SOLVED TIME AND DISTANCE

FROM THE CLUES GIVEN FINDING THE UNKNOWN

In solving the mathematics one has to analyse the given clues and finding the unknown. Also all the data should be deduced in common unit. Like kilometers, seconds, minutes, hours etc. 

WHY WE FORGET AN ANIMAL IS THE SAME AS HUMANS ? EARTH IS EQUAL TO ALL.

Elementary math again with Speed and Time relationship. Math is fun and finding unknown from the given clues , Enjoy Math

Series on elementary mathematics on time and speed.

WHEN INSTEAD OF SPEED TIME TAKEN BY THE TRAIN IS GIVEN LENGTH OF THE STATION CAN BE DETERMINED.NEXT MATH.

A series of solved elementary mathematics on time and speed

CONVERT MINUTES INTO SECONDS

SURFACE AREA INCREASED WHEN SPHERES ARE REDUCED IN SIZE

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One math in finding surface area . Do know water, surface, container , kaacconsultant@gmail.com

DEPRECIATION

UNDERSTANDING DEPRECIATION ON ACCOUNTING PRINCIPLE

EVERY EQUIPMENT OR ITEM HAS ITS OWN USEFUL LIFE AFTER THAT IT CEASES TO BE USEFUL ONE.
IN THIS LOGIC , WHEN  WE USE ANY  EQUIPMENT , ITS ORIGINAL PURCHASE PRICE ALSO  REDUCES THROUGHOUT ITS USEFUL LIFE TILL ITS PRICE REDUCES TO ZERO. 

 THAT IS THE EQUIPMENT DEPRECIATES ITS PRICE. IT DEPENDS ON ITS USEFUL LIFE OF THAT PARTICULAR ITEM. THE PRICE OF THE EQUIPMENT IS DIVIDED BY THE USEFUL LIFE AND THAT AMOUNT IS REDUCED FROM ITS PREVIOUS PRICE. 
THERE ARE SEVERAL METHODS OF CALCULATING DEPRECIATION.


A EXAMPLE IS GIVEN LIKE 

ISHAAN BOUGHT A CAR FOR RUPEES 300000. ITS PRICE DEPRECIATES AT THE RATE OF 10 % PER YEAR.

AFTER 1 YEAR 10 % OF  RUPEES 300000 WILL BE REDUCED FROM RS 300000

SO AMOUNT WILL BE  300000* 10/100= RUPEES 30000

SO, DEPRECIATED PRICE OF THE CAR AFTER 1 YEAR WILL BE  300000 - 30000 = RS.270000

NOW AFTER 2 YEAR AGAIN 10% WILL BE DEPRECIATED FROM RS. 270000 

SO, 10 % OF RUPEES 270000 IS  270000*10/100= RS. 27000

RUPEES 27000 WILL BE DEDUCTED FROM  RS.270000

ONE METHOD CALCULATION OF DEPRECIATION IS LIKE THIS.

PROBLEM SOLVER ON QUADRILATERAL

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An interesting problem in trapezium

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Again returned to Operations on numbers

PROBLEM GIVEN


What least no must be  subtracted from 1672 to obtain a number  which is completely divisible by  17 ?




LET US   DIVIDE 



 17| 1672 | 98
         153
_________
            142
             136
__________
                   6


SO  6 needs to be subtracted from 1672 to get exactly divisible by 17.




ANOTHER INTERESTING MATH>
FIND THE TOTAL NUMBER OF PRIME FACTORS IN THE 

((4)11 X  7 5 X  (11)2 ) SOLUTION:
((2 X 2)11 X  7 5  X ( 11 )2
((22)11 X  7 5 X  ( 11 )2
(2)22 X  7 5 X  (11)  2
REQUIRED NO OF  FACTORS   = 22 +5 +2 = 29

This problem is interesting

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Maths are interesting , when you grow interested

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mathematics is fun, area of the rhombus

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mathematics drawn on pictorial

Mensuration on cylinders and cubes

Which has a greater volume , a cylinder of height 21 Cm, and a base of radius 10 Cm.
or, a cube with an edge by measuring 19 cm.
solution
volume of the cylinder =    π *  Radius 2 * Height = π*10*10 *21=							6600	cm 3
Volume of the cube = 19*19 *19=				6859	cm 3
The cube is greater than by =                                             259			cm 3

An interesting math applied on practical life

Find the area covered by a road roller in 50 revolutions if it's diameter is 140 Cm. and it,s width is 120 Cm. Convert the area in Square Meter

Before going to the mathematics solution, this formulas needs to be memorized

1. Volume of a cube ( length L * Breadth B * Height H ) , if the cube is of equal dimensions then it is  L *L*L   cubic unit ,

2. Surface area of a equal unit of cube   6 L 2 3 .For pure water  1 ml = 1 cm3 4. surface area of a cuboid = 2 ( L*B + B*H + L*H)  where L =length, B= Breadth, H= Height 5. Volume of a cuboid = (L*B*H) where L =length, B= Breadth, H= Height

solution
When the wheel of the road roller moves it covers an area equal to its lateral surface area per revolution
Given data		width of the road roller wheel   L = 120 Cm
		Radius of the road roller wheel  R = diameter/2 = 140/2= 70 Cm
		on per revolution , it covers an area = 2 *π* R* L					52800		Sq  Cm
Now the road roller wheel has taken 50 revolutions , so total lateral area is  50*52800 = 264000 square Cm
The area covered in square  Meter  264000/(100*100)						26.4	square meter		M2

save energy , fuel of life

SAVE ENERGY SAVE FUEL  

TIPS ON ENERGY SAVING

IN HOME APPLIANCES AND ELECTRICITY SAFETY

The Domestic Sector accounts for 30% of total energy consumption in the country. There is a

tremendous scope to conserve energy by adopting simple measures.

This information is a guide, which offers easy, practical solutions for saving energy in Home

Appliances. Please, take a few moments to read the valuable tips that will save energy & money

and ultimately help conserve our natural resources.

It would be useful to know which gadget consumes how much electricity. Economic use of home

appliances can help in reducing electricity bills.



By following these simple tips one can save energy to a large extent.

Lighting

Ø Turn off the lights when not in use

Ø Take advantage of daylight by using light-colored, loose-weave curtains on your windows

to allow daylight to penetrate the room. Also, decorate with lighter colors that reflect

daylight

Ø De-dust lighting fixtures to maintain illumination

Ø Use task lighting; instead of brightly lighting an entire room, focus the light where you need

it

Ø Compact fluorescent bulbs are four times more energy efficient than incandescent bulbs

and provide the same lighting

Ø Use electronic chokes in place of conventional copper chokes

Fans

Ø Replace conventional regulators with electronic regulators for ceiling fans

Ø Install exhaust fans at a higher elevation than ceiling fans

Electric iron

Ø Select iron boxes with automatic temperature cutoff

Ø Use appropriate regulator position for ironing

Ø Do not put more water on clothes while ironing

Ø Do not iron wet clothes

Kitchen Appliances

Ø Mixers

§ Avoid dry grinding in your food processors ( mixers and grinders) as it takes longer

time than liquid grinding

Ø Microwaves ovens

§ Consumes 50 % less energy than conventional electric / gas stoves

§ Do not bake large food items

§ Unless you're baking breads or pastries, you may not even need to preheat

§ Don't open the oven door too often to check food condition as each opening leads to a

temperature drop of 25°C

Ø Electric stove

§ Turn off electric stoves several minutes before the specified cooking time

§ Use flat-bottomed pans that make full contact with the cooking coil

Tips on Energy Savings Page 3 of 5

Ø Gas stove

§ When cooking on a gas burner, use moderate flame settings to conserve LPG

§ Remember that a blue flame means your gas stove is operating efficiently

§ Yellowish flame is an indicator that the burner needs cleaning

§ Use pressure cookers as much as possible

§ Use lids to cover the pans while cooking

§ Bring items taken out of refrigerators (like vegetables, milk etc) to room temperature

before placing on the gas stove for heating

Ø Use Solar Water Heater – a good replacement for a electric water heater

Electronic Devices

Ø Do not switch on the power when TV and Audio Systems are not in use i.e. idle operation

leads to an energy loss of 10 watts/device

Computers

Ø Turn off your home office equipment when not in use. A computer that runs 24 hours a

day, for instance, uses - more power than an energy-efficient refrigerator.

Ø If your computer must be left on, turn off the monitor; this device alone uses more than half

the system's energy.

Ø Setting computers, monitors, and copiers to use sleep-mode when not in use helps cut

energy costs by approximately 40%.

Ø Battery chargers, such as those for laptops, cell phones and digital cameras, draw power

whenever they are plugged in and are very inefficient. Pull the plug and save.

Ø Screen savers save computer screens, not energy. Start-ups and shutdowns do not use

any extra energy, nor are they hard on your computer components. In fact, shutting

computers down when you are finished using them actually reduces system wear - and

saves energy

Refrigerator

Ø Regularly defrost manual-defrost refrigerators and freezers; frost buildup increases the

amount of energy needed to keep the motor running.

Ø Leave enough space between your refrigerator and the walls so that air can easily

circulate around the refrigerator

Ø Don't keep your refrigerator or freezer too cold.

Ø Make sure your refrigerator door seals are airtight

Ø Cover liquids and wrap foods stored in the refrigerator. Uncovered foods release moisture

and make the compressor work harder.

Ø Do not open the doors of the refrigerators frequently

Ø Don't leave the fridge door open for longer than necessary, as cold air will escape.

Ø Use smaller cabinets for storing frequently used items

Ø Avoid putting hot or warm food straight into the fridge

Tips on Energy Savings Page 4 of 5

Washing machines

Ø Always wash only with full loads

Ø Use optimal quantity of water

Ø Use timer facility to save energy

Ø Use the correct amount of detergent

Ø Use hot water only for very dirty clothes

Ø Always use cold water in the rinse cycle

Ø Prefer natural drying over electric dryers

Air Conditioners

Ø Prefer air conditioners having automatic temperature cut off

Ø Keep regulators at “low cool” position

Ø Operate the ceiling fan in conjunction with your window air conditioner to spread the

cooled air more effectively throughout the room and operate the air conditioner at higher

temperature

Ø Seal the doors and windows properly

Ø Leave enough space between your air conditioner and the walls to allow better air

circulation

Ø A roof garden can reduce the load on Air Conditioner

Ø Use windows with sun films/curtains

Ø Set your thermostat as high as comfortably possible in the summer. The less difference

between the indoor and outdoor temperatures, the lower will be energy consumption.

Ø Don't set your thermostat at a colder setting than normal when you turn on your air

conditioner. It will not cool your home any faster and could result in excessive cooling.

Ø Don't place lamps or TV sets near your air-conditioning thermostat. The thermostat senses

heat from these appliances, which can cause the air conditioner to run longer than

necessary.

Ø Plant trees or shrubs to shade air-conditioning units but not to block the airflow. A unit

operating in the shade uses as much as 10% less electricity than the same one operating

in the sun.

Tips on Energy Savings Page 5 of 5

Electrical Safety Tips for Homes

Electrical Hazards

Ø Shocks

§ Electric Shock causes an involuntary grip which prolongs the period of contact.

§ More the period of contact, more the damage

§ Passage of current through the heart , stops the blood supply to the brain , resulting in

loss of consciousness and termination of breathing

§ When a person standing at a height receives an electrical shock , it is most likely that

he will fall

§ Personal sensitivity to electrical shock varies from person to person

Ø Burns

§ Whenever an electrical flash appears, and if a part of a body comes within flashing

distance, burns can be caused

§ Burns may be caused by short circuits as well, because a short circuit could create an

electrical fire
Fuels are NOT EVERLASTING. ENERGY SAVING  IS RETAINING NATIONAL AND INTERNATIONAL PROPERTY SAVING
Preventive Measures

Ø Allow only a qualified person to attend to your electrical repairs

Ø Service your electrical equipment at frequent intervals through a competent electrician

Ø In case of a short circuit or a fire, switch off the mains instantly Make sure that you have

easy access to switch off the supply source quickly, in case of an emergency

Ø Make sure your extension cords are free from cuts, improper insulation, or joints

Ø Ensure pins of your plugs are tight and not loose

Ø Use switches of the correct current rating and preferably with indicators to indicate whether

the switch is ON/OFF

Ø Use appliances with 3 pin plugs and connect them to 3 pin sockets

Ø Do not overload electrical outlets or use extension cords in place of additional outlets

Ø Switch off electrical appliances when not in use

Ø Provide proper earthing for the building/house

Mathematics on unitary methods

A  can  complete a  work in 45 days  while B can complete the work in  50 days and  C  can  do in 55 days.

After  8 days of working  by A , B joins with A and on  20 day C joined for till completion of rest of the work.

How much time it took for the total work ?

SOLUTION

Let the total work  is  1

A  can complete  the  work  in 45 days  when does alone.

So in 1 day A can do  1/45  parts of the work.

A  worked till 8 days. So in  8 days  8/45 parts of the work is completed=

0.17778

parts

Now  B can complete the work in 50 days

So in 1 day B can do 1/50 parts of the work.

A and B did work upto 20 th. day.

In one day A and B  in together does  (1/45+ 1/50 ) parts of the work = 19/450 parts

For 12 days total work done is =12* 19/450   =

0.50667

Total work completed = 0.17778+0.50667=

0.68445

Work left  = 1 - 0.68445 =

0.31555

parts

Now, this 0.31555 parts of the work A, B and C worked together

C can do  1/55 parts of the work in one day.

In one day   1/45 +1/55+ 1/60 =

0.057071

parts of the work can be executed

Work left is  0.31555 , so time will be

5.529078

days

Total time taken  A alone 8  days

And A and B  12 days

A,B and C  together 5.53 days

25.53

days.

ANS

A water tank can be filled up with  a  filling line by 10 Hrs. and other by 14 Hrs.

How much time it will take when both are filling simultaneosly

solution :

Let   we consider the filled up tank quantity is 1

In 10 hours the tank is filled up by one line

so , in 1 hour the tank is filled up by 1/10  parts quantity

By other line in 14 hrs. the tank can be filled

so in 1 hour the tank is filled up by 1/14 parts

Now , when both the filling lines are being used ,

simultaneously  1/10 + 1/14 parts are being filled up in 1 hour

0.1714

parts are filled up in 1 hour when both the filling lines are opened.

Now let us calculate

0.1714 parts are filled up in 1 hour

1 that is full tank is filled up 1/0.1714 hr=

5.8343

hrs.

the tank will be filled up in 5.8384 hrs.

A water tank can be filled up with  a  filling line by 10 Hrs. and other by 14 Hrs.

How much time it will take when  first filling line is opened for 5 hrs . And second line started

to fill the tank. calculate the time taken for filling the tank

solution

First filling line was opened for 5 hours.

Let us suppose that the filling volume of the tank is 1

first filling line takes 10 hrs. to completely fill up the tank

so in 1 hr 1/10 parts of the tank is filled up

In five hours 5*1/10 parts

0.5

parts of the tank is filled up

remaining part of the tank will be  1-0.5 = 0.5 parts

now let us take the second line  which takes 14 hrs to fill up the full tank

but in this case 0.5 parts that is half of the tank  needs to be filled up

so , in mathematically to deduce

1 volume of  tank is filled up in 14 hours

0.5 volume of tank will require 14 * 0.5 = 7 Hrs.

A water tank can be filled up with  a  filling line by 10 Hrs. and other by 14 Hrs.

How much time it will take when  second filling line is opened for 5 hrs . And first line started

to fill the tank. calculate the time taken for filling the tank

solution

let us consider the volume, that is filled up tank is  1 unit

the second filling line takes 14 hrs to fill up the tank

so in one hour second filling line fills up 1/14 volume of the tank

Second filling line opened for five hours

total filled up volume by the second line till five hours is  5/14 unit

0.3571

unit

we have taken

total volume as 1

so empty tank is 1- 0.3571

0.6429

unit

now the  first line is started which fills up the tank in  10 hrs. so in one hour

tank filled up by 1/10 unit

now we can say that  1/10 unit is filled up in  1 hour

1 unit will be filled up in  10  hours

0.6429 unit will be filled  10*0.6429

6.429

hrs.