Question:easy

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?

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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.
Updated On: Jul 20, 2026
  • 1 : 2
  • 2 : 5
  • 3 : 2
  • 4 : 3
  • 5 : 6
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The Correct Option is C

Solution and Explanation

Instead of working with fractions of an unknown $N$, this can be solved faster by simply assuming a convenient value for the number, since the answer only depends on a ratio.

Because the equation involves halves, quarters and fifths, pick $N = 20$ (a common multiple of 2, 4 and 5) to avoid fractions entirely.

Let the first part be $x$ and the second part be $20-x$.

Condition: half of the first part plus one fourth of the second part equals two-fifths of 20.
$$\frac{x}{2}+\frac{20-x}{4}=\frac{2}{5}\times20=8$$

Multiply through by 4:
$$2x+(20-x)=32$$
$$2x+20-x=32$$
$$x+20=32$$
$$x=12$$

So the first part is 12, and the second part is $20-12=8$.

Ratio of first part to second part $=12:8=3:2$

This matches the ratio found algebraically, confirming the answer.
\[\boxed{3:2}\]
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