Question

Chaayos has stock of teas and herbs in a $5:11$ ratio at one of its warehouses. To cut overhead costs, the owners close this warehouse and transfer its stock to a larger warehouse, which increases warehouse's inventory of items by $20\%$. Which of the following could be the number of items at the larger warehouse after the transfer?

• A. $198$
• B. $386$
• C. $480$
• D. $573$

Answer 1

The correct option is C $480$

The ratio of teas to herbs is $5:11.$

Which means that the total number of teas and herbs is $5x+11x=16x$.

Because this represents a $20\%$ increase in the larger warehouse's stock, it follows that $16x$ is $20\%$ or, of the large warehouse's initial stock: $16x\times 5=80x$.

The final stock in the warehouse = $80x+16x=96x$.

This means that the answer must be a multiple of $96$, or in other words, evenly divisible by $96$.

$\Rightarrow$ $480$ is the only one that is evenly divisible by $96$, so correct answer is option $C$.