What Is The Sum Of Two Numbers? I. The Bigger Of These Two Numbers Is 6 More Than The Smaller Number. II. 40% Of The Smaller Number Is Equal To 30% Of The Bigger Number. III. The Ratio Between Half Of The Bigger Number And One-third Of The Smaller Number Is 2: 1. (A) II And III Are Sufficient. (B) Only I And II Are Sufficient. (C) Only II And III Are Sufficient. (D) I And Either II Or III Are Sufficient.

The correct answer is (D) I and either II or III is sufficient.

Sol:

Let the two numbers be x and y such that x < y

Given:

  1. y = x + 6 —[1]
  1. 40% of x = 30% of y
[latex] \Rightarrow \frac{40}{100} * x = \frac{30}{100} * y \\\Rightarrow 0.4x = 0.3y [/latex] [latex]\Rightarrow  \frac{x}{y} = \frac{3}{4}[/latex] —[2]

III. [latex](\frac{1}{2} * y):(\frac{1}{3} * x) = 2 : 1\\\Rightarrow \frac{\frac{y}{2}}{\frac{x}{3}} = \frac{2}{1}\\\Rightarrow \frac{3y}{2x} = \frac{2}{1}\\\Rightarrow \frac{y}{x} = \frac{4}{3}\\\Rightarrow \frac{x}{y} = \frac{3}{4}[/latex] [latex]\Rightarrow 4x = 3y[/latex]—[3]

Let us multiply the equation [1] with equation [3] [latex]\Rightarrow 3y = 3x + 18\\\Rightarrow 4x = 3x + 18 \\\Rightarrow x = 18.[/latex]

By substituting the value of x in equation [1], we get:

[latex]\Rightarrow y = 18 + 6\\\Rightarrow y = 24[/latex]

Therefore, the sum of x and y is 18 + 24 = 42

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