Mixed Quantitative Aptitude Questions Set 6

Shubhra
  1. While filling his age in a form, a student mistakenly filled his age 10% less than his actual age. To correct the age in the form, by how much percent he will have to increase his age, if his actual age is 15 years?
    A) 12 2/3%
    B) 11 1/9%
    C) 16 1/5%
    D) 16 2/3%
    E) 10 2/5%
    View Answer
    Option B
    Solution:
    To increase age, use:
    10/(100-10) * 100 = 100/9%
  2. Veena, Shweta and Charu started a business by investing Rs 2000, Rs 2500 and Rs 3000 respectively. After 8 months from start of business, due to some problem all of them withdrew Rs 500 for next 2 months. If after this they reinvest the withdrawn amount, then what is the share of Shweta out of a total profit of Rs 66,000 after a year?
    A) Rs 20,900
    B) Rs 33,700
    C) Rs 22,000
    D) Rs 37,000
    E) Rs 23,500
    View Answer
    Option C
    Solution:
    Let Veena = A, Shweta = B, Charu = C
    A invested 2000 for total 10 months (first 8 months and last 2 months) and 1500 for 2 months (9th and 10th month). Similarly with others. So A : B : C is
    2000*10 + 1,500*2 : 2500*10 + 2,000*2 : 3000*10 + 2,500*2
    23 : 29 : 35
    So B gets = [29/(23+29+35)] * 66,000 = (29/87) * 66,000 = 66000/3 = 22000
  3. A certain sum of money amounts to Rs 1320 in 2 yrs and to Rs 1410 in 3.5 yrs. Find the sum and the rate of interest.
    A) Rs 1360, 9%
    B) Rs 1400, 5%
    C) Rs 1220, 6%
    D) Rs 1200, 5%
    E) Rs 1100, 5%
    View Answer
    Option D
    Solution:
    SI for 1.5 yrs = 1410 – 1320 = Rs 90
    So, for 2 yrs SI = (90/1.5) * 2 = Rs 120
    Amount for 2 yrs is Rs 1320, so P = 1320 – 120 = Rs 1200
    This gives, r = 100*120/1200*2 = 5%
  4. A bag contains 3 red balls, 5 white balls and 4 green balls. 3 balls are drawn at random. What is the probability that at least 1 ball is white in color?
    A) 21/22
    B) 27/44
    C) 18/33
    D) 37/44
    E) None of these
    View Answer
    Option D
    Solution:
    For at least 1 white, we can have prob = 1 – none is white
    None is white means 3 balls from 7 balls (3 red + 4 green), ways are 7C3 = (7*6*5)/(3*2*1) = 35
    There are a total of 12 balls. Ways for drawing 3 balls is 12C3 = (12*11*10)/)3*2*1) = 220
    So prob. of none white = 7C3 / 12C3 = 35/220 = 7/44
    So prob. of at least 1 white = 1 – 7/44 = 37/44
  5. Bhavna’s age 8 years ago was four more than Anjali’s age that time. If the ratio of Bhavna’s age 8 years hence to Anjali’s age 8 years hence will be 7 : 6, what will be the ratio of Anjali’s age 4 years hence to Bhavna’s age that time
    A) 2 : 5
    B) 3 : 4
    C) 5 : 7
    D) 6 : 5
    E) 5 : 6
    View Answer
    Option E
    Solution:
    Let Anjali = A, Bhavna = B
    Let the present ages of A and B are x and y respectively.
    8 years ago, x-8 = (y-8) – 4. This gives x – y = -4
    After 8 years, x+8/ y+8 = 6/7. This gives 7x – 6y = -8
    Solve both equations, x = 16, y = 20
    So required ratio = (16+4) : (20+4) = 20 : 24 = 5 : 6
  6. The speed of the stream is 5 km/hr and speed of the boat in still water is 9 km/hr. if a boat takes 55 hrs to travel downstream from point A to B and coming back to point C midway between A and B, the what is the total distance travelled by the boat?
    A) 280 km
    B) 320 km
    C) 420 km
    D) 380 km
    E) 450 km
    View Answer
    Option C
    Solution:
    Downstream speed = 9+5 = 14
    Upstream speed = 9-5 = 4
    Let the distance from A to B is x km
    downstream distance = x, upstream distance is half of x because boat goes half way upstream, then
    x/14 + (x/2)/4 = 55
    solve, x = 280
    so boat covered 280 + 280/2
  7. Cylindrical vessel A having radius 7 cm ad height 10 cm contains water. Another cylindrical vessel B having radius 14 cm ad height 12 cm contains milk. Half of the water and half of the milk from both vessels is taken out and mixed in another vessel. Find the % of water (approximate) in the third vessel?
    A) 22%
    B) 12%
    C) 17%
    D) 18%
    E) 15%
    View Answer
    Option C
    Solution:
    Water in 1st vessel = volume of vessel A = (22/7)*7*7*10 = 1540 cm3
    Milk in 2nd vessel = volume of vessel B = (22/7)*14*14*12 = 7392 cm3
    In third vessel, water taken is 1540/2 = 770 cm3 and milk taken is 7392/2 = 3696 cm3
    So total is 770+3696 = 4516
    So percentage of water in third vessel = (770/4466)*100 = 17%
  8. Raman starts driving from city A with speed 60 km/hr. After 2 hours Ravish starts driving from the same place with speed 75 km/hr. Find the distance from city A they have covered when they meet.
    A) 480 km
    B) 800 km
    C) 600 km
    D) 570 km
    E) None of these
    View Answer
    Option C
    Solution:
    Raman’s speed = 60, so after 2 hrs when Ravish starts, Raman has covered 2*60 = 120 km
    Now Ravish also starts, in order to meet Raman, he has to cover 120 km with relative speed of 75-60 = 15 [because both travelling in same direction]
    So the time after which Ravish meets Raman is 120/15 = 8 hrs
    So distance that Ravish has travelled in 8 hours = 8*75 = 600 km = distance both have travelled
  9. A bag contains 50 paise, Re 1, and Rs 2 coins in the ratio 2 : 5 : 7 respectively. If the total value of money in bag is Rs 200, what is the total number of coins in the bag?
    A) 100
    B) 140
    C) 120
    D) 85
    E) 125
    View Answer
    Option B
    Solution:
    Coins – 2x, 5x, 7x, so
    Value of 50 paise coins = (50/100)*2x = x, of Re 1 coin = 1*5x = 5x, of Rs 2 coins = 2*7x = 14x
    So total value is x+5x+14x = 20x which equals 200, so x = 10
    Total coins = 2x+5x+7x = 14x = 140
  10. A is 25% more efficient than B. If A can complete a work in 20 days, then in how many days A and B together can complete twice the work?
    A) 23 1/3 days
    B) 22 2/9 days
    C) 26 2/7 days
    D) 20 1/4 days
    E) 22 2/5 days
    View Answer
    Option B
    Solution:
    Let efficiency of B is x, so of A = (125/100)*x = 5x/4
    So ratio of efficiencies = 5x/4 : x = 5 : 4
    So ratio of days = 4 : 5
    A can do in 24 days, so 4y = 20, y = 5
    So B can do in 5*5 = 25 days
    A+B can do 1 work in (20*25)/(20+25) = 100/9 days
    So twice work in (100/9)*2 = 200/9 days

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