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Ratio and Proportion Exercise 2

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  1. Question 1 of 23
    1. Question

    The ratio of the number of boys and girls in a college is 7: 8. If the percentage increase in the number of boys and girls be 20% and 10 % respectively, what will be the new ratio?

    Hint

    Originally, let the number of boys and girls in the college be 7x and 8x respectively.

    Their increased number is (120% of 7x) and (110% of 8x)

    ratio-and-proportion-q-62137.png

    ratio-and-proportion-q-62131.png

    ∴ Required ratio

    = ratio-and-proportion-q-62125.png

  2. Question 2 of 23
    2. Question

    In what proportion must a number be divided so that ¼ of the first part and ⅓ of the second part are together equal to ½ of the original number?

    Hint

    Let number be divided in ratio x : y. Then

    First part ratio-and-proportion-q-62112.png,

    second part ratio-and-proportion-q-62106.png

    Now, ratio-and-proportion-q-62100.png

  3. Question 3 of 23
    3. Question

    Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 28.8 kg of zinc has been consumed in it?

    Hint

    For 9 kg zinc, mixture melted = (9 + 11) kg.

    For 28.8 kg zinc, mixture melted

    = ratio-and-proportion-q-62094.png

  4. Question 4 of 23
    4. Question

    The Binary Ice-cream Shopper sells two flavours : Vanilla and Chocolate. On Friday, the ratio of Vanilla cones sold to Chocolate cones sold was 2 : 3. If the store had sold 4 more Vanilla cones, then, the ratio of Vanilla cones sold to the Chocolate cones sold would have been 3 : 4. How many Vanilla cones did the store sell on Friday?

    Hint

    ratio-and-proportion-q-62874.png and ratio-and-proportion-q-62868.png …(1)

    ∴ C = ratio-and-proportion-q-62862.png

    ⇒ ratio-and-proportion-q-62856.png [From (1)]

    where V denoted for vanilla and C for chocolate.

    ⇒ 4V + 16 = ratio-and-proportion-q-62850.png

    ⇒ 8V + 32 = 9V

    ⇒ V = 32

  5. Question 5 of 23
    5. Question

    The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is:

    Hint

    A : B = 2 : 3 = 2 × 5 : 3 × 5 = 10 : 15

    and B : C = 5 : 8 = 5 × 3 : 8 × 3 = 15 : 24

    Therefore, A : B : C = 10 : 15 : 24

    Let the numbers be 10x, 15x and 24x.

    Then, 10x + 15x + 24x = 98

    ⇒ 49x = 98

    ⇒ x = 2

    ⇒ Second number = 15x = 15 × 2 = 30

  6. Question 6 of 23
    6. Question

    The ratio of number of ladies to gents at a party was 1 : 2, but when 2 ladies and 2 gents left, the ratio became 1 : 3. How many people were originally present at the party?

    Hint

    Let number of ladies = x

    and, number of gents = 2x

    Now, ratio-and-proportion-q-62843.png

    ⇒ x = 4

    ∴ Total number of people originally present = 4 + 8 = 12

  7. Question 7 of 23
    7. Question

    A man divides his property so that his son’s share to his wife’s and the wife’s share to his daughter are both in the ratio 3 : 1. If the daughter gets Rs 10,000 less than the son, find the total worth of the property.

    Hint

    Let Son’s share = Rs S;

    Daughter’s share = Rs D;

    and Wife’s share = Rs W.

    Also, S : W = W : D = 3 : 1

    ∴ S : W : D = 9 : 3 : 1

    then S = 9x , D = x

    and 9x – x = 10,000

    ⇒ x = Rs 1250

    ∴ Total worth of the property

    = (9 + 3 + 1) x = 13x

    = 13 × 1250 = Rs 16,250

  8. Question 8 of 23
    8. Question

    Mrs X spends Rs 535 in purchasing some shirts and ties for her husband. If shirts cost Rs 43 each and the ties cost Rs 21 each, then what is the ratio of the shirts to the ties, that are purchased?

    Hint

    Let S denotes the shirts and T denotes the ties.

    We have, 43S + 21T = 535

    By hit and trial, S = 10, T = 5

    ⇒ 43 × 10 + 21 × 5 = 535

    ∴ Ratio of shirts to ties = 10 : 5 = 2 : 1

  9. Question 9 of 23
    9. Question

    The ratio between the number of passengers travelling by I and II class between the two railway stations is 1 : 50, whereas the ratio of I and II class fares between the same stations is 3 : 1. If on a particular day, Rs 1325 revenue collected from the passengers travelling between these stations, then what was the amount collected from the II class passengers?

    Hint

    Let, the number of passengers travelling by I and II class be x and 50x and fares of I and II class be 3y and y.

    ∴ Revenue is x × 3y + 50x × y = Rs 1325

    53xy = 1325

    ⇒ xy = 25

    ∴ Amount collected from the II class passengers

    = 50xy

    = 50 × 25

    = Rs 1250.

  10. Question 10 of 23
    10. Question

    Railway fares of 1st, 2nd and 3rd classes between two stations were in the ratio of 8 : 6 : 3. The fares of 1st and 2nd class were subsequently reduced by 1/6 and 1/12, respectively. If during a year, the ratio between the passengers of 1st, 2nd and 3rd classes was 9 : 12 : 26 and total amount collected by the sale of tickets was Rs 1088, then find the collection from the passengers of 1st, class.

    Hint

    Fare after reduction.

    1st classes2nd classes3rd classes
    8 – ⁸⁄₆6 – ⁶⁄₁₂3
    ²⁰⁄₃¹¹⁄₂3
    403318

    Ratio of revenue

    1st2nd3rd
    9 × 4012 × 3326 × 18

    Ratio of revenue of all three classes

    = 10 : 11 : 13

    ∴ Collection for 1st class

    ratio-and-proportion-q-63725.png

  11. Question 11 of 23
    11. Question

    The income of A and B are in the ratio 3 : 2 and expenses are in the ratio 5 : 3. If both save Rs 200, what is the income of A?

    Hint

    Let income of A = Rs 3x,

    income of B = Rs 2x

    and expenditure of A = Rs 5y,

    expenditure of B = Rs 3y

    Now, saving = income – expenditure

    ∴ 3x – 5y = 2x – 3y = 200

    ⇒ x = 2y and y = 200

    ∴ x = 400

    ∴ A’s income = Rs 1200

  12. Question 12 of 23
    12. Question

    A sum of money is divided among A, B and C in the ratio of 3¾ : 4 : 5.5. If the lowest share is Rs 30, then the total amount of money is

    Hint

    Let A’s share ratio-and-proportion-q-63719.png,

    B’s share = Rs 4x and

    C’s share = Rs 5.5x

    Given ratio-and-proportion-q-63713.png

    ∴ Total amount = 30 + 32 + 44 = Rs 106

  13. Question 13 of 23
    13. Question

    At a start of a seminar, the ratio of the number of male participants to the number of female participants was 3 : 1. During the tea break 16 participants left and 6 more female participants registered. The ratio of the male to the female participants now became 2 : 1. What was the total number of participants at the start of the seminar?

    Hint

    Let the number of male and female participants be 3x and x respectively.

    therefore total no. of participants are 4x.

    During the tea break, the number of male participants are

    ratio-and-proportion-q-63707.png … (i)

    and the number of female participants are

    ratio-and-proportion-q-63700.png … (ii)

    Now, ratio-and-proportion-q-63694.png

    ⇒ 3x – 12 = 2x + 4

    ⇒ x = 16

    Therefore, the total number of participants = 4 × 16 = 64.

  14. Question 14 of 23
    14. Question

    The ratio of the present ages of Sushma and Karishma is 6:7 respectively. The ratio of their ages 8 years hence would be 8:9 respectively. What would be the respective ratio of their ages after 12 years?

    Hint

    Let the present ages of Sushama and Karishma be 6x and 7x respectively.

    ∴ ratio-and-proportion-q-61332.png

    or 56x + 64 = 54x + 72

    ratio-and-proportion-q-61326.png

    Required ratio

    =ratio-and-proportion-q-61320.png

    = 9 : 10

  15. Question 15 of 23
    15. Question

    The ratio of the present ages of Smita and Kavita is 3:8 respectively. Seven years hence the respective ratio of their ages will be 4:9. What is Kavita’s present age?

    Hint

    Let the present ages of Smita and Kavita be 3x and 8x years respectively

    According to questions,

    ratio-and-proportion-q-61394.png

    ⇒ 32 x + 28 = 27x + 63

    ⇒ 32x – 27x = 63 – 28

    ⇒ 5x = 35

    ⇒ x = ratio-and-proportion-q-61387.png = 7

    ∴ Kavita’s present age = 8x = 8 × 7 = 56 years

  16. Question 16 of 23
    16. Question

    The average age of a man and his son is 48 years. The ratio of their ages is 5 : 3 respectively. What is the son’s age?

    Hint

    Let the ages of man and his son be 5x and 3x respectively.

    5x + 3x = 2 × 48

    ⇒ 8x = 96

    ⇒ x = ratio-and-proportion-q-61370.png = 12

    ∴ Son’s age = 12 × 3 = 36 years

  17. Question 17 of 23
    17. Question

    The ages of Nishi and Vinnee are in the ratio of 6 : 5 respectively. After 9 years the ratio of their ages will be 9 : 8. What is the difference in their ages?

    Hint

    Difference in age

    ratio-and-proportion-q-61364.png

    ratio-and-proportion-q-61358.png

    = 3 years

  18. Question 18 of 23
    18. Question

    The difference between the present ages of Arun and Deepak is 14 years. Seven years ago the ratio of their ages was 5 : 7 respectively. What is Deepak’s present age?

    Hint

    Let Arun’s present age be x years.

    Then, Deepak’s present age = (x + 14) years

    Then, ratio-and-proportion-q-61958.png

    ⇒ 7x – 5x = 35 + 49

    ratio-and-proportion-q-61951.png

    ∴ Deepak’s present age

    = 42 + 14 = 56 years

  19. Question 19 of 23
    19. Question

    At present Meena is eight times her daughter’s age. Eight years from now, the ratio of the ages of Meena and her daughter will be 10 : 3 respectively. What is Meena’s present age?

    Hint

    Present age of Meena

    = ratio-and-proportion-q-61945.png

    = ratio-and-proportion-q-61939.png

    = 32 years

  20. Question 20 of 23
    20. Question

    The ratio of the ages of a father and son is 17 : 7 respectively. 6 years ago the ratio of their ages was 3 : 1 respectively. What is the father’s present age?

    Hint

    Let the present age of father and son be 17x and 7x respectively.

    Then, ratio-and-proportion-q-61933.png

    ⇒ 21x – 17x = 18 – 6

    ⇒ x = 12 ÷ 4 =3

    ∴ Father’s present age

    = 17 × 3 = 51 years.

  21. Question 21 of 23
    21. Question

    The respective ratio of the present ages of Swati and Trupti is 4: 5. Six years hence the respective ratio of their ages will be 6 : 7. What is the difference between their ages?

    Hint

    Let the present ages be 4x and 5x respectively.

    Then, ratio-and-proportion-q-61927.png

    ⇒ 30x – 28x = 42 – 36

    ⇒ x = ⁶⁄₂ = 3

    ∴ Difference in age

    = 5x – 4x = x = 3 years

  22. Question 22 of 23
    22. Question

    The average age of three boys is 25 years and their ages are in the proportion 3: 5 : 7. The age of the youngest boy is:

    Hint

    Total age of 3 boys

    = (25 × 3) years

    = 75 years

    Ratio of their ages = 3 : 5 : 7.

    Age of the youngest boy

    = ratio-and-proportion-q-62082.png years

    = 15 years

  23. Question 23 of 23
    23. Question

    A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is Rs 35, how many coins of each type are there?

    Hint

    Let number of each type of coin = x. Then,

    1 × x + 0.50 × x + 0.25 x = 35

    ⇒ 1.75x = 35

    ⇒ x = 20 coins

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