Question

Of the three numbers, the ratio of the first and the second is $8:9$ and that of the second and third is $3:4$. If the product of the first and third numbers is $2400$, then what is the second number?

• A. $45$
  
• B. $38$
• C. $22$
• D. None of these
  

Answer 1

Answer: (A)

Let the first and the second number be $8x$ and $9x$ respectively.
Given $9x:ThirdNumber=3:4$
$\Rightarrow \frac{9x}{ThirdNumber}=\frac{3}{4}\Rightarrow ThirdNumber=\frac{9x\times 4}{3}=12x$

Given $8x\times 12x=2400$
$\Rightarrow x^2=\frac{2400}{96}=25\Rightarrow x=5$
$\therefore$ Second number $=9\times 5=45$.