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

Answer 1

The correct option is C I and either II or III is sufficient

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

Given:

I. $y=x+6$ $...\left(1\right)$

II. $40\%$ of $x=30\%$ of $y$

$\Rightarrow \frac{40}{100}\times x=\frac{30}{100}\times y$

$\Rightarrow 0.4x=0.3y$

$\Rightarrow \frac{x}{y}=\frac{3}{4}$ $...\left(2\right)$

IIII. $(\frac{1}{2}\times y):(\frac{1}{3}\times x)=2:1$

$\Rightarrow \frac{\frac{y}{2}}{\frac{x}{3}}=\frac{2}{1}$

$\Rightarrow \frac{3y}{2x}=\frac{2}{1}$

$\Rightarrow \frac{y}{x}=\frac{4}{3}$

$\Rightarrow \frac{x}{y}=\frac{3}{4}$

$\Rightarrow 4x=3y$ $...\left(3\right)$

Let us multiply the equation $\left(1\right)$ 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 $18+24=42$