Time and work (method - 2)

 We solve time and work problems also by using time and efficiency. So now, we see hoe to solve in this method.

               

	A	B
Time T
Efficiency E

The table is the basic rule. Now when we fill the columns in table, Ta * Ea  = Tb * Eb

ie., efficiency should be appropriate. Here Efficiency is nothing but the ratio in reverse order.

Efficiencies should be noted in reverse order..  of ratios.

If Ratios of A and B are 2:3, then efficiencies must be.. 3:2… Now Ea=3 and Eb=2

Now,  work done is..W = T x E (of  either A or B, as both are same)

Work done by A = W/Ea                 ;(Ea=Efficiency of A)

Work done by B = W/Eb                  ; (Eb=Efficiency of B)

Work done by A+B = W/E(a+b)     ; (Ea+b=Sum of Efficiencies of A and B)

Example:

A can do a work in 10 days. B can complete the same work in 20 days. If they work together, how many days they take to complete.

Ans : 6 2/3 days

Solution:

    A   B

T  10 20                                                                                                 w = 20

E   2   1 (as Ratio of A and B but in reverse order…)            Wa+b = 20/3 = 6 2/3 days…

 Refer Method - 1 here..

3 digit multiplication

As you already saw 2-digit multiplication, now we see how to slove 3digit ones.

The Rule is    |  X  *  X  |



                                   a  b  c


                               x   d  e  f            
 and answer will be |  X  *  X  |


 same as the 2digit ones.. there must be a minimum of 5 digits in the answer when you multiply two 3-digit numbers.

 coming from right end to left end... (as it is the rule to solve multiplications)
first | denotes               c x f
next X denotes            bf + ec ie., (b x f) + (e x c)
then *  denotes        af + dc + be
next X denotes            ae + bd
 and last | denotes        a x d 



In every digit,, if you have a carry, then u can transfer it to the very next left digit.

and for this 2 digit or 3-digit multiplication, please don't remember  a x f,b x c like that, jut remember the method to solve it.. ie.,  for 2 digit |  X  |
                               and for 3 digit    |  X  *  X  |


here remember..  that star in middle for 3-digit  is like     \|/
                                                                                  .. /|\
Will be back to u soon
If u have any doubts in any topic such as percentages, train problems, and any thing. Please post here. I'll try to get back to you with shortcut and answers soon. 

Time and work ( Method - 1 )

Time and work is a very tough. But it is very easy topic if you know the 'shortcut'. That is why i am here. Now lets see the basic formula to solve this.

                  M1 x  D1 x H1          =       M2  x  D2  x  H2
                       W1 x  E2                            W2  x  E1

where
M is number of men
D is number of days
H is number of hours per day (if mentioned)
W is work done
E is efficiency (if required or given)



Example 1 : Find how many days  could 12 men work, if  4 men can work in 3 days.

Answer :  M1 = 12         M2 = 4
                D1 =  ?           D2 = 3

12 x ? = 4 x 3
So  12 men can work in one day... That's the answer.

Here you can ignore others (hours, work and efficiency). As all these can be taken as constant. And as it is ratio it can be cancelled.

You also find one more method of  time n work problems(ie., man, child, woman combo type). I will explain you in my next post.

Will be back to u soon
If u have any doubts in any topic such as percentages, train problems, and any thing. Please post here. I'll try to get back to you with shortcut and answers soon.