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Quiz: Ratio and Proportion

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Number of Questions: 25

Question: 21 -

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

Options:

  1. 6:7

  2. 3 : 5

  3. 2 : 5

  4. 4 : 5

    5. Answer:

    4 : 5
    Solution:

    Let the third number be x.

    Then, first number = 120% of x = 120x = 6x
    100 5
    Second number = 150% of x = 150x = 3x
    100 2
     Ratio of first two numbers = 6x : 3x = 12x : 15x = 4 : 5.
    5 2

Question: 22 -

A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?

Options:

  1. Rs. 1500

  2. Rs. 500

  3. None of these

  4. Rs. 2000

    5. Answer:

    Rs. 2000
    Solution:

    Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.

    Then, 4x - 3x = 1000

     x = 1000.

     B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.

Question: 23 -

Vessels A and B contain mixtures of milk and water in the ratios 4: 5and 5: 1respectively. In what ratio should quantities of the mixture be taken from A and B to form a mixture in which milk to water is in the ratio 5: 4?

Options:

  1. 2: 5

  2. 4: 3

  3. 2: 3

  4. 5: 2

    5. Answer:

    5: 2
    Solution:

    Let the quantity of vessels A and B in the ratio x: y to form a mixture of water and milk in the ratio 4: 5.
    Or, Milk: water = 5: 4.
    From vessel A, milk: water = 4x/9: 5x/9
    From vessel B, milk: water = 5y/6: 1y/6

    Now, ATQ quantities of the mixture should be taken from A and B.
    Ratio of milk: water = [4x/9 +5y/6]: [5x/9+ 1y/6] = 5/4
    Take the LCM of 9 and 6 = 54
    Or, [24x + 45y]/54: [30x+9y]/54 = 5/4
    Or, [8x + 15 y]: [10x + 3y] = 5/4
    Or, [8x + 15y] * 4 = [10x + 3y] * 5
    Or, (60-15) y = (50-32) x
    Or, 45y = 18x
    Or, 5y = 2x
    Or, x: y = 5: 2
    Hence, the quantity of mixture should be taken from A and B in the ratio 5: 2.

Question: 24 -

In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quantity of water to be further added is:

Options:

  1. 40 litres

  2. 20 litres

  3. 60 litres

  4. 30 litres

    5. Answer:

    60 litres
    Solution:

    Quantity of milk = 60 x 2 litres = 40 litres.
    3

    Quantity of water in it = (60- 40) litres = 20 litres.

    New ratio = 1 : 2

    Let quantity of water to be added further be x litres.

    Then, milk : water = 40 .
    20 + x
    Now, 40 = 1
    20 + x 2

     20 + x = 80

     x = 60.

     Quantity of water to be added = 60 litres.

Question: 25 -

If 0.75 : x :: 5 : 8, then x is equal to:

Options:

  1. 1.25

  2. 1.30

  3. 1.12

  4. 1.2

    5. Answer:

    1.2
    Solution:

    (x x 5) = (0.75 x 8)    x =6/5= 1.205