Work and ratio

1. Work from Days:

If A can do a piece of work in n days, then A's 1 day's work =1/n

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2. Days from Work:

If A's 1 day's work =1/n, then A can finish the work in n days.

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3. Ratio:

If A is thrice as good a workman as B, then:
Ratio of work done by A and B =3:1.
Ratio of times taken by A and B to finish a work =1:3

4. If A is 'x' times as good a workman as B, then he will take(1/n)th of the time by B to do the same work.

5. A and B can do a piece of work in 'a' days and 'b' days respectively, then working together, they will take  x*y/(x+y) days to finish the work and in one day, they will finish((x+y)/x*y)th part of work.

Percentage in Apatitue

1. Concept of Percentage:
   By a certain percent, we mean that many hundredths.
   Thus, x percent means x hundredths, written as x%.

   To express x% as a fraction: We have, x% =	x	.
   	100

   
   

   To express	a	as a percent: We have,	a	=		a	x 100	%.
   	b		b			b

   
   
2. Percentage Increase/Decrease:
   If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:

   	R	x 100	%
   	(100 + R)

   If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:

   	R	x 100	%
   	(100 - R)

3. Results on Population:
   Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:

   1. Population after n years = P		1 +	R		n
   			100

   2. Population n years ago =	P
   	1 + R n 100

4. Results on Depreciation:
   Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:

   1. Value of the machine after n years = P		1 -	R		n
   			100

   2. Value of the machine n years ago =	P
   	1 - R n 100

   3. If A is R% more than B, then B is less than A by		R	x 100	%.
   		(100 + R)

   4. If A is R% less than B, then B is more than A by		R	x 100	%.
   		(100 - R)

   
   
   
   5. When a value is multiplied by a decimal more than 1 it will be increased and when multiplied by less than 1 it will be decreased.
   6. The percentage increase or decrease depends on the decimal multiplied.
    

DIVISIBILITY RULES

DIVISIBILITY RULES:::

The simple divisibility rules will help you to find factors of a number.
The number is divisible by:

• 2 if the last digit is 0, 2, 4, 6, or 8 (example: 345568);
• 3 if the sum of digits in the number are divisible by 3
  (example: 1236, because 1+2+3+6 = 12 = 3 x 4);
• 4 if the last 2 digits are divisible by 4
  (example: 897544, because 44 = 4 x 11);
• 5 if the last digit is 0 or 5
  (example: 178965 or 40980);
• 6 if it is divisible by 2 and 3;
• 8 if the last 3 digits are divisible by 8
  (example: 124987080, because 080 = 8 x 10;
• 9 if the sum of digits is divisible by 9
  (example: 234612, because 2+3+4+6+1+2 = 18 = 9 x 2);
• 10 if the last digit is 0
  (example: 99990 );
• 100 if the last 2 digits are 0
  (example 987600);