Pipe A & B can fill a tank in 20 hours, 30 hours respectively. And pipe C can empty the tank in 40 hours. If all pipes are opened together, how much time will be needed to make tank full?

Ans:
      = 1/20+1/30-1/40
      = 7/120
   
      = 120/7
      = 17 1/7
     

A,B,C partners invest 1600, 1800, 2300. Divide profit of 399Rs.

Ans:
      16+18+23=57
      16/57*399= Ans.
      18/57*399= Ans.
      23/57*399= Ans.

IIf asked.."In How Many Ways.."

(n-1)!=permutation
Suppose, in how many ways, 8 persons can be seated in a round table conference?


Ans:
       (n-1)! = 7!= 5040 Ans

See Short Cut Method

8 1/3 % of ? = 150

 25/3 * ? = 150

 ?= 150*3/25
   =18

X,Y,Z share money in ratio of 7:8:16. If Z receives Rs. 27 more than X, then find the total money.

Ans:
      7x, 8x, 16x
      16x= 7x + 27
       9x=27
         x=3
    
     7x+8x+16x = 31x=31*3= 93 Rs.

Money deposited by P,Q,R in ratio of 3:5:7. Q's share is 1500. What is the difference between p and Q's share?

Ans: 3x,5x,7x
    Q=5x=1500
           x=300

    P=900
    R=2100
   
    Diff=2100-900=1200

If a:b=2:3, b:c=4:5, then find ratio of a:b:c?

Ans:
        a : b : c
        2   3
             4   5

        a=2*4=8
        b=3*4=12
        c=3*5=15


Ans: 8:12:15


Q & A:

a:b=2:3
b:c=4:5
c:d=6:7

a : b : c : d
2   3
     4   5 
          6   7

a=2*4*6=48
b=3*4*6=72
c=3*5*6=90
d=3*5*7=105

48:72:90:105

If it takes 10 days to die a trench of 100 m long, 50 m broad, 10 m deep, what length of trench, 25 m broad, 15 m deep can be dug in 30 days?

Ans:

       D          L            B            D

      10        100         50           10

      30         x            25           15

     x=100*30*50*10/10*25*15

       = 400m

20 Men-20 Days
25 Men-??days

   =20*20/25
   =16 days


14 Pumps-6 Days
?? Pumps-4 Days

   = 14*6/4
   = 21 days

5 chairs cost as much as 12 stools, 7 stools cost as much as 2 tables, 3 tables cost as much as 2 sofas. If the cost of  5 sofas be Rs. 8750. Find that of a chair.

Ans:
        x rupees=1 chair
        5 chair=12 stools
        7 stools=2 tables
        3 tables=2 sofas
        5 sofas= 8750/-

        x=1*12*2*2*8750/5*7*3*5
          =800/-

Polygons:

Traingles

In right triangle, one angle = 90

and total sum = 180 as in above traingle

A factory produces 470 toy-cars a day. How many cars did it produce in the year 1988, if there are 86 holidays? [Hint: 1988 is a leap year]

Ans: 366-86=280
        =470*280=131600


A factory produces 144 ball-pens in a carton. They have 395 cartons to be filled. They have already made 57000 ball-pens. Do they need to make more ball-pens in order to fill all the cartons?


Ans: 395*144=56880= NO NEED  

Place Value

Find the place value:
7 in 87930= 7000

diff between the place values:
two fours in 12494=400-40=360

Smallest whole number =0

Smallest counting number=1

Average

1..A train runs 3 hours at a speed of 65 km per hour and for next 2 hours at a speed of 70 km per hour. Find the average speed of the train for the 5 hours' journey.

solution: Total distance covered in first 3 hours: (65*3)      = 195 km
             Total distance covered in next 2 hours: (70*2)      = 140 km
             Total distance covered in first 5 hours: (195+140) = 335 km

  so, Average speed for 5 hours' journey= 335/5= 67 km/hr.


2..Find the average of 7 numbers if the sum of the first four is 76 and the sum of the last three s 78.


Solution:  Sum of first four numbers = 76
               Sum of last seven numbers = 78
               Total of seven numbers= 76+78=154
         
              So, Average of 7 numbers = 154/7= 22

Roman Numerals

There are four basic principles for reading and writing Roman numerals:

• 1. A letter repeats its value that many times (XXX = 30, CC = 200, etc.). A letter can only be repeated three times.
• 2. If one or more letters are placed after another letter of greater value, add that amount.

  VI = 6 (5 + 1 = 6)

  LXX = 70 (50 + 10 + 10 = 70)

  MCC = 1200 (1000 + 100 + 100 = 1200)

3. If a letter is placed before another letter of greater value, subtract that amount.

IV = 4 (5 – 1 = 4)

XC = 90 (100 – 10 = 90)

CM = 900 (1000 – 100 = 900)

Several rules apply for subtracting amounts from Roman numerals:
• a. Only subtract powers of ten (I, X, or C, but not V or L)

  For 95, do NOT write VC (100 – 5).
  DO write XCV (XC + V or 90 + 5)

• b. Only subtract one number from another.

  For 13, do NOT write IIXV (15 – 1 - 1).
  DO write XIII (X + I + I + I or 10 + 3)

• c. Do not subtract a number from one that is more than 10 times greater (that is, you can subtract 1 from 10 [IX] but not 1 from 20—there is no such number as IXX.)

  For 99, do NOT write IC (C – I or 100 - 1).
  DO write XCIX (XC + IX or 90 + 9)

• 4. A bar placed on top of a letter or string of letters increases the numeral's value by 1,000 times.

  XV = 15, = 15,000

  One	I	Eleven	XI	Thirty	XXX
  Two	II	Twelve	XII	Forty	XL
  Three	III	Thirteen	XIII	Fifty	L
  Four	IV	Fourteen	XIV	Sixty	LX
  Five	V	Fifteen	XV	Seventy	LXX
  Six	VI	Sixteen	XVI	Eighty	LXXX
  Seven	VII	Seventeen	XVII	Ninety	XC
  Eight	VIII	Eighteen	XVIII	One hundred	C
  Nine	IX	Nineteen	XIX	Five hundred	D
  Ten	X	Twenty	XX	One thousand	M