There are four numbers - A, B, C and D. C is equal to 30% of average of A and B and D is 10% more than A. If ratio of A to B is 3 : 5 and sum of C and D is 180, then find average of all four numbers.
Answers
Step-by-step explanation:
There are four numbers - A, B, C and D. C is equal to 30% of average of A and B and D is 10% more than A. If ratio of A to B is 3 : 5 and sum of C and D is 180, then find average of all four numbers.
Therefore the average of A , B , C and D is 125.
There are four numbers - A, B, C and D. C is equal to 30% of average of A and B and D is 10% more than A. If ratio of A to B is 3 : 5 and sum of C and D is 180.
We have to find the average of all four numbers.
Step 1 : C is 30% of average of A and B.
C = 30/100 × [(A + B)/2]
⇒20C = 3(A + B) ...(1)
Step 2 : D is 10 % more than A.
⇒D = A + 10% of A = A + 10/100 × A
= 110A/100 = 11A/10
⇒10D = 11A ...(2)
Step 3 : A/B = 3/5
let x be proportionality constant.
∴ A = 3x , B = 5x
from equation (1), C = 24x/20 = 6x/5
from equation (2), D = 33x/10
Step 4 : C + D = 180
⇒33x/10 + 6x/5 = 180
⇒45x/10 = 180
⇒x = 40 ...(3)
step 5 : now Average of A , B , C and D
= (A + B + C + D)/4
= (3x + 5x + 6x/5 + 33x/10)/4
= (8x + 45x/10)/4
= (8x + 9x/2)/4
= 25x/8
= 25 × 40/8 [ ∵ x = 80 from equation (3) ]
= 125