Question

A number is divided into two parts such that half of the first part added to one fourth of the second part is equal to two-fifth of the number. What is the ratio of the two parts?

• A. 1 : 2
• B. 2 : 5
• C. 3 : 2
• D. 4 : 3
• E. 5 : 6

Hint:

Let the two parts be x and N - x, translate the word condition directly into a single linear equation in x and N, and clear the fractions using the LCM of the denominators.

Answer 1

The Correct Option is C

Step 1: Set up the equation.
Let the number be \(N\), the first part be \(x\), and the second part be \(N-x\).
Given: \(\frac{x}{2}+\frac{N-x}{4}=\frac{2N}{5}\)

Step 2: Clear the denominators.
Multiply throughout by 20 (LCM of 2, 4, 5):
\(10x+5(N-x)=8N\)
\(10x+5N-5x=8N\)
\(5x=8N-5N\)
\(5x=3N\)
\(x=\frac{3N}{5}\)

Step 3: Find the second part.
Second part \(=N-x=N-\frac{3N}{5}=\frac{2N}{5}\)

Step 4: Form the ratio.
First part : Second part \(=\frac{3N}{5}:\frac{2N}{5}=3:2\)

So the ratio of the two parts is 3 : 2, matching option (c).