Mixed Quantitative Aptitude Questions Set 208

Shubhra
  1. A person got a loan amount of Rs. 60000, from that some amount at simple interest of 12% per annum and the remaining at 10% per annum. If at the end of 3 years, he paid Rs. 79500 to settle the whole loan amount, and then find the amount borrowed at 10% per annum?
    Rs. 35000
    Rs. 25000
    Rs. 55000
    Rs. 65000
    Rs. 45000
    Option A
    According to the question,

    = > [(x* 12 * 3)/100] + [((60000 – x)* 10 * 3)/100] = 19500

    = > (36x/100) + 18000 – (30x/100) = 19500

    = > 18000 + (6x/100) = 19500

    = > (6x/100) = 19500 – 18000

    = > (6x/100) = 1500

    = > x = 25000

    The amount borrowed at 10 % per annum = 60000 – x = Rs. 35000

     

  2. A, B and C enter into a partnership by investing in the ratio of (3/7) : (5/3) : (7/6). After 6 months, A increased his investment by 50 %. If the total profit at the end of the year is Rs. 169800, then find the share of C?

    Rs. 38800
    Rs. 48800
    Rs. 58800
    Rs. 98800
    Rs. 68800
    Option C
    A, B and C enter into a partnership by investing in the ratio

    = > (3/7) : (5/3) : (7/6).

    = >18 : 70 : 49

    The shares of A, B and C

    = > [18 * 6 + 18 *(150/100)* 6] : [70 * 12] : [49 *12]

    = >270 : 840 : 588

    = >45 : 140 : 98

    Total profit = 169800

    283’s = 169800

    1’s = 600

    The share of C= 98 * 600 = Rs. 58800

     

  3. 5years ago, the age of the mother and daughter is in the ratio of 7: 2. Eight years after, the age of the mother and 5 years after the age of the daughter is in the ratio of 12 : 5. The average Present age of the mother, father, daughter and son is 25 years. The difference between the age of the father and his son is 25 years. Then find the present age of son?
    6 years
    10 years
    9years
    12 years
    14 years
    Option B
    5 years ago, the ratio of age of the mother and daughter = 7: 2 (7x, 2x)

    8 years after, the ratio of age of the mother and 5 years after, the age of daughter = 12: 5

    According to the question,

    (7x + 13)/(2x + 10) = (12/5)

    35x + 65 = 24x + 120

    11x = 55

    x = 5

    The present age of the mother and his daughter = (7x + 5), (2x + 5) = 40, 15

    The average Present age of the father, mother, son and daughter = 25

    Total Present age of the father, mother, son and daughter = 25 * 4 = 100

    Total present age of the father and his son = 100 – 55 = 45

    Let the present age of father and son be A and B,

    A + B = 45 —> (1)

    A – B = 25 —> (2)

    By solving the equation (1) and (2),

    A = 35, B = 10

    The present age of son = 10 years

     

  4. 1 and 2 together can complete the job in 20 days, 2 and 3 together can complete the job in 24 days. First 1 did the job for 8 days, 2 did the job for 14 days and 3 completed the remaining job in 20 days. Find the number of days in which 3 alone can complete the job?

    40 days
    10 days
    30 days
    50 days
    20 days
    Option A
    LCM of 20 and 24 = 120 units

    (1 + 2)’s one day work = 6 units

    (2 + 3)’s one day work = 5 units

    1’s 8days work + 2’s 14days work + 3’s 20 days work = 120

    (1 + 2)’s 8 days work + (2 + 3)’s 6days work + 3’s 14 days work = 120

    (8 * 6) + (5 * 6) + 3’s 14 days work = 120

    3’s 14 days work = 120 – 48 – 30 = 42

    3’s one day work = 42/14 = 3 units

    3 alone can complete the work in, (120/3) = 40 days

     

  5. Lalitha spent 20 % of her monthly salary on fruits, 18 % on education, 12 % on insurance and X % on other expenses. If the difference between the amount spent on education and insurance is Rs. 4500 and the saving is Rs. 22500, then find the value of X?

    20 %
    60 %
    50 %
    70 %
    10 %
    Option A
    According to the question,

    (18 % – 12 %) of salary = 4500

    6 % of salary = 4500

    Total salary = 4500* (100/6) = Rs. 75000 = 100 %

    Savings % = (22500/75000)* 100 = 30 %

    Total salary (100 %) = Expense (70 %) + Savings (30 %)

    Given,

    Expense = 70 %

    70 % = (20 % + 18 % + 12 % + X %)

    X % = 70 % – 50 % = 20 %

     

  6. A single letter is selected at random from the word ‘PROBABILITY’ . The probability that it is a vowel, is ?
    4/11
    7/11
    6/11
    5/11
    3/11
    Option A
    Total number of letters = n(S) = 11
    whereas, number of vowels = n(E) = 4
    ∴ Required probability = n(E)/n(s) = 4/11

     

  7. The probability of drawing a black card from a deck of playing cards is
    1/5
    1/4
    1/2
    1/6
    1/3
    Option C
    Total number of cards n(S) = 52
    Number of black cards n(E) = 26
    ∴ P(E) = n(E)/n(S) = 26/52 = 1/2

     

  8. The probability of getting a composite number when a six-faced unbiased die is tossed, is
    1/3
    1/2
    1/4
    1/6
    1/5
    Option A
    n(S) = 6, n(E) = (4, 6) = 2
    ∴ P(E) = 2/6 = 1/3

     

  9. When two dice are rolled, what is the probability that the sum of the numbers appeared on them is 11?
    5/18
    4/18
    1/18
    3/18
    2/18
    Option C
    n(S) = 36
    n(E) = {(5,6), (6,5)} = 2
    ∴ p(E) = n(E) / n(S) = 2/36 = 1/18

     

  10. Find the probability that a vowel selected at random from the 5 vowels is an ‘a’. ?
    1/5
    1
    4/5
    3/5
    2/5
    Option A
    Here, n(5) = {a, e, i,o, u}
    and E = Event of selecting the vowel a = {a}
    ∴ P(E)= n(E)/n(S) = 1/5

     

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