Quantitative Aptitude Questions for IBPS Exam Set – 31

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1. Two pipes A and B can fill a cistern in 37 1/2 minutes and 45 minutes resp. Both pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after
   A. 5 min
   B. 9 min
   C. 10 min
   D. 15 min
   
   Answer

   B. 9 min
   Explanation:
   Let B is turned off after ‘x’ min.
   Cistern fills in 30 min, this means pipe A works for 30 mins.
   37 1/2 min = 75/2 min
   1/(2/75) * 30 + 1/45 * x = 1
   
   
2. A boat takes 90 minutes less to travel 36 km downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 km/hr, the speed of stream is
   A. 2 km/hr
   B. 2.5 km/hr
   C. 3 km/hr
   D. 4 km/hr
   
   Answer

   A. 2 km/hr
   Explanation:
   Let speed of stream = x km/hr
   Speed downstream = 10+x, speed upstream = 10-x
   36/(10-x) – 36/(10+x) = 90/60
   
   
3. The sides of a rectangular field are in the ratio 3 : 4. If the area of the field is 7500 sq. m, the cost of fencing the field @ 25 paise per metre is
   A. Rs 55.50
   B. Rs 67.50
   C. Rs 86.50
   D. Rs 87.50
   
   Answer

   D. Rs 87.50
   Explanation:
   Length = 3x, breadth = 4x
   3x * 4x = 7500 gives x = 25
   Length = 75m, breadth = 100m
   Perimeter = 2(75+100) = 350m
   Cost of fencing = 350 * 0.25 = Rs 87.50
   
   
4. A and B can do a piece of work in 15 days and 20 days respectively. They start working on alternate days with B starting the work. In how many days the work will be completed.
   A. 17 days
   B. 18 2/3 days
   C. 16 1/4 days
   D. 17 1/4 days
   
   Answer

   D. 17 1/4 days
   Explanation:
   LCM (15, 20) = 60
   So total work = 60
   A’s efficiency = 60/15 = 4
   B’s efficiency = 60/20 = 3
   2 days work (A+B) = 4+3 = 7
   Multiply by 8 both side
   16 days work (A+B) = 56
   Remaining work = 60-56 = 4
   Now B’s turn on 17th day, he does work with efficiency 3
   Now remaining work = 4-3 = 1
   Now A’s turn, he will complete remaining work in 1/4 day
   So total 17 1/4 days.
   
   
   
5. One card is drawn from a pack of 52 cards. What is the probability that the card drawn is either a red card or a king?
   A. 1/2
   B. 6/13
   C. 7/13
   D. 15/26
   
   Answer

   C. 7/13
   Explanation:
   26C1/52C1 + 2C1/52C1
   
   
6. A and B start from the same place and have to travel a distance of 25 km. A leaves at 9 AM and walks at a speed of 4 km/hr, while B leaves at 11:30 AM on a bicycle at a speed of 9 km/hr. When do they meet?
   A. 12:00 noon
   B. 1:00 PM
   C. 1:30 PM
   D. 2:30 PM
   
   Answer

   C. 1:30 PM
   Explanation:
   At 11:30, i.e. after 2 n half hours from 9 AM, A (speed = 4 km/hr) has covered a distance of 5/2 * 4 = 10 km
   So now at 11:30 AM, A is 10 km far from B, B has to overcome this 10 km distance
   They are travelling in same direction, so relative speed = 9- 4 = 5 km/hr
   After 11:30 AM, they meet at 10/5 = 2 hrs
   11:30 + 2 hrs = 1:30 PM
   
   
7. Two trains start at the same time from A and B and proceed towards each other at 80 km/hr and 95 km/hr resp. When the trains meet, it is found that one has travelled 180 km more than the other. Find the distance between A and B.
   A. 210 km
   B. 2000 km
   C. 2100 km
   D. 2010 km
   
   Answer

   C. 2100 km
   If one has covered x km, then other has covered (x+180) km. The one with more speed (95) must have covered more distance (x+180).
   Since both start at same time, when they meet they have travelled equal time. So
   x/80 = (x+180)/95
   x = 960
   Total distance covered by them = x + x+180 = 2x+180 = 2*960 + 180 = 2100
   
   
8. A can finish a work in 15 days at 8 hrs a day. B can finish it in 6 2/3 days at 9 hrs a day. Find in how many days can they finish the work working together 10 hrs a day
   A. 4 days
   B. 6 days
   C. 10 days
   D. 40 days
   
   Answer

   A. 4 days
   Explanation:
   A completes a work in 15*8 = 120 hrs
   B completes a work in 20/3 *9 = 60 hrs
   So together they finish in 120*60/(120+60) = 40 hrs
   Since they work for 10 hrs a day, they complete work in 40/10 = 4 days
   
   
   
9. How many different groups can be selected for playing tennis out of 4 women and 3 men, there being one woman and one man on each side?
   A. 72
   B. 75
   C. 80
   D. 64
   
   Answer

   A. 72
   Explanation:
   For first group:
   For 1 woman out of 4 women, we have 4C1 ways
   For 1 man out of 3 men, we have 3C1 ways
   So total 4C1 * 3C1 = 12
   For second group: 3 women and 2 men left
   For 1 woman out of 3 women, we have 3C1 ways
   For 1 man out of 2 men, we have 2C1 ways
   So total 3C1 * 2C1 = 6
   So total different groups = 12*6 = 72
   
   
   
10. A certain number of men can do a work in 60 days. If there were 8 men more it could be finished in 10 days less. How many men are there?
    A. 20
    B. 30
    C. 40
    D. 50
    
    Answer

    C. 40
    Explanation:
    Let initially ‘x’ men, they work in 60 days
    ‘x+8’ men do work in (60-10) = 50 days. So
    x * 60 = (x+8) * 50
    x = 40