SimpleMaths

Pipes and Tanks Problems : 1) One tap fills one tank in 10 hours, another tap fills that tank in 20 hours, how long will it take to fill the tank if both taps are started simultaneously. Ans. : Time to fill the tank = ( 10 × 20 ) / ( 10 + 20 ) Time to fill the tank = 200 / 30                                      = 20 / 3                                      = 6.66 hours. So it will take 3.66 hours to fill the tank. 2) One tap fills one tank in 10 hours, another tap fills that tank in 15 hours, how long will it take to fill the tank if both taps are started simultaneously. Ans. : Time to fill the tank = ( 10 × 15 ) / ( 10 + 15) Time to fill the tank = 150 / 25                                      = 6 hours. So it will take 6 hours to fill the tank. 3) One tap fills one tank in 10 hours and the other tap empties the tank in 20 hours. How long will it take to fill the tank if both taps are started at the same time? Ans. : Here, Time to fill the tank = ( 10 × 20 ) / (

Age word problems : 1) The age ratio of Ram and Hari is 3:5 . If the sum of their ages is 56 years, how old is Hari today? Ans. : Hari's Age = { ( Hariys age ratio ) / The sum of his age ratios ) } × The sum of  their ages. Hari's Age = { 5 / ( 3 + 5 ) } × 56                     = ( 5 / 8 ) × 56                     = 5 × 7                     = 35. therefore, Hari's age = 35 years old. 2) The age ratio of Ram and Hari is 2 : 7 . If the sum of their ages is 72 years, how old is Ram today? Ans. : Ram's Age = { ( Ram's age ratio ) / The sum of his age ratios ) } × The sum of  their ages. Hari's Age = { 2 / ( 2 + 7 ) } × 72                     = ( 2 / 9 ) × 72                     = 2 × 8                     = 16 therefore, Ram's age = 16 years old. 3) The age ratio of Ram and Ganesh is 2: 7 and their age difference is 25 years. So how old is Ram today? Ans. : Ram's age = { ( Ram's age ratio ) / ( The difference of

Work and Time problems: Work and Time Problems : Rules : 1) Keep the unknown number right and all the remaining numbers left. 2) If a man does a work in 5 days, then his work of one day = 1 / 5. 3) If a man's one - day work is 1 / 5 , then the total work will be finished in 5 days. 4) Work is compared by understanding the work of one man each day. 5) If the answer is to come in excess, then multiply by the left and right numbers. if the answer is to come in low, then divide by the left and right number. Examples : 1) It takes a person 10 days to complete a task. If it takes another 15 days for the other to do the same work, how many days will it take for both of them to complete the work? Ans. : Days of both = ( Multiplication of two numbers ) / ( The sum of two numbers ) Days of both = ( 10 × 15 ) / ( 10 + 15 )                          = 150 / 25                           = 6 days. 2) It takes a person 20 days to complete a task. If it takes ano

Series Order tricks : A category of three, four or some numbers is given in the competitive examination. There is a mutual relationship among these numbers. The same relationship has to be understand and the same basis is to be increased further. Examples : 1) What will be the next number in the following series. 3, 10, 31, 94, ----- Ans. : Each terms is increasing by : ( n × 3 ) + 1. Therefore, ( 3 × 3 ) + 1 = 10 ( 10 × 3 ) + 1 = 31 ( 31 × 3 ) + 1 = 94 ( 94 × 3 ) + 1 = 283 Therefore, next number : 283. 2) Find the next order in the category. 1, 4, 9, 16, ---- Ans. : Each term is a squares of consecutive numbers. therefore, 5 × 5 = 25. therefore, next number = 25. Examples : Q. What will be the next number in the following series .  1) 3, 6, 10, 15, 21, ---- Ans. : The difference in each term is increasing in the form of consecutive numbers. that is 3 + 3 = 6. 06 + 4 = 10. 10 + 5 = 15. 15 + 6 = 21. 21 + 7 = 28. There

Fractions for kids : " A number that is not a whole number is called a fraction numbers " There are two types of fraction numbers : Ordinary fraction / Vulgar fraction Decimal fractions. Ordinary fractions :      Which is in the form of a different p/q, is called ordinary fraction. Examples: 3/2, 5/7, 21/8, etc. Decimal fractions :       Numbers that have a decimal mark are called decimal fractions. Examples : 1.3, 4.5, 2.3, etc. Comparison of fractions : Rule 1 :      If two or more fractions have the same denominator, then the fraction will be the largest whose numerator value is the largest and the fraction will be the smallest whose numerator value is the smallest. Examples : 1) What is the largest and smallest fractions between 1/5, 2/5, 6/5 and 7/5. Ans. : 1/5 is the smallest fractions in 1/5, 2/5, 6/5 and 7/5 and 7/5 is the largest fractions. 2) What is the smallest fractions between 12/15, 7/15, 3/15 and 9/15. Ans. :

Time, Speed & Distance  formulas, tricks : Some important formulae : Distance = Time × Speed Speed = Distance / Time. Time = Distance / Speed. Important facts : If two objects move parallel in the same direction, then their  relative speed is equal to the difference of their movements. If two objects move in a parallel opposite direction, then their relative speed is equal to the sum of their movements. When converting km/hr to meters/ second, multiply by 5/18. When converting meters/second to km/hr, multiply by 18/5. The sum of the speed opposite the direction of the train should be added. If the direction of the train is the same, the speed should be subtracted. In mathematics, add up all the long distance and calculate the distance to the total lobby. If a person covers a certain distance at a speed of X km/hr and an equal distance with Y km/hr, then the average speed for the entire journey = ( 2XY ) / (X + Y ) km/hr If the boat moves in the direction of

GCD ( HCF )and LCM questions and answers : GCD stands for greatest common divisors. Or HCF stands for highest common factor. LCM stand for Lowest Common Multiple. LCM it a small number that can be divided completely by the other given numbers. GCD it is the largest number which can divided the given numbers. GCD is always smaller or equal to a smaller number. LCM is always equal to or larger than a large number. LCM of fraction : LCM = LCM of numerators / GCD of denominators. GCD of fraction : GCD = GCD of numerators / LCM of denominators. LCM of prime numbers is theirs multiplication. GCD of prime numbers is always one. Relation between LCM and GCD in two numbers is : First number × second number = LCM × GCD Lowest Common Multiple ( LCM ) : LCM it a small number that can be divided completely by the other given numbers. Methods of finding LCM : List Method : Question: Find the LCM  1) 5 , 8.            2) 4, 6.           3) 3, 7 1) 4, 6