Maths Guru Old-24-March-15

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PERCENT

SOME BASIC TERMS-

Of- Of means multiply.

Is- Is means equals.

What- What is the value you are looking for (i.e. the variable).

From- From means subtract.

Less Than- Less than means subtract

More Than- More than means addition

As- As means a ratio.

Into- Into means divide.

By using the words above, we can set up an equation that should be simple enough to

Solve

Ex .1- 20% of 54 is 9% of _________.

a. (.20 x 54) = .09 x n

b. (20 x 54)/9 = n

c. (20 x 54)/ 9= 20 x 6= 120.

d. Answer is 120.

Ex.2- If x% of 140 is 16.8, then x = __________.

a. 140 x = 16.8.

b. Solving we get x = 16.8/140 or x = 168/1400

c. The answer is 12/100= 12%.

Ex 3. 5 more than 12% of 15 is __________.

a. 5 + .12 x 15 = ____.

b. Solving we get 5 + 1.8 = 6.8.

c. Answer is 6.8.

Ex. 4- 14 is what percent more than 10? __________.

a- In other words, 10n + 10 = 14.

b. Solving 10n + 10 = 14 we get 10n = 4 or n = .4 or 40%.

c. Answer is 40.

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Multiplying Two Numbers Greater Than 100, But Close To 100:

A. From algebra we learn:

(100 + a) (100 + b) = 100(100 + a + b) + ab

B. Using numbers instead of variables we get the following:

1. Multiply the one’s digits together. Write this number down (make sure that it takes up 2 place values).

2. Add the one’s digits together. Write the result (make sure that it takes up 2 place values).

3. Write 1.

Ex [1] 104 x 102 =_________.

a) 4 x 2 = 8. Write 08 to take up 2 place values.

b) 4 + 2 = 6. Write 06 to take up 2 place values.

c) Write 1.

d) The answer is 10608.

Ex [2] 106² =_________.

a) 6 x 6 = 36. Write 36.

b) 6 + 6 = 12. Write 12.

c) Write 1

d) The answer is 11236.

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Short Tricks Of Multiplication

When digits are in the same column(between 11-20, 21-30-31-40, etc.)

1) Fix the first no. and break the other no. in nearest tens and rest no. Ex.-15x18=15 x (8+10)

2) Then add the first no. and another part of second no. and then multiply by tens.

Ex.—(15+8) x10=230

3) Now multiply the unit digits of both numbers and add in second method. Ex. 8 x5=40

230+40=270 ANSWER

EXAMPLE—27x 25

=27 x (5+20)

= (27+5) X 20 =>640

= 640 + (7x5)

=675 answer

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SHORT TRICK OF COMPOUND INTEREST (C.I.) AND SIMPLE INTEREST (S.I.)

Average

Q.1. The average of 50 numbers is 38. If two numbers, are 45 and 55 the average of the remaining numbers is :

(1) 37.5 (2) 23.22 (3) 11.22 (4) 44.32 (5) None of these

Q.2. The mean of 100 observations was calculated as 40. It was found later on that one of the observations was misread as 83 instead of 53. The correct mean is :

(1) 39.7 (2) 112.2 (3) 21.32 (4) 44.32 (5) None of these

Q.3. The average of six numbers is 30. If the average of first four is 25 and that of last three is 35, the fourth number is :

(1) 25 (2) 33 (3) 28 (4) 44 (5) None of these

Q.4. The average of 25 results is 18. The average of first twelve of them is 14 and that of last twelve is 17, the thirteenth result is :

(1) 78 (2) 48 (3) 55 (4) 75 (5) None of these

Q.5. Out of four numbers, the average of first three is 16 and that of the last three is 15. If, the last number is 18, the first number is :

(1) 34 (2) 22 (3) 21 (4) 112 (5) None of these

EXPLANATION

Q.1.(1) The total sum of 48 numbers

= [(50×38) - (45 + 55)]

= 1900 - 100

= 1800

\ Average = 1800/48 = 37.5

Q.2.(1) Given mean of 100 = 40

One is 53 - 83 = - 30

\ Correct sum = (40 × 100) + (53 - 83)

= 4000 - 30

= 3970

\ Correct mean = 3970/100 = 39.7

Q.3.(1) Given average of 6 numbers = 30

Average of first 4 is = 25

Average of last 3 is = 35

The fourth number is

= (4 × 25) + (3× 35) - (6×30)

= 100 + 105 - 180

= 205 - 180 = 25

Q.4.(1) Given Average of 25 results = 18

Average of first 12 result = 14

Average of last 12 result =17

\ The thirteenth result = (25x18) - {(12x14) + (12x17)}

= 450 - (168 + 204) = 450-372 = 78

Q.5.(3) Given average of first three = 16

Average of last three = 15

And last number =18

\Sum of 2nd and 3rd number = (3x 15) - 18

= 45-18 = 27

The first number = (3 x 16 ) - 27

= 48 - 27

= 21

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