Average Part - 1

Quantitative Aptitude

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Average Part - 1                                                    Next- Boats and Streams

Rule : Average = Sum of data / No. of data Ex. The average of 13 results is 40 and that of first six is 30 and last six is 34. Find the value of 7 th number. Solution : 7 th number will be = Sum of 13 results - ( Sum of first six + Sum of last six ) = ( 13 * 40 ) - ( 6 * 30 + 6 * 34 ) = 136 Ex. In a class, there are 20 students whose average age is decreased by two months, when one student aged 18 years is replaced by a new student, find the age of the new student ? Solution : Age of new student = Age of removed student - Numbers of students * Decrease in average age   = 18 - 20 * ( 2 / 12 ) = 44 / 3 = 14 years 8 months Rule : If a person travels a distance at a speed of x km/hr, and the same distance at a speed of y km /hr, then the average speed during the whole journey is given by :       Rule : If a person travels three equal distances at a speed of x km / hr, y km / hr and z km / hr respectively. Then the average speed during the whole journey is :       Ex. A man divides his total journey into three equal parts and decides to travel the three parts with speeds 60 km / hr , 24 km / hr and 45 km /hr . Find the average speed during the whole journey ? Solution : Average speed = 3 * 60 * 24 * 45 / 60 * 24 + 24 * 45 + 45 * 60 = 37.24 km / hr Ex. The mean temperature of Monday to Wednesday was 27 °C and of Tuesday to Thrusday was 24 °C. If the temperature on Thrusday was 2 / 3 rd of the temperature on Monday, What was the temperature on Thrusday ? Solution : Mon + Tue + Wed = 81       Tue + Wed + Thu = 72      hence    Mon - Thu = 9      Also Thu = ( 2 /3 ) * Mon      So the temperature of Thrusday = 18 °C Ex. The average of five consecutive numbers is n . If the next two numbers are also included, the average will . (a) increase by 1      (b) remain the same (c) increase by 1.4      (d) increase by 2 Solution : Ex. If the average of 50 numbers is 38. If two numbers 45 and 55 are discarded, the average of the remaining number will be ? Ex. There were 42 students in a hostel. If the number of students increases by 7, the expenses of the mess increases by Rs 49 per day.While the average expenditure per head diminishes by Rs. 1. Find the original expenditure of the mess. Solution : Let the average expenditure was Rs. x So total expenditure will be 42x. When 7 more students join the mess, total expenditure= 42x+49    So x= 14, therefore original expenditure of the mess= 42*14=Rs 588 Ex. The average age of a family of 8 members is 23 years. If the age of the youngest membe be 7 years, then what was the average age of the family member at the birth of the youngest member ? Solution: Total age of all members= 8 * 23 =184 years 7, years ago, total sum of ages= 184 - ( 8 * 7 ) = 128 years But 7 years before there were only 7 members in the family so, Ex. Find the average of first 10 multiples of 8 ? Solution : Ex. A batsman makes a score of 70 runs in the 15 th inning and thus increases average by 2 runs. Find the average after 15 th inning ? Solution : Let the average after 15 th inning be x The average after 14 th inning = (x-2) Now 14 (x-2)+70=15x So x=42