Mixed Quantitative Aptitude Questions Set 205

Directions (1-4 ): Study the following information carefully and answer the given questions:

In a college have three different degrees D1, D2 and D3.

In 2013, the total number of students in the college is 120, in 40% are D1 students and 20% are D2 students.

In 2014, the number of students of D1 and D3 is 125% and 112.5% of the number of students of D1 and D3 students in previous year. The ratio of the number of students of D2 and D3 is 2:3.

In 2015, the number of students of D1, D2 and D3 is 40, 50 and 36 respectively.

In 2016, the total number of students in the college is 20% more than that of the number of students in 2014. The number of students of the D1, D2 and D3 in the ratio of 2:5:3.

In 2017, the number of students of D1, D2 and D3 is 8, 5 and 4 greater than the number of students in previous year respectively.

1. Sum of the D3 students in 2017 and 2013 together is approximately what percent of the total number of students in 2014 all the degrees together?
   71
   67
   55
   45
   82
   Option A
   2013:

   Total number of students = 120

   D1 = 40/100 * 120 = 48

   D2= 20/100 * 120 = 24

   D3 = 120 – (48 + 24) = 48

   2014:

   D1 = 125/100 * 48 = 60

   D3= 112.5/100 * 48 = 54

   D2= 2/3 * 54 = 36

   Total = 150

   2015:

   D1 = 40

   D2 = 50

   D3 = 36

   Total = 126

   2016:

   Total = 150 * 120/100 = 180

   D1= 2/10 * 180 = 36

   D2= 5/10 * 180 = 90

   D3 = 3/10 * 180 = 54

   2017:

   D1= 36 + 8 = 44

   D2 = 90 + 5 = 95

   D3 = 4 + 54 = 58

   Total = 44 + 95 + 58 = 197
   Required percentage = (58 + 48)/150 * 100 = 71%

    

2. What is the ratio of the sum of the D1 students in all the years together to sum of D2 students in all the years together?
   228:300
   18:313
   228:310
   228:313
   220:313
   Option D
   Required ratio = (48 + 60 + 40 + 36 + 44):(24 + 54 + 50 + 90 + 95)

   = 228:313

    

3. Difference between the total number of D3 students in 2016 and D1 students in 2015 together and the total number of D2 students in 2014 and 2013 together?
   13
   14
   16
   15
   17
   Option C
   Difference = (54 + 40) – (54 + 24) = 16

    

4. Total number of students in 2017 all the degrees together is approximately what percent more than that of the total number of students in 2013 of all the degrees together?
   45
   64
   66
   77
   78
   Option B
   Required percentage = (197 – 120)/120 * 100 = 64%

    

5. In a stationery the owner bought some sketches at rate of 18 sketches for Rs.126 and sold it at the rate of 24 sketches for Rs.216. If he earns the profit is Rs.130, then how many sketches he sold?
   260
   250
   230
   270
   220
   Option A
   Let the owner bought = 100x sketches

   CP = 126/18 * 100x = Rs.700x

   SP = 216/24 * 100x = Rs.900x

   Profit = 900x – 700x = Rs.200x

   200x/100x * 130 = 260

    

6. Man 1, 2 started the business with the investment in the ratio of 4:5. After 6 months man1 increased his investment by 25% and man2 increased his investment by 20%. At the end of one year the profit share of man2 is Rs.2200, find the total profit?
   3000
   1000
   5000
   4000
   2000
   Option D
   Profit ratio = (4x * 6 + 4x * 125/100 * 6):(5x * 6 + 5x * 120/100 * 6)

   = (24x + 30x):(30x + 36x)

   = 54:66 = 9:11

   Total profit = 20/11 * 2200 = 4000

    

7. Person 3 is 40% less efficient than person 1. Person1 and Person2 together can finish a piece of work in 10 days. Person2 and Person3 together can do it in 15 days. In how many days can Person1 alone finish the same piece of work?
   11
   15
   14
   12
   13
   Option D
   The efficiency ratio of Person 1 and 3 = 100 : 60 = 5 : 3

   The day ratio of 1 and 2 = 3 : 5 (3x, 5x)

   (1 + 2)’s one day work = 1/10

   (2 + 3)’s one day work = 1/15

   (1 – 3)’s one day work = (1/10) – (1/15) = 1/30

   According to the question,

   (1/3x) – (1/5x) = 1/30

   2x / (3x * 5x) = 1/30

   2/15x = 1/30

   60 = 15x

   x = 4

   Person1 alone can finish a work in = 3x = 12 days

    

8. The ratio of present ages of friend1 and friend2 of a man is 7 : 8 and the age of man is sum total ages of his friend2 and friend1. If the ratio of ages of friend1 after 3 years and the age of friend2 6 years ago is 4 : 3 then what will be the ratio of the present age of a man and the age of his friend1 after four years?
   7 : 5
   6 : 5
   9 : 6
   9 : 5
   10 : 5
   Option D
   The ratio of present ages of friend1 and friend2 of a boy = 7 : 8 (7x, 8x)

   The present age of man = 7x + 8x = 15x

   According to the question,

   (7x + 3) / (8x – 6) = 4/3

   21x + 9 = 32x – 24

   11x = 33

   x = 3

   friend1’s present age = 21 years

   friend2’s present age = 24 years

   Present age of man = 45 years

   Required ratio = 45 : (21 + 4) = 45 : 25 = 9 : 5

    

9. A merchant offers two successive discounts of 10 % and 15 % on a dress and is still able to earn 53 % profit. If he offers only 20 % discount, then what will be his profit percentage?
   60 %
   70 %
   30 %
   40 %
   50 %
   Option A
   Let us assume the marked price of the article be Rs. 100,

   Sp= 100 * (90/100) * (85/100) = Rs. 76.5

   (153/100) * Cp = 76.5

   Cp = 76.5 * (100/153) = Rs. 50

   If the merchant offers only 20 % discount, the profit % will be,

   Sp = 100 * (80/100) = Rs. 80

   Profit % = [(80 – 50)/50] * 100 = (30/50) * 100 = 60 %

    

10. In a box, there are 6 red balls and 4 green balls. Three balls are picked at random. What is the probability that two balls are red and one ball is green colour?
    1/6
    1/5
    1/4
    1/3
    1/2
    Option E
    Total probability n(S) = 10C3

    Required probability n(E) = 6C2 and 4C1

    P(E) = n(E)/n(S) = (6C2 and 4C1) / 10C3 = 1/2