Question

Monica wishes to purchase three articles of A, B, and C type with a total of $\$$214. The unit prices of the articles A, B, and C are $\$$33, $\$$24, and $\$$28 respectively. She purchases 5 articles of Type B. What is the ratio of the number of articles purchased of Type A to that of Type C, if she purchases at least one of each type?

• A. 1:1
• B. 2:1
• C. 1:2
• D. 3:2

Answer 1

The correct option is B 2:1

Amount spent on Type B $=24\times 5=\$120$

Amount left with Monica $=214-120=\$94$

Since she spends all of $\$$94, and gets at least one item of each type (A and C), we can see these combinations:

Case 1:
$\text{2 items of Type A + 1 item of Type C}$
$=2\times 33+1\times 28=94$

Or

Case 2:
$\text{1 item of Type A + 2 item of Type C}$
$=1\times 33+2\times 28=89$

Clearly, Case 1 satisfies the required condition. Thus, the required ratio is $1:2$.