  Question

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
Only II and III are sufficient  B
Only I and II are sufficient  C
I and either II or III is sufficient  D
All, II and III together are sufficient  Solution

The correct option is C I and either II or III is sufficientLet the two numbers be $$x$$ and $$y$$ such that $$x<y$$Given: I.  $$y=x+6$$                $$...(1)$$  II.  $$40\%$$ of $$x=30\%$$ of $$y$$$$\Rightarrow \dfrac{40}{100}\times x=\dfrac{30}{100}\times y$$$$\Rightarrow 0.4x=0.3y$$$$\Rightarrow \dfrac {x}{y}=\dfrac {3}{4}$$           $$...(2)$$IIII.  $$\bigg(\dfrac{1}{2}\times y\bigg): \bigg(\dfrac{1}{3}\times x\bigg)= 2:1$$$$\Rightarrow \dfrac{\ \dfrac y2\ }{\ \dfrac x3\ }=\dfrac{2}{1}$$$$\Rightarrow \dfrac{3y}{2x}=\dfrac{2}{1}$$$$\Rightarrow \dfrac {y}{x}=\dfrac {4}{3}$$$$\Rightarrow \dfrac {x}{y}=\dfrac {3}{4}$$$$\Rightarrow 4x=3y$$         $$...(3)$$Let us multiply the equation $$(1)$$ with $$3$$$$\Rightarrow 3y=3x+18$$$$\Rightarrow 4x=3x+18$$$$\therefore x=18$$Substitute the value of $$x$$ in equation $$1$$$$\Rightarrow y=18+6$$$$\Rightarrow y=24$$$$\therefore$$ Sum of $$x$$ and $$y$$ is $$18+24=42$$Mathematics

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