Question

A number is divided into two parts such that half of the first part added to the one fourth 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

Hint:

Translate the sentence into one linear equation in the two parts and simplify.

Answer 1

The Correct Option is C

Step 1: Set up variables. Let the number be N, and let its two parts be x and y, so \(x + y = N\).
Step 2: Translate the condition into an equation. Half of the first part added to one fourth of the second part equals two fifths of the number: \(\dfrac{x}{2} + \dfrac{y}{4} = \dfrac{2N}{5}\).
Step 3: Clear the fractions. Multiplying every term by 20 (the LCM of 2, 4 and 5) gives \(10x + 5y = 8N\).
Step 4: Substitute N = x + y. \(10x + 5y = 8(x+y) = 8x + 8y\).
Step 5: Simplify. \(10x - 8x = 8y - 5y\), so \(2x = 3y\).
Step 6: Write the ratio. \(\dfrac{x}{y} = \dfrac{3}{2}\), so the two parts are in the ratio 3 : 2.\[\boxed{3:2}\]