, then b to b, and then b to c.

    i.e., A: B: C = 3*2: 4*2: 4*3
    Or, A: B: C = 6: 8: 12
    Or, A: B: C = 3: 4: 6
    Sun of ratios = 13
    Now, the share of B = [4/13] * 7800 = 2400
    Share of C = [6/13]* 7800 = 3600

    The difference between the share of B and C = 3600- 2400 = 1200

Question: 19 -

The ratio of copper and zinc in a 63 kg alloy is 4: 3. Some amount of copper is extracted from the alloy, and the ratio becomes 10: 9. How much copper is extracted?

Options:

  1. 6

  2. 8

  3. 10

  4. 12

    5. Answer:

    6
    Solution:

    Amount of copper in alloy = [copper ratio/ sum of ratios]* total quantity of alloy

    Copper = {4/7}* 63 = 36 kg
    Similarly, the amount of zinc in alloy = [3/7] * 63 = 27 kg
    Let the extracted copper from alloy = x kg
    Remaining copper in alloy = 36-x
    The new ratio = 10: 9
    i.e., 36-x: 27 = 10: 9
    36-x: 3 = 10: 1
    36-x = 10* 3
    36-x = 30
    x = 36-30 = 6 kg.
    Hence, the extracted amount of copper is 6 kg.

Question: 20 -

 B is inversely proportional to the cube of A. If B=3, A=2. If B = 8/9. Find the value of A.

Options:

  1. 3

  2. 6

  3. 4

  4. 5

    5. Answer:

    3
    Solution:

    As per the question, B is inversely proportional to A3
    i.e., B α 1/A3
    Or, B =k/ A3
    Given that, B=3, A=2
    So, 3 = k/ 8, or k=24
    Given that, B = 8/9
    So, 8/9 = 24/A3
    A3 = (9*24)/8 = 27
    So, A = 3√ 27 = 3