Average Related to speed (Notes-2)
Theorem (1) : If a person travels a distance of 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
If a man goes to a certain place at a speed of x km/hr and returns to the original place at a speed of y km/hr, then the average speed during up and down journey.
Theorem (2) : 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
Problem 1: A train travels from A to B at the rate of 20km/hr and from B to A at the rate of 30km/hr. what is the average rate for the whole journey?
Problem 2 : A person divides his total journey into three equal parts and decides to travel the three parts with speeds of 40, 30 and 15 km/hr respectively. Find his average speed during the whole journey.
Problem 3: One third of a certain Journey is covered at the rate of 25km/hr, one-fourth at the rate of 30km/hr and the rest at 50km/hr. find the average speed for the whole journey.
Problem 4 : The average salary of the entire staff in an office is Rs. 120 per month. The average salary of officers is Rs. 460 and that of non- officers is Rs. 110. If the numbers of officers is 15, then find the numbers of non- officers in the office.
Solution :-Let the required number of non-officers be x
Method of allegation:
Number of officers : number of non-officers
=10 : 340 =1 : 34
Problem 5: There were 35 students in a hostel. If the numbers of students increase by 7, the expenses of the mess increases by Rs. 42 per day while the average expenditure per head diminishes by Rs.1 find the original expenditure of the mess.
Suppose, the average expenditure was Rs. x. then total expenditure =35x, when 7 more students join the mess, total expenditure=35x+42