Question

The sum of 4 numbers is 46. When 6 and 2 are added to the first two; and 2 and 5 are multiplied from the 3rd and 4th, the numbers will be equal. What is the ratio of 4 numbers?
1. 2 : 5 : 9 : 7
2. 7 : 9 : 5 : 2
3. 9 : 7 : 2 : 5
4. 5 : 2 : 7 : 9

Answer 1

Correct Answer - Option 2 : 7 : 9 : 5 : 2

Given:

The sum of 4 numbers = 46

Calculation:

Let the 4 numbers be a, b, c and d

⇒ a + b + c + d = 46   ----(1)

⇒ a + 6 = b + 2 = 2c = 5d = k

⇒ a = k - 6   ----(2)    

⇒ b = k - 2   ----(3)  

⇒ c = k/2   ----(4)    

⇒ d = k/5   ----(5)     

From [2] + [3] + [4] + [5]

⇒ a + b + c + d = k - 6 + k - 2 + k/2 + k/5

⇒ a + b + c + d = (27/10)k - 8   ----(6)     

From [1] and [6]

⇒ 46 = (27/10)k - 8     

⇒ 54 = (27/10)k

⇒ k = 20

⇒ The 4 numbers are [a = 20 - 6 = 14, b = 20 - 2 = 18, c = 20/2 = 10, d = 20/5 = 4]

∴ The ratio of numbers = 14 : 18 : 10 : 4 = 7 : 9 : 5 : 2