Discussion Forum

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 the second number is

Answer:

Explanation:

Let the numbers $a,b,c$

Given $a : b$ $= 8 : 9$

$b : c$ $= 3 : 4$

$a : b : c$ $= 8\times 3 : 9\times 3 : 9\times 4$

$= 24 : 27 : 36$ $= 8 : 9 : 12$

Let  $\frac{a}{8}=\frac{b}{9}=\frac{c}{12}$

$a=8k$, $b=9k$, $c=12k$

Given $8k\times 12k$ $= 2400$

$k^{2}=\frac{2400}{96}$

$k = 5$

Second number $= 9k$ $= 9\times 5 $ $= 45$