Solution to Problems on Time and work ( problem 1 -10)

1. 5 men can  prepare 10 toys in 6 days working 6 hours a day. then in how many days can 12 men prepare 16 toys working 8 hrs a day ? (a) 12                              (b) 3 (c)15                               (d)10 Answer: (b) 3 Solution: We have to use the formula,            M1D1H1W2 = M2D2H2W1 Where,  M1 , D1 ,H1,W2 are the men, days, hours and work( 10 toys) required and this applies same for the M2, D2,H2 and W1. Note: The Work (W1) for the first equation has been multiplied on the right hand side and the work W2 has been multiplied on the Left hand side of the equation. All the values are given except for the value of D2. Put in the given values in the above formula, We get,                           5  x 6 x 6 x 16 = 12 x D2 x 8 x 10  Solving for D2,                                    D2 = 3 days             2. A can do a piece of work in 5 days, B can do it in 6 days. how log will they take if both work together? (a) 22/11                         (b)44/11 (c)51/11                          (d)30/11 Answer: (d) 30/11 days Solution: For such cases, where two different person can finish the same work in the different days and we are required to find the days in which they both can finish the work, we have to use the formula                                 Days ( both working together) =  (ab)/(a + b)  Where,                                  a is the number of days A can  finish the work ,                       and  b is the number of days B can finish the same work. Put the given values to get                                                  Days= (5 x 6)/( 5 + 6) = 30/11 days 3. A can a piece of work in 5 days and B can do it in 6 days. if C who can do the work in 12 days joins them, how log will they take to complete work? (a) 20/9                             (b)5/7 (c) 32/5                            (d)12/3 Answer: (a) 20/9                             Solution:  It the same kind of problem as in question 2 , its just one more men C joined the work. Then formula required is                                                   Days=  ( a x b x c)/(ab + bc + ac) Put in the values for A , B and C to get                                                  Days = ( 5 x 6 x 12)/(30 + 60 + 72)                                                             = (360)/( 162)                                                             = 20/9    4. A and B together can do a piece of work in 6 days and A can do it in 9 days. in how many days can B alone do it ? (a) 22                              (b)4 (c)18                              (d)24 Answer: (c)18     Solution: Given that A and B can do a work in 6 days and A alone can do it in 9 days. Then, Let B can do the same work in b days. Using the formula for calculating days when A and B work together.  i.e.                          Total Days = (ab)/(a + b) Given , Total Days = 6 , a = 9, Put these values in the above formula                                              6 = (9b)/(9 + b)                        =>   54 + 6b = 9b                        =>             3b = 54                        =>               b =  18 days 5. If 3 men or 4 women can reap a field in 43 days,  how log will 7 men and 5 women take to reap it ? (a) 20                               (b) 20 (c) 42                               (d) 12 Answer:     (d) 12 Solution: Work done by a man in one day = 1/( 43x3)              Work done by a woman in one day = 1/( 43x4)              Work done by a  7 man and 5 woman in 1 days = 7/129 + 5/172  Therefore, the days it will take them to complete the work = 1/( 7/129 + 5/172) = 516/43 = 12 days 6. If 12 men and 16 boys can finish of a piece of work in 5 days and 13 men and 24 boys can do in 4 days, how long will 7 men and 10 boys take to do it ? (a) 17/2                          (b) 32/4 (c) 58/8                          (d) 25/3 Answer: (d) 25/3 Solution: Let work done be 1 unit and the work done by a men is m and a boy is b. 1)Then it took 12 men and 16 boys to finish the work in 5 days or 5( 12m + `16b)= 1 2)And it took 13 men and 24 boys to finish the work in 4 days or 4( 13m + `24b) = 1 Equating both the equations to get                                                             5( 12m + `16) = 4( 13m + `24b)                                   60m + 80        =  52m + 96b                              or   8m = 16b                                        m = 2b That is a man does twice the job as a boy do. Then the first equation becomes  20 men completed the job in 5 days and 25 men completed the work in 4 days and we have to find how much time 12 men will take to do the job. Using the equation,                                      20x5 = 12xd2  om solving for d2, we have                                d2 = 100/12 = 25/3                             7.A certain number of men can do a work in 60 days. if there were 8 man less it could be finished in 10 days more how many men there? (a) 20                             (b)36 (c) 56                             (d) 32   Answer:  (c) 56 Solution: Let there are X men, using the equation                                     M1D1W2=M2D2W1 ( here w1=w2=1)                                 =>        X60 =( X-8)70                                                        =>         60X= 70X - 560                                 =>         10X = 560                                 =>             X = 56 There were 56 men.           8. A is thrice as fast as B, and is there fore able to finish a work in 60 days less than  B. find the time in which they in which they can do it working together? (a) 44.5                          (b)11.5 (c) 22.5                          (d)66.5  Answer: 22.5   Solution: Let it took B, D days to finish the work, and work done in 1 day by B = 1/D Then A took (D-60) days to finish it, and work don by A in 1 day = 1/(D-60) Given that A=3B = > 1/(D-60) = 3/(D)                                    => D = 3D - 180                                    => D=90 Therefore, Work Done in 1 day by A= 1/(30)              and   Work Done in 1 day by B= 1/(90) And Let they took X days to finish it together, Then                                                         X(1/30 + 1/90) = 1                                                        X(4/90) = 1                                                        X = 90/4  = 22.50 days  9. A can do a work in 6 days. B take 8 days to complete it. C  takes as long as A and B would take working together. how long will it take B and C, A and C, and A, B and C to complete the work together? (a) 12/5,24/11,12/7                  (b)8/3,7,11/5 (c) 15/2,22/3,18/5                    (d)8/3,19/5,21/9 Answer:(a) 12/5,24/11,12/7    Solution: A and B working together would take = 48/14 = 24/7 days Therefore,  C would take 24/7  days together. Now,  Time Taken by B and C together = (8x24/7)/(8 + 24/7)                                                                                  = 192/80 =48 /20 = 12/5 days Looking at the options, we can see that only option (a) has the correct value.  10. A is twice as good a workman as B. together, they finish the work in 14 days. in how many days can it be done by B separately ? (a) 48                              (b) 32 (c) 42                              (d) 50  Answer: (c) 42        Solution: Given that A is twice as good as B, then A would take half the days taken by B to complete the work. Let B take 2D days to complete the work then it would take A D days to complete the work. Using the equation for calculating of days when Two man work together and put the values to get                                       Days ( together) = (xy)/(x + y)                                   => 14 = (2DxD)(3D) = (2D/3)                                   => D= 21 days Therefore A could do it in 21 days and B would do it in 42 days.