Three Science classes A, B and C take a Life Science test. The average score of class A is 83. The average score of class B is 76. The average score of class C is 85. The average score of class A and B is 79 and average score of class B and C is 81. Then the average score of classes A, B and C is
Options:
A . 80.5
B . 80
C . 81
D . 81.5
Answer: Option D Answer: (d)Using Rule 10, If the average of '$n_1$' numbers is $a_1$ and the average of '$n_2$' numbers is $a_2$, then average of total numbers $n_1$ and $n_2$ is$Average = {n_1a_1 + n_2a_2}/{n_1 + n_2}$ Students in class A ⇒ x Students in class B ⇒ y Students in class C ⇒ z For classes A and B, ${83x + 76y}/{x+y}$ = 79 ⇒ 83x + 76y = 79x + 79y ⇒ 83x – 79x = 79y – 76y ⇒ 4x = 3y For classes B and C ${76y+85z}/{y+z}$= 81 ⇒ 76y + 85z = 81y + 81z ⇒ 5y = 4z∴ 20x = 15y = 12z ⇒ ${20x}/60$ = ${15y}/60$ = ${12z}/60$ ⇒ $x/3$ = $y/4$ = $z/5$ ∴ Required average${83×3+76×4+85×5}/{3+4+5}$${249+304+425}/12$ = $978/12$= 81.5
Submit Comment/FeedBack