Question

There are two numbers. The first number is 120 more than the second number. The average of the two numbers is 80. If 20 is added to both the numbers, find the ratio of the new numbers.
1. 3 ∶ 1
2. 1 ∶ 3
3. 4 ∶ 1
4. 2 ∶ 1

Answer 1

Correct Answer - Option 3 : 4 ∶ 1

Let, 'X' be the first number and 'Y' be the second number.

Now, it is given that the first number is 120 more than the second number.

⇒ X = Y + 120 

⇒ X - Y = 120      ----(1)

It is also given that the average of the two numbers is 80.

⇒ (X + Y) / 2 = 80

⇒ X + Y = 160      ----(2)

Solve equation (1) and (2), we get,

⇒ X = 140 and Y = 20

Now, add 20 to both the numbers, the new numbers will be X₁ and Y₁,

⇒ X₁ = X + 20

X1 = 140 + 20

X1 = 160

⇒ Y1 = Y + 20

Y1 = 20 + 20 

Y1 = 40

The ratio of both the numbers X1 and Y1 will be,

⇒ X1 : Y1 = 160 : 40

⇒ X1 : Y1 = 4 : 1

Therefore, the ratio of the new numbers X1 and Y1 is 4 : 1.

Hence, the correct answer is 4 : 1.