Mixed Quantitative Aptitude Questions Set 197

1. Find the rate of interest per annum, if the sum 4 times itself at simple interest in 12 years.
   22
   23
   25
   26
   27
   Option C
   Let the principle be x,
   SI = 4x – x = 3x
   Given,
   3x = (x * 12 * r)/100
   r = (100 / 12) * 3
   r = 25 %
   The rate of interest (r) = 25 %
   
   
    



2. Friend 1 and 2 are partners in a project. friend 1 contributes 5/8th of the capital for 8 months and friend 2 received 3/7th of the profit. How long friend 2’s money was used?
   15
   10
   5
   20
   25
   Option B
   The ratio of investment of F1 and 2 = (5/8) : (3/8) = 5 : 3
   The ratio of profit of F1 and 2 = (4/7) : (3/7) = 4 : 3
   Given,
   (5 * 8) / (3 * x) = (4/3)
   x = 10
   F2’s money used for 10 months
   
   
    



3. The ratio of age of friend 1, after 3 years and the age of friend 2, 5 years ago is 3 : 5. The sum of the present age of friend1 and friend 2 together is 58 years. Find the age of friend 1, 7 years hence?
   25
   26
   27
   28
   29
   Option A
   The ratio of age of f1, after 3 years and the age of F2, 5 years ago = 3 : 5 (3x, 5x)
   The present age of F1 and F2 = 3x – 3 and 5x + 5
   Given,
   3x – 3 + 5x + 5 = 58
   8x + 2 = 58
   8x = 56
   x = 7
   The age of F1, 7 years hence = 3x – 3 + 7 = 3x + 4 = 25 years
   
   
    



4. A person invested Rs. 40000 in SI at the rate of 2x % per annum for two years and the same amount is invested in CI at the same rate of interest. The interest received by him in CI is Rs. 576 more interest than the interest received by him in S.I.Find the rate of interest.
   10
   11
   12
   13
   14
   Option C
   CI – SI = 576
   40000 * [(1 + 2x/100)2 – 1] – (40000 * 2x * 2)/100 = 576
   40000 * ([(100 + 2x) /100]2 – 1) – 1600x = 576
   40000 * [(10000 + 400x + 4x2 – 10000)/10000] – 1600x = 576
   1600x + 16x2 – 1600x = 576
   16x2 = 576
   x2 = 36
   x = 6
   The rate of interest = 2x % = 12 %
   
   
    



5. A yacht takes two hours more to travel upstream than travel the same distance in downstream. If the distance travelled by the yacht is 120 km and the ratio of the speed of boat in still water to speed of stream is 5: 1, then what is the speed of the boat in still water?
   15
   20
   25
   30
   35
   Option C
   Distance = speed * time
   120/4x – 120/6x = 2
   (30 – 20)/x = 2
   10 = 2x
   = > x = 5
   Speed of the yacht in still water = 5 * 5 = 25 kmph
   
   
    



6. A plane covered a distance of 840 km in 14 hours. Ratio of the speed of train to speed of the plane is 4: 3 and the ratio of the speed of bus to train is 1: 2. In how much distance will the bus cover in 8 hours?
   300
   310
   320
   330
   340
   Option C
   Distance = Speed * Time
   Speed of plane = 840/14 = 60 kmph
   Speed of the train = 4/3 * 60 = 80 kmph
   Speed of the bus = ½ * 80 = 40 kmph
   Distance covered by in 8 hours = 40 * 8 = 320 km
   
   
    



7. A container contains 90 kg of the mixture of rice and wheat in the ratio of 5: 4 and 45 kg of the mixture is taken out. Then added x kg of the wheat in the remaining mixture, the ratio of the rice and wheat becomes 2: 3. Find the value of x
   17.5 kg
   18.5 kg
   19.5 kg
   15.5 kg
   16.5 kg
   Option
   rice = 5/9 * 90 = 50 kg
   Wheat = 4/9 * 36 = 40 kg
   rice in 45 kg = 5/9 * 45 = 25 kg
   Water in 45 kg = 4/9 * 45 = 20 kg
   (50 – 25)/(40 – 20 + x) = 2/3
   40 + 2x = 75
   2x = 35
   x = 17.5 kg
   
   
    



8. cistern A can fill a tank in 40 hours and ratio of the efficiency of cistern A to B is 3: 2. cistern B and C together can fill the tank in 30 hours. In how many hour cisterns A, B and pipe C together can fill the tank?
   17 (1/7) hours
   19 (1/7) hours
   16 (1/7) hours
   17 (1/5) hours
   13 (1/7) hours
   Option A
   The work done by A in one hour,
   A = 1/40
   The tank will be filed by B in,
   B = 3/2 * 40 = 60 hours
   Cistern B and C together can fill the tank in 30 hours,
   B + C = 1/30
   C = 1/30 – 1/60
   C = 1/60
   A + B + C = 1/40 + 1/60 + 1/60
   = (3 + 2 + 2)/120
   = 7/120
   Required time = 120/7 hours = The work done by A in one hour,
   A = 1/40
   The tank will be filed by B in,
   B = 3/2 * 40 = 60 hours
   Cistern B and pipe C together can fill the tank in 30 hours,
   B + C = 1/30
   C = 1/30 – 1/60
   C = 1/60
   A + B + C = 1/40 + 1/60 + 1/60
   = (3 + 2 + 2)/120
   = 7/120
   Required time = 120/7 hours = 17 (1/7) hours
   
   
   
    



9. The ratio of the ages of Akil and Bheema is 4: 5 and after 4 years the ratio of the ages of Bheema and Cimoan is 3: 4. If sum of the ages of Akil, Bheema, and Cimoan is 64 years, what is the present age of Bheema?
   10
   20
   30
   40
   50
   Option B
   A + B + C = 64
   A/B = 4/5
   A = (4/5) * B
   (B + 4)/(C + 4) = ¾
   3C + 12 = 4B + 16
   3C – 4B = 4
   3C = 4B + 4
   A + B + C = 64
   (4/5) * B + B + (4B + 4)/3 = 64
   12B + 15B + 20B + 20 = 64 * 15
   47B = 940
   B = 20 years