Mixed Quantitative Aptitude Questions Set 18

Quantitative Aptitude Questions for SBI PO, NIACL, NICL, IBPS PO, IBPS RRB and other exams

1. Pipe A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened to fill a tank. The time when the tank should be full, it was found that a leak pipe was also opened along with pipes A and B. It is turned off immediately and then after 5 minutes, the tank gets full. Find the time in which the leak pipe can empty the full tank?
   A) 720/49 minutes
   B) 728/49 minutes
   C) 829/49 minutes
   D) 832/49 minutes
   E) None of these
   
   View Answer

     Option A
   Solution:
   Pipes A and B can fill the tank in – 15*20/(15+20) = 60/7 minutes
   But along with leak pipe, it took 5 minutes more. Let leak pipe can empty tank in x minutes
   So A and B were opened for (60/7) + 5 = 95/7 minutes
   And the leak was opened for 60/7 minutes
   So (7/60) * 95/7 – (1/x) * 60/7 = 1
   Solve, x = 720/49 minutes
   
2. Two mixtures A and B contain milk and water in ratio 7 : 1 and 6 : 1 respectively. 48 litres of mixture A is mixed with some quantity of mixture B and the resultant mixture C has milk and water in ratio 13 : 2. If 14 litres of mixture C is taken out, find the remaining quantity of mixture C.
   A) 79 l
   B) 72 l
   C) 75 l
   D) 76 l
   E) 71 l
   
   View Answer

     Option D
   Solution:
   Milk in A = 7/8, in B = 6/7 and in C is 13/15
   So by allegation method
   (48 l)…………………………(x l)
   7/8……………………………6/7
   …………….13/15
   1/105……………………….1/120
   So ratio is 1/105 : 1/120 = 8 : 7
   So, 48/x = 8/7
   x = 42 l
   So quantity of C = 48+42 = 90l, SO after 14 l is removed, remaining = 90 – 14 = 76 l
   
3. A person wants to sell his chair and table. If he sells them at a total of Rs 525, he gets a profit of 20% on table and 10% on chair. But if he sells them at a total of Rs 510, he gets a profit of 10% on table and 20% on chair. Find the cost price of chair.
   A) Rs 250
   B) Rs 200
   C) Rs 150
   D) Rs 320
   E) Rs 270
   
   View Answer

     Option C
   Solution:
   When the profit % gets reversed, following formula can be used.
   Cost price of (table + chair) = [(525+510)]/(110% + 120%) =  1035/(1.10 + 1.20) = 450
   And Cost price of (table – chair) = [(525 – 510)]/(120% – 110%) =  15/(1.20 – 1.10) = 50   
   Solve both equations, CP of chair = Rs 150
4. A and B started a business. A invests Rs 400 less than B. A invests for 7 months while B invests for 8 months. If out of a total profit of Rs 7700, B got Rs 1100 more than A, then find the investment of B.
   A) Rs 2800
   B) Rs 2400
   C) Rs 2500
   D) Rs 2100
   E) Rs 2300
   
   View Answer

     Option A
   Solution:
   A’s investment = Rs x so B’s investment = (x+400)
   So ratio of shares of A and B is
   x * 7 : (x+400) * 8
   Now according to question, (x+400) * 8/[15x + 3200] * 7700 = 1100 + 7x/[15x + 3200] * 7700
   So , (x+400) * 8/[15x + 3200] * 7700  – 7x/[15x + 3200] * 7700  = 1100
   Gives [8x + 3200 – 7x] /[15x + 3200] * 7700  = 1100
   Gives [x + 3200] /[15x + 3200]   = 1/7
   Solve, x = Rs 2400
5. The difference between Simple Interest and Compound Interest after 3 years on a certain sum of money is Rs 12.16. If the rate % is 4% per annum, find the sum.
   A) Rs 2700
   B) Rs 3300
   C) Rs 3600
   D) Rs 2500
   E) None of these
   
   View Answer

     Option D
   Solution:
   Formula for difference between SI and CI for 3 years
   Difference = P * r²/100² * (300+r)/100
   So 12.16 = P * 16/10000 * 304/100
   So P = 1216 * 10000/(16 * 304) = 76*100*100/304 = Rs 2500
    
6. Ratio between the ages of Shilpa and Meera is 4 : 5 and that between Shilpa and Sheetal is 2 : 3. If the sum of ages and Shilpa and Meera is one and a half times of the age of Sheetal. Find the total sum of ages of all three.
   A) 64
   B) 87
   C) 83
   D) 76
   E) Cannot be determined
   
   View Answer

     Option E
   Solution:
   Meera/Shilpa = 5/4 and Shilpa/Sheetal = 2/3
   So Meera : Shilpa : Sheetal = 5*2 : 4*2 : 4*3 = 5 : 4 : 6
   Also given = (Shilpa + Meera) = 3/2 * Sheetal
   So (4x + 5x) = 3/2 * (6x) gives 9x = 9x, so cant be determined  
7. A bucket contains 2 red balls, 4 blue balls, and 6 white balls. Two balls are drawn at random. What is the probability that either both are blue or both are non-blue?
   A) 5/11
   B) 14/33
   C) 12/33
   D) 6/11
   E) 17/33
   
   View Answer

    Option E
    Solution:
   Two cases
   Case 1: both are blue
   Prob = ⁴C₂ / ¹²C₂ = 3/33
   Case 2: both non-blue (means red or white)
   Prob = ⁸C₂  / ¹²C₂ = 14/33.
   Add both cases
8. Amit, Aman and Anil start a business by investing Rs 2500, Rs 3500 and Rs x respectively. They invest for 7 months, 5 months and 7 months respectively.  If out of a total profit of Rs 6400, Anil got Rs 2400, find the total investment of all three.
   A) Rs 9150
   B) Rs 9600
   C) Rs 9000
   D) Rs 9250
   E) None of these
   
   View Answer

     Option C
   Solution:
   Ratio of shares of Amit : Aman : Anil is
   2500*7 : 3500*5 : x*7
   = 2500 : 2500 : x
   So x/(5000+x) * 6400 = 2400
   Solve, x = Rs 3000
   So total investment = 2500 + 3500 + 3000 = Rs 9000
   
9. A vessel is in the form of a hemi-spherical bowl on which is mounted a hollow cylinder. The diameter of the sphere is 14 cm and the total height of vessel is 25 cm, find the capacity of the vessel.
   A) 3450.45 cu cm
   B) 4450.28 cu cm
   C) 3490.67 cu cm
   D) 4950.49 cu cm
   E) 3830.27 cu cm
   
   View Answer

     Option C
   Solution: 
   Diameter is 14, so radius is 7 cm
   Total height = 25 cm, so height of cylinder = 25-7 = 18 cm (because height of hemisphere is same as its radius)
   Capacity of vessel = volume of cylinder + vol of hemisphere
   So                         = πr²h + 2/3 *πr³
   .                            = 22/7 * 7 * 7 * 18 + 2/3 * 22/7 * 7 * 7 * 7
   .                            = 2772 + 718.67
   .                            = 3490.67 cu cm
    
10. The average age of 8 persons increased by 2 when a new person comes in place of one of them whose age is 26 kg. What might be the age of the new person?
    A) 36 years
    B) 42 years
    C) 39 years
    D) 44 years
    E) 48 years
    
    View Answer

     Option B
     Solution:
    Total age increased = (8 * 2) = 16 years.
    Age of new person = (26 + 16) = 42 years.