Quantitative Aptitude: Time and Work Set 2

Time and Work Questions in Quantitative Aptitude section for SBI PO, IBPS PO, LIC, RBI, IPPB and other banking and insurance exams.

Directions (1-3): 18 men can complete a work in X days and 22 women can complete the same work in (X+5) days. The ratio of work done by 14 men and 11 women in same time is 8 : 3.

1. Find the value of X.
   A) 7 days
   B) 8 days
   C) 6 days
   D) 9 days
   E) 12 days
   
   View Answer

     Option A
   Explanation:
   The ratio of work done by 14 men and 11 women in same time is 8 : 3.
   So 14 men can complete the work in 3y days and 11 women in 8y days
   Now 18 men in X days and 14 in 3y days
   So 18 * X = 14 * 3y
   AND
   22 women in X+5 days and 11 in 8y days
   So 22 * (X+5) = 11 * 8y
   Divide both equations to find the value of X, X = 7 days
2. 6 men and 8 women work for 7 days on the same work and the remaining work is completed by 20 boys in 11 days. Find the number of days in which 25 boys can complete the whole work.
   A) 7 days
   B) 6 days
   C) 4 days
   D) 5 days
   E) 3 days
   
   View Answer

     Option C
   Explanation:
   18 m in 7 days, so 6 men in (18*7)/6 = 21 days
   22 w in 12 days, so 8 w in (22*12)/8 = 33 days
   They work for 7 days, so complete (1/21 + 1/33) * 7 = 6/11 work
   So remaining work = 5/11 – to be done by 20 boys in 11 days
   So let 25 men complete whole work in x days
   So
   20 * 11 * 5/11 = 25 * x * 1
   Solve, x = 4 days
3. Find the ratio of efficiencies of 6 men and 8 women together and 9 men and 6 women together.
   A) 34 : 23
   B) 25 : 31
   C) 24 : 29
   D) 29 : 22
   E) None of these
   
   View Answer

     Option C
   Explanation:
   18 m in 7 days, so 6 men in (18*7)/6 = 21 days
   22 w in 12 days, so 8 w in (22*12)/8 = 33 days
   So their 1 day work = 1/21 + 1/33 = 6/77
   18 m in 7 days, so 9 men in (18*7)/9 = 14 days
   22 w in 12 days, so 6 w in (22*12)/6 = 44 days
   So their 1 day work = 1/14 + 1/44 = 29/(4*77)
   So their efficiencies ratio = 6/77 :  29/(4*77)  = 24 : 29
4. A can complete the work in 60% less time than B. Beginning with the second day, the amount of work which can they do keeps of doubling. If in this way they can complete the work together in 2 days, then in how many days they can complete the work if their efficiencies remain constant?
   A) 2.5 days
   B) 3.5 days
   C) 4 days
   D) 3 days
   E) 5 days
   
   View Answer

     Option D
   Explanation:
   Days of A : B = 40 : 100 = 2 : 5
   Days in which A can complete work  = 2x, and B = 5x
   They complete the work in 2 days with their efficiencies doubling the second day.
   So (1/2x + 1/5x) + (1/4x + 1/10x) = 1/2  
   Solve, x = 21/10 days
   So A does work in 2 * 21/10 days = 21/5 days and B in 5 * 21/10 = 21/2 days
   So together:
   5/21 + 2/21 = 7/21 = 1/3 work in 1 day or whole work in 3 days
5. 50 persons are employed to complete a work in 30 days working 12 hours each day. Due to some reason, they work for only 10 hours for the first 15 days. After this, 10 persons leave the work and rest continues the work as before. How many more days are needed to complete the work than the actually estimated time?
   A) 11 1/4 days
   B) 12 2/3 days
   C) 10 1/2 days
   D) 12 days
   E) None of these
   
   View Answer

     Option A
   Explanation:
   50 men work for 10 hours for first 15 days. Let they complete x work
   So 50 * 12 * 30 * x = 50 * 10 * 15 * 1
   Solve, x = 5/12
   So remaining work = 7/12 which is to be done by 40 men (as 10 men leave after 15 days). Let they complete work in y days. So
   50 * 12 * 30 * 7/12 = 40 * 10 * y * 1
   So y = 105/4 days
   So extra days = 105/4 – 15 = 45/4 days
6. A, B and C have to complete a work. They decide to divide work in the ratio 2 : 3 : 5 respectively. Their rates of work is in the ratio 1 : 2 : 3. If it takes 12 days by A to complete his part of work, then how much of work can they complete in 8 days?
   A) 2/5
   B) 4/7
   C) 2/3
   D) 4/5
   E) 3/7
   
   View Answer

     Option D
   Explanation:
   Let total work = 2 +3 + 5 = 10
   So A completes 2 units of work in 12 days, so whole 10 units he can do in 10/2 *12 = 60 days
   Now ratio of their efficiencies = 1 : 2 : 3
   So days ratio = 1/1 : 1/2  : 1/3  = 6 : 3 : 2
   So 6x = 60, x = 10
   So A can complete work in 60 days, B in 3*10 = 30 days, C in 2*10 = 20 days
   So work together in 8 days = (1/60 + 1/30 + 1/20) * 8 = 4/5
7. There are two filling pipes A and B. If A fills bottom 3/4^th tank and B fills the rest tank, then they can fill the tank in 18 minutes. If B fills bottom 3/4^th tank and A fills the rest tank, then they can fill the tank in 22 minutes. What is the time taken by both the pipes to fill the tank together?
   A) 8 1/4 minutes
   B) 10 1/3 minutes
   C) 9 3/5 minutes
   D) 10 3/5 minutes
   E) None of these
   
   View Answer

     Option C
   Explanation:
   Let A can fill complete tank in x minutes, then 3/4 in 3/4 * x minutes
   Let B can fill tank in y minutes, so 1/4 in 1/4  * x minutes
   So from given information:
   3x/4 + y/4 = 18
   and x/4 + 3y/4 = 22
   Solve both the equations, x = 16, y = 24
   So together they complete 1/16 + 1/24 = 5/48 tank in 1 minute or whole tank in 48/5 minutes
8. An emptying pipe A can empty the tank in 30 minutes. It is opened in a tank which is full of water. After 12 minutes another pipe B which can fill the tank in 15 minutes is also opened. In what total time will the tank get filled again?
   A) 8 minutes
   B) 12 minutes
   C) 15 minutes
   D) 20 minutes
   E) 24 minutes
   
   View Answer

    Option E
   Explanation:
   A can empty the tank in 30 minutes, it is opened for 12 minutes, so it emptied 1/30 * 12 = 2/5 of tank
   Now 2/5 of this empty tank is to be filled by both the pipes
   When both pipes are opened together, in 1 minute they fill  = 1/15 – 1/30 = 1/30 of the tank
   So 2/5 tank in  2/5 * 30 = 12 minutes
   So total time = 12 + 12 = 24 minutes [earlier 12 minutes when A was opened, next 12 minutes when both opened]  
9. 2 groups A and B contain some people each.  Efficiencies of all people in group A is same while that in group B is same. 3 workers from group A and 6 from group B can complete the work in 20 days. 8 workers from group A and 4 from group B can complete the work in 10 days. Find the number of days in which 1 person from each group can complete the work working together.
   A) 96 days
   B) 72 days
   C) 90 days
   D) 54 days
   E) None of these
   
   View Answer

     Option B
   Explanation:
   The question is same as 3 m and 6 w complete work in 20 days. And 8 m and 4 w complete work in 10 days.
   So 3A + 6B = 20 => 60 A + 120B = 1
   And 8A + 4B = 10 => 80 A + 40B = 1
   So 60 A + 120B =  80 A + 40B
   80B = 20A
   B = A/4
   So – 8A + 4 * A/4 = 10
   or 9A = 10
   So 9 workers of group A can complete work in 10 days
   Required to find A + B = A + A/4 = 5A/4
   So
   9 * 10 = 5/4 * x
   Solve, x = 72 days
10. A and B can complete a work in 12 and 20 days respectively. After 4 days, they are joined by C who can complete the same work in 24 days, how much work will remain uncompleted after 2 more days?
    A) 53/60
    B) 41/60
    C) 13/60
    D) 11/60
    E) 7/60
    
    View Answer

      Option E
    Explanation:
    They work for 4 days. So complete
    (1/12 + 1/20) × 4 = 8/15 of work
    Now: In next 2 days all A, B, C completed
    (1/12 + 1/20 + 1/24) × 2 = 7/20 of work
    So total work completed = 8/15 + 7/20 = 53/60
    So remaining work = 1 – 53/60 = 7/60