answer : Determining the sum of serial numbers ********************* Sutra (when starting from 1) Sum S = half of the last number * (last number +1) eg: 1 to 100 What is the sum of the serial numbers ? The sum S = half of the last number × ( last number +1) = 50 × 101 [here the last number is 100] = 5050 (answer) Formula 2. The formula for determining the sum of consecutive (when different from 1) numbers such as: What is the sum of the numbers from 5 to 35 ? Formula: sum = (sum from 1 to 35) - (sum from 1 to 4) = 35/2 × 36-2 × 5 [according to the previous formula but here are two parts] = 630-10 = 720 # b. Dr is asked to find the sum from 5 to 35, so the sum from 1 to 35 is babe, from which the sum from 1 to 4 (the previous number of 5 is 4) is omitted . Mean number = (1st number + last number) / 2 eg: 1 + 3 + 5 + ......... + 21 = ? Mean Number = (1 + 21) / 2 = 11 Addition S = ( Mean Number ) 2 = (11) 2 = 121 (Answer) ৬ + .............. + 100 = ? Sum = median × ( median-1) median = = 2 + 100) / 2 = 51 Sum = 51 × 50 = 2550 Type-1 ---- ------ * 10 consecutive numbers are given , If the sum of the first 5 is 560, what is the sum of the last 5 ? Technique: -1 The sum of the first number to be given + the sum of the last 5 of the number to be taken out = the sum of the first five + 5 ^ 2 = 580 + 25 = 575 ✿ ------------- ---------- ----- ------------------ _ Type - 2 ---------- * consecutively 6 Numbers Given Yes , if the sum of the last 3 is 36, what is the sum of the first 3 ? Technique: The sum of the last number will be given --- the sum of the number of numbers to be found is the sum of the first 3 = the sum of the first 3 - 3 ^ 2) 36-3 ^ 2 = 36-9 = 26 Remember: 1st five / If you want three, add (+) and if you want the last, subtract (-) 7 Sum Oh Average Diagnosis Formula 3 Of the stream Number of terms = {( last term - 1st term) ÷ Difference of terms } The sum of the clauses = {( 1st term + last term) × Number of terms } ÷ 2 Of the stream Average = ( 1st Terms + Terms ) ÷ 2 _ Small By Although Write tnx . - There are a total of 4 formulas in the class: -. Formula: If square intervals or differences are given , in the case of determining the larger number - Technique: Larger number = (square interval + 1) 2. Q: If the square of two consecutive numbers is 47 , what is the larger number ? Solution: Large number = ( 47 + 1) / 2 = 24. Formula: Given the difference between two squares , in case of finding the smaller number-. Technique: Small number = (square difference - 1) 2. Question: The difference between the squares of two serial numbers is 33 . What is the smallest number ? Solution: The smaller number = ( 33-1) 2 = 16 (n ). Sutra: The bigger the .... the smaller / the smaller .... the greater the number mentioned in the case of determining the number-. Technique: Number = (sum of two given numbers) 2. Q: A number as big as 742 is as small as 830 . What is the number ? Solution: Number = ( 7 42 + 830) 2 = 786 (n ). Source: The product of two numbers and if one number is given, the other number is determined. Technique: The product of two numbers ÷ a number. Q: The product of 2 numbers is 2304. If one number is 96 , what is the other number ? . Solution: The other number = ( 2304 ÷ 96) = 24 (n ) 3 Sum Oh Average Diagnosis Formula 3 Of the stream Number of terms = {( last term - 1st term) ÷ Difference of terms } The sum of the clauses = {( 1st term + last term) × Number of terms } ÷ 2 Of the stream Average = ( 1st Terms + Terms ) ÷ 2 _ Field Diagnosis formula 7 Rectangle Area = ( length × width) square unit Rectangle Range = 2 × ( length + width ) Parallel Of the field Area = land × height (square unit ) Square Area = ( arm ) ² ( square unit ) Of the square Range = 4 ুর Arm length The area of a square = the square unit Rectangular Solid Volume = ( length × width × height) cubic unit Triangular Of the field Area = ( land × height) square unit Trapezium Area = 1/2 ( a + b ) × h [ length and height of parallel arms a and b ] . Cube Surface Area = 6 _ The surface area of a rectangular solid is = 2 ( ab × bc × ca) [a length , b width , c height] . Of the circle Circumference = 2 πr , Area of the circle = πr² = 22 / 7r² { Here is the radius of the circle r} Area of four walls = 2 × ( length + width ) height Length Measurement 3 1 What . M = 1000 Meters ❉ 1 key. M = 10 hectometers 6 1 What . Mr. _ = 0 . 72 Miles 3 1 Hectometer = 10 Deka Meters 3 1 Deka M = 10 Meters 3 1 M = 10 Decimeter 3 1 M = 100 Meters 3 1 M = 1000 Mr. _ M 3 1 Decimeter = 10 Centimeters 3 1 Centimeters = 10 Ml Meters 3 1 Inches = 2 . 54 cm 8 12 Inches = 1 foot 3 3 Feet = 1 Yards 3 160 Yards = 1 mile 3 1 Mile = 1 . 61 What . Mr. _ 3 1 Meter = 39 . 36 Inches ( approximately ) 6 144 Square Inch = 1 Square Feet 3 1 Miles = 160 Yards 3 1 Nautical Miles = 1853 . 16 Meters 3 1 Fadham = _ Feet ( of water ) Depth Of measurement Single ) 6 100 Sq m = 1 acre 6 100 Century = 1 Acre 3 4640 Square Yards = 1 Acre 3 1 Square Miles = 640 Acre 3 1 Acre = 4048 . 3 Square M 3 L , sa , nd and c. Sa. Nd - the rule 7 Fractions L , Sa , Nd = Lobandlor L , Sa , Nd ÷ Hrandlor G , Sa , Nd . Fractions C , sa , nd = lobandlor c , sa , nd ÷ londalor l , sa , nd . The product of two numbers = the sum of two numbers , sa , ng , g , sa , nd . L , sa , nd = the result of two numbers ÷ g , sa , nd C , sa , nd = the result of two numbers ÷ l , sa , nd A Number = ( l , sa , nd × g , sa , nd ) ÷ given number Liquid Oh Tough Substance Of measurement Single 3 1000 Milligam = 1 Gam ❉ 1000 gm = 1 kg ❉ 1000 Game = 2 . 2 Pound 3 100 Kilogram = 1 Quintal 3 10 Quintal = 1 Metric Tons 3 10 Quintal = 1000 Kilograms 3 1 Short Ton = 2240 Pound 3 1 Liter = 1000 mili litter 1 liter = 1000 cubic cm: (for measuring water at a temperature of only 4 degrees) . 1 Barrel = 159 Litter ( approximately ) 6 1 Barrel = 34 . 9826 Galen 3 1 Galen = 4 . 548 Litter ( approximately ) 6 1 Carat = 2 Game ( carat ) Precious Stone Oh Gems Weight Of measurement Single ) 6 1 Heavy = 18 Bring 3 100 kg = 1 Quintal 3 Place - Land Measurement 3 1 Air = 100 Square m 7 1 Hector = 100 Air 3 1 Hector = 1000 Square Centimeters 3 1 Hector = 2 . 46 Acre ( approximately ) 6 1 Square M = 100 Square Decimeter 3 1 Square M = 1000 Square Centimeters 3 1 Square M Tar = 10 . 3 Square feet ( approximately ) 6 1 Acre = 4840 Square yards 3 1 Acre = 10 Square Chain 3 1 A tax = 3 bighas ৮ chhatak 1 Bigha = 20 Cut 3 1 Bigha = 1 Square 3 1 Bigha = 1800 Square yards 3 1 Cut = 60 Square yards 3 1 Cut = 16 Scatter 3 1 Chhatak = 5 Square yards 3 1 Square yards = 5 Square feet 3 1 Sqft = 144 Square inch 3 1 Chain = 22 Yards 3 1 Squarechain = 484 Square yards 3