Question : Three numbers are in the ratio 5 : 6 : 7. If the product of the number is 5670, then the greatest number is:
Option 1: 15
Option 2: 18
Option 3: 21
Option 4: 28
Correct Answer: 21
Solution :
Given: Three numbers are in the ratio 5 : 6 : 7.
Let the numbers be $5x,6x,$ and $7x$, respectively.
The product of the number is 5670.
According to the question,
$5x×6x×7x = 5670$
⇒ $x^{3}=\frac{5670}{5×6×7}$
⇒ $x^{3} = 27$
$\therefore x = 3$
$\therefore$ The greatest number $=7x = 7 ×3= 21$
Hence, the correct answer is 21.
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