Wednesday, 31 August 2016

कार्य समय : Maths Time and Work Short Tricks In Hindi कार्य समय शार्ट ट्रिक्स

Time and work short Tricks in Hindi कार्य समय शार्ट ट्रिक्स 

In this post we are going to share some most important short tricks of Time and work problem which is very important for those candidates who are appearing in the various competitive examination. With the help of following tricks aspirants will able to solve numerical problems based on time and work.

Introduction:
  1. If A done a work in n days, then his work of one day = 1/n part.
  2. If work of one day of A is 1/n part, then to complete his full work he needs n days.
  3. If ratio of  working people is X:Y, then ratio of time taken by them will be Y:X.
  4. If ratio of working capacity of A and B is a:b, then ratio of time to complete same work by them will be b:a.
Type and Time Work Short trick 1:-


     If A and B finish any work alone in sequentially X days and Y days, then time to complete that work together  =  XY / (X+Y) days.
or
Time to complete that work by A and B together    =    L/{(L/X)+(L/Y)}days
                                                                                        ,[there L= LCM of X and Y]


Example :- If Mohan and Sunil alone complete a work sequentially in 16 days and 24 days. then how much days did they need to complete that work together?

Important questions Asked in Exam



Ex. 1.
A and B undertake to do a piece of work for Rs 600. A alone can do it-in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days.
Find the share of each.
और B एक काम को 600Rs मे करते है। A अकेले उस काम को 6 दिन मे जबकि B इस काम को 8 दिन मे कर सकता है। C की हेल्प से वे इस काम को 3 दिन मे पूरा कर लेते है। सभी के हिस्से ज्ञात करो।
Sol.
C’s 1 day’s work = 1/3 - (1/6 +1/8) = 1/24
.. A: B : C = Ratio of their 1 day’s work =1/6 : 1/8:1/24
= 4:3:1
.. A’s share = Rs. (600 x 4/8)= Rs. 300,
B’s share = Rs. (600 x 3/8)= Rs. 225.
C’s share = Rs. [600 — (300 + 225)] = Rs. 75.
Ex. 2.
45 men can complete a work in 16 days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining
work?
एक काम को 45 आदमी 16 दिन मे करते है। 6 दिन बाद वो काम करना प्रारम्भ करते है। 30 आदमी और जॉइन करते हैकितने दिन और लगेंगे बचे हुए काम करने के लिए।
Sol
(45 x 16) men can complete the work in 1 day.
1 man’s 1 day’s work = 1/720
45 men’s 6 days’ work = (1/16 x 6 =3/8 
Remaining work = (1-3/8 = 5/8
75 men 1 day s work = 75/720
=5/48
Now, 5/48 work is done by them in 1 day.
5/8 work is done by them in (48/5)x(5/8)= 6 days.
Ex. 3
2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boy,  can do the same work in 8 days. In how many days can 2 men and 1 boy do the
एक काम को 2 आदमी और 3 लड़के 10 दिन मे करते हैजबकि उसी काम को 3 आदमी और 2 लड़के 8 दिन मे पूरा करते है। अब बताओ की 2 आदमी और 1 लड़का उसी कम को कितने दिन मे पूरा करेंगे।
Sol
Let 1 man’s 1 day’s work = x and 1 boy’s 1 day’s work = y.
Then. 2x + 3y = 1/10 and 3x + 2y 1/8
Solving, we get: x = 7/200 and  y =1/100
(2 men + 1 boy)’s 1 day’s work = (2 x(7/200) +(1x(1/100) = 16/200 = 2/25
So, 2 men and 1 boy together can finish the work in = 25/2
= 12 (1/2) days

Type and Time Work Short trick 2:-


      If A, B and C finish any work alone in sequentially X days, Y days and Z days, then time to complete that work together  =  XYZ / (XY+YZ+ZX) days.
                                                                                  or
Time to complete that work by A, B and C together    =    L/{(L/X)+(L/Y)+(L/Z)}days
                                                                                        ,[there L= LCM of X, Y and Z]
Example :- If A , B and C alone complete a work sequentially in 10 days , 15 days and 12 days. then how much days did they need to complete that work together?


Type and Time Work Short trick 3:-


 1.  If (A+B),(B+C) and (A+C) complete any work in X days, Y days and Z days sequentially , then        time to complete that work by (A+B+C):-

                                         = 2XYZ / XY+YZ+ZX    days 
                                                             or
                                         = 2L / (L/X)+(L/Y)+(L/Z) 
                                                                                               [there L= Lcm of X, Y and Z]

2.  Time to complete that work by A:-
                                         =  2XYZ / XY+YZ-ZX    days 
                                                               or
                                           = 2L / (L/X)+(L/Z)-(L/Y) 
                                                                                               [there L= Lcm of X, Y and Z]
3.  Time to complete that work by B:-
                                         =  2XYZ / YZ + XZ - XY    days 
                                                               or
                                           = 2L / (L/X)+(L/Y)- (L/Z) 
                                                                                               [there L= Lcm of X, Y and Z]


Example :- If (A+B) complete a work in 20 days, (B+C) complete that work in 24 days and (A+C) in 30 days, then in how much days did (A+B+C) will complete that work?





Type and Time Work Short trick 4:-





 1.  If A and B together complete a work in X days, A alone complete that work in Y days, then time         to complete that work by B = XY / (Y - X) days

 2.  If A , B and C together complete that work in X days and A and B complete that work in Y days ,      then time to complete that work by C:-

                         = XY / (Y-X) days      or       = L / (L/X)-(L/Y) days       [where L= LCM of X and Y]





Example :- A and B complete a work in 18 days. If A alone complete that work in 30 days, then in how much time did B alone complete that work?










Type and Time Work Short trick 5:-




                    If A complete a work in X days. After working for T1 days B alone continues that work and complete it in T2 days , then:-


  1. Time to complete the hole work by B                =    (X x T2) / (X - T1) days
  2. Time to complete the hole work by A and B     =    (X x T2) / (X - T1 + T2) days



Example :- A completes a work in 15 days. He works for 5 days and then B continues that work and complete it in 20 days. In how much time did B alone can complete the hole work?




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Type and Time Work Short trick 6:-




                    A and B sequentially complete a work in X days and Y days. If A leave the work after working for T1 days , then time to complete the remain work by B alone   =   (X-T)Y / X days



note:- If B leave the work, then time to complete the remain work by A alone   =   X(Y-T) / Y days





Example :- A completes a work in 20 days and B complete that work in 25 days , B work for only 10 days, in how much days did remaining work was completed by A?








Type and Time Work Short trick 7:-





                    A and B sequentially complete a work in X days and Y days. If both started the work and after T days A leaves the work, then :-



1.  Time to complete the remaining work by B   =   XY - (X+Y)T / X days.

    note:- If B leave the work, then time to complete the remain work by A  =   XY - (X+Y)T / Y days



2. Total time to complete the hole work = (X -T)Y / X days





Example :- A and B sequentially complete a work in 10 days and 20 days. They work for 5 days and after that A leave the work, In how much days did B completes the remaining work?







Type and Time Work Short trick 8:-



                    A, B and C sequentially complete a work in X days, Y days and X days. If all 3 starts working together but,

1.  If A leaves the work after T days, then time to complete the remaining work,
                 = {YZ / (Y+Z)} {1 - (T/X)} days
2.  If A leaves the work after T1 days and B leaves the work after T2 days , then time to complete the      remaining work            =        Z {1- (T1/X) - (T2/Y)} days


Example :-  A, B and C sequentially complete a work in 10 days, 15 days and 12 days. All of them together started the work, but A leaves the work after 1 day. In how much time did remaining work will be complete?





Type and Time Work Short trick 9:-

                    A and B sequentially complete a work in X days and Y days. Both started work together but A leaves the work before last T days of finishing the work, then total time to complete the work,   =   {XY / (X+Y)}{1- (T/X)}  =  (X+T)Y / (X+Y) days

note:- If B leave the work, then time to complete the remain work:-
           =   {XY / (X+Y)}{1+ (T/X)}  =  (X+T)Y / (X+Y) days


Example :-  A and B sequentially complete a work in 20 days and 30 days. Both started work together but A leaves the work before last 5 days of finishing the work, then in how much time total work will be complete?




Type and Time Work Short trick 10:-

                    A, B and C sequentially complete a work in X days, Y days and Z days. If all three together started the work but,

1.  A leaves the work before last T days of finishing the work, then total time to complete the work,          =   {XYZ / (XY+YZ+ZX)}{1+ (T/X)} days  
     =  (X+T)YZ / XY+YZ+ZX) days

2.  If A leaves the work before T1 days and B leaves the work before T2 days , then time to complete      the remaining work            =        {XYZ / (XY+YZ+ZX)} {1+ (T1/X)+ (T2/Y)} days


Example :-   A, B and C sequentially complete a work in 15 days, 20 days and 12 days. If all three together started the work but, A leaves the work before last 5 days of finishing the work, then in how much time did work will be complete?




Type and Time Work Short trick 11:-

                    A, B and C sequentially complete a work in X days, Y days and Z days. If all three together started the work but,

1. A leave the work after T1 days of starting the work and B leaves before T2 days of finishing the         work, then total time to complete work:-
        = YZ / (Y-Z) {1- (T1/X) + (T2/Y)} days

2.  B leave the work after T1 days of starting the work and C leaves before T2 days of finishing the         work, then total time to complete work:-

        = XZ / (X-Z) {1- (T1/Y) + (T2/Z)} days



Example :-    A, B and C sequentially complete a work in 10 days, 15 days and 12 days. If all three together started the work but,  A leave the work after 2 days of starting the work and B leaves before 1 days of finishing the work, then in how much time did total work will be complete?

Questions asked in exams



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