simple equations STD V

• Three Consecutive integers add up to 51. What are these integers?

          Let the integers be y-1, y, y +1.

         Given that y-1 + y + y +1 = 51

         Or, 3y = 51

         Or, y = 17

         So, the three numbers are 16, 17 and 18.

• The sum of 3 consecutive multiples of 8 is 888. Find the multiples?

          Let the numbers be y-8, y and y +8

         Given that y-8 + y + y + 8 = 888

         Or, 3y = 888

         Or, y = 296

         So, the three numbers are 288, 296, 304

• The ages of Rahul and Haroon are in the ratio of 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?

         Let the age of Rahul four years hence be y.

         So, age of Haroon is 56 – y.

         Present age of Rahul = y – 4

         Present age of Haroon = 56 – y – 4 = 52 – y

        Given y-4 : 52 – y = 5 : 7

         The product of mean = product of extreme. So,

         7(y – 4 ) =5(52 – y)

        Or, 7y – 28 = 260 – 5y

        Or, 12y = 260 + 28 = 288

        Or, y = 288/ 12 = 24

        So, Haroon’s age 4 years hence is = 56 – y = 32

        So, the present age of Rahul and Haroon are = 20 and 28.

• The number of boys and girls in a class are in the ratio of 7:5. The number of boys is 8 more than the number of girls. What is the total class strength?

          Answer:

          Let the number of girls in the class be y

          So, the number of boys = y + 8

          Given that, (y+8):y = 7:5

          Product of mean = product of extreme, so,

          5(y+8) = 7y

         Or, 5y + 40 = 7y

         Or, 2y = 40

         Or, y = 20

         So, the total strength of the class is = y + y+8 = 20 + 28 = 48. 

simple equations STD V

• If you subtract ½ from a number and multiply the result by ½, you get 1/8. What is the Number?  

         Answer:

          Let the number be y

          Then, (y- ½ ) x ½ = 1/8

          Or, y – ½ = 2/8 = ¼

          Or, y = ½ + ¼ = ¾ 

• The base of an isosceles triangle is 4/3 cm. The perimeter of the triangle is 4 2/15cm. What is the length of either of the remaining equal sides?

          Answer

          Let the side be y.

          Since it is an isosceles triangle, the 2 sides are equal.

          So, the equation would be y + y + 4/3 = 4 ²/₁₅ = 62/15

          Or, 2y = 62/15 – 4/3

          Or, 2y = (62 – 20)/15

          Or, 2y = 42/15

          Or, y = 42 / (15 x 2) = 21/15 = 1 ⁶/₁₅

• The sum of two numbers is 95. If one exceeds the other by 15, find the numbers.

         Answer:

         Let one of the number be y.

         Then the other number is y + 15.

         Given that y + y + 15 = 95

         Or, 2y + 15 = 95

         Or, 2y = 95 -15

         Or, 2y = 80

         Or, y = 40

         Therefore the other number is y + 15 = 40 + 15 = 55.

         The two numbers are 40 and 55.

• Two numbers are in the ration of 5:3. If they differ by 18, what are the numbers?

         Answer

         Let one of the number be y.

         The other number is y-18

         We are given that y: y-18 = 5:3

         Product of mean = product of extreme.

         So, 3y = 5(y-18)

         Or, 3y = 5y -90

         Or, 2y = 90

         Or, y = 45

         Therefore, y -18 = 27

         So, the 2 numbers are 27 and 45.

Simple Equations STD V

reference Books, maths, ncert, for all classes

http://www.ncert.nic.in/ncerts/textbook/textbook.htm?

If you are looking for text books in math, science and other subjects in English or Hindi or Urdu, you may visit the URL given above.
You have books from STD 1 to 12. They are all free.
They are extraordinary in content, prepared by some of the best brains in the country.
I am sure you will find them very useful.

http://www.mathtutor.ac.uk/

Very good math tutorials available here. Video tutorial, exercises, texts. you will certainly like it.

http://www.mathportal.org/. --for higher mathematics. 

indicies STD VII

indicies (STD VII)

learning by sharing

                             Learning by Sharing

ipm mega finals STD. IV answers

The temperatures are measured in degree Celcius and degree Fahrenheit. To convert degree Celcius to degree Fahrenheit the formula (F - 32) x 5/9 = C is used. The boiling point of water in Celcius is 100, What is the boiling point in Fahrenheit?



Answer:

(F - 32) x 5/9 = C

To find F we must  arrange the equation in a  manner to read F = ........
let us try to do that

What ever we do on the left side of equation, we will repeat the same on the right. other wise the balance will get disturbed.
(F - 32) x 5/9 x 9/5 = C x 9/5   ---------multiply both sides by 9/5
or, F - 32 = C x 9/5
but C = 100
So, F -32 = 100 x 9/5 = 900/5
or, F -32 + 32 = 900/5 + 32
or, F = 900/5 + 32 = 180 + 32 = 212 Answer

IPM mega finals STD IV answers

In the addition Problem at the right, find the sum of the digits represented by B and C. Different letters represent different digits. Each time a same letter appears, it represents the same digit.

                                      2   B   A
                                +   C   6    D
                                      8   A   D




Answer:

Since A + D = D , So, A = 0
since B + 6 = 0 , B must be 4. There is carry 1 to the next place.
2 + C + 1 (carry) = 8
or, C = 5

So, B + C = 4 + 5 = 9

IPM mega finals STD IV answers

Grandma baked a cake for her grand children who will visit in the afternoon. Unfortunately she forgot whether only 3, 5  or 6 of her grand children will come over. She wanted to ensure that every child gets the same amount of cake. Then to be prepared for all the possibilities, she should cut the cake into how many pieces.




Answer:
The minimum no. of pieces she should make so that it can be equally distributed is the LCM of 3,5 and 6.

So, the answer is 30.

So, in case 3 grand children come ----she will give 10 pieces each.
in case 5 grand children come ----she will give 6 pieces each.
in case 6 grand children come ----she will give 5 pieces each.

IPM Mega finals STD IV answers

In the year 2012, Mrs. Gokhale celebrated her 20th marraige anniversary on the 163rd day of the year. On which of the date did she marry?





Answer:
month             days            cummulative 

Jan                  31                      31
Feb                 29                      60
march             31                      91
april               30                     121
may                31                    152

Now 163 - 152 = 11 days
So, her anniverary date is 11th of June
So, she got married on 11th June 1992   (20 years back)

IPM mega final STD IV answers

A 12 litre tank is filled with water at the rate of 1/4 litre in 5 secs. How much time will it take to fill 5/6 of the tank?




Answer

Water to be filled = 5/6 x 12 = 10 litres = 10000 ml 

now 250 ml is filled in 5 sec.

therefore, time taken by  water to fill the tank = (10000 /250) x 5 = 200 secs = 3 mins and 20 sec

IPM mega final STD IV answer

on a play ground the number of bicycles are 5 times than the number of tricycles. if the total number of wheels are 39, then how many children in all were playing with their cycles?





Answers:
if the number of tricycle is y
then number of bicycle is 5y
so, 3y + 2 x 5y = 39
13y = 39
y = 3
bicycles = 5 x 3 = 15
total number of cycles = 3 + 15 = 18.

IPM mega finals STD IV answer

An electronic digital watch shows 20:07. What time should pass at the earliest after which the same digits apppear again in a different order?


checking the combinations in ascending order.
00.27
00.72
02.07
02.70
07.20
07:02

So, 00:27 is the time when all digits will reappear for the first time.
therefore, 00:27 - 20:07 = 4 hrs 20 mins will pass at the earliest.

Mega final Question STD IV answer

A student writes seven consecutive natural numbers and the sum of the smallest three number is 33, which of the following is the sum of the largest numbers?



Answer:

if the numbers are "a-1", "a", "a + 1". Then a = 33/3  = 11
so, the numbers are 10, 11, 12.
so the last three numbers are 14, 15, 16 
sum of 14, 15, 16 = 45

rationalization

7-time and work

Machine A and B produce 8000 clips in 4 hr and 6 hr respectively. They work alternately for 1 hour. Starting first with A, then 8000 chips will be produced in ..........................hours.

6-Time and work

A and B can do a job in 12 days. B and C can do the job in 16 days. After A has worked for 5 days and B has worked for 7 days, C can finish the rest in 13 days. In how many days can C do the work alone?

profit and loss

A sells a Car to B at a profit of 10%, B sells it to C at a profit of 20%. If C pays $ 2000, what did A pay for it?




Answer

Cost of Car to A = y

So, Buying price of B = 1.10y

Buying price of C = 1.10y x 1.2 = 2000

or, y = 2000 / (1.1x 1.2) = $ 1515.15

profit and loss

Two third of a consignment was sold at a profit of 6% and the rest at a loss of 3%. If however, there was an overall profit of Rs 540, the value of the consignement was ........................





Answer

Cost price of consignment = y

so, (2/3)y x 1.06 + (1/3)y x .97 = 540 + y

or, (2.12 + .97)y = 540 x 3 + 3y

or, 0.09y = 540 x 3 

or, y = 18000