In an exam, considering marks of two students, one of them scored 10 more than the other, and his marks was 60% of the sum of their scores. Find the scores of two individuals.
Score of Student-1 = x; Score of Student-2 = y Given, x = y+10 i.e. y = x - 10 x = 60% of (x + y) = 0.6 (x + y) = 0.6 (x + x - 10) = 1.2x - 6 x = 1.2x - 6 0.2x = 6 x = 30 = score of student-1 y = 20 = score of student -2
What is unbalanced system and its effect?
In a system having one or more rotating masses, if the center of mass of the system does not coincide with the axis of rotation, then the system is said to be unbalanced. Vibrations occur in an unbalanced system, which has adverse effects such as damage to the vehicle or machine. Therefore, balancing of inertia forces and couples is necessary.
Three large and two small pumps can fill a tank in 6 hours. One large and four small pumps can fill the same tank in 6 hours. How many hours does five large and five small pumps take to fill the tank?
L= Work rate by Large pump ; S = Work rate by Small pump; t = time taken Given, 3L+2S = 1/6 ..................... (1) L + 4S = 1/6 ..................... (2) For 5L + 5S, t = ? Solving equations (1) and (2), L = S = 1/30 5L + 5S = 5(1/30) + 5(1/30) = 1/3 Therefore, Work rate by 5L and 5S = 1/3 i.e. it takes 3 hours to fill the tank.