Question:easy

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?

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Translate the sentence into one linear equation in the two parts and simplify.
Updated On: Jul 21, 2026
  • 1 : 2
  • 2 : 5
  • 3 : 2
  • 4 : 3
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The Correct Option is C

Solution and Explanation

This can also be solved by working with fractions of the whole number instead of two separate variables.
Step 1: Let the number be 1 (100%). Suppose the first part is a fraction p of the number, so the first part is p and the second part is \(1-p\).
Step 2: Write the given condition. \(\dfrac{p}{2} + \dfrac{1-p}{4} = \dfrac{2}{5}\).
Step 3: Clear the fractions. Multiplying through by 20 gives \(10p + 5(1-p) = 8\).
Step 4: Simplify. \(10p + 5 - 5p = 8\), so \(5p = 3\), giving \(p = \dfrac{3}{5}\).
Step 5: Find both parts. The first part is \(3/5\) of the number and the second part is \(1 - 3/5 = 2/5\) of the number.
Step 6: Write the ratio. First part to second part is \(\dfrac{3}{5} : \dfrac{2}{5} = 3 : 2\), confirming the earlier answer.\[\boxed{3:2}\]
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