Question

which of the following proportions is parallel? 500 g : 2 tablets :: 1 tablets : x g; 10 mg : 1 tablet :: 10 g : x tablets; 100 mg : 2 tablets :: x g : 2 tablets; 100 mg : 1 tablet :: 500 mg : x tablets

Explanation:

Step1: Recall proportion - equality of ratios.

Proportions are of the form $a:b = c:d$ which means $\frac{a}{b}=\frac{c}{d}$. Also, convert units for consistency (1 g = 1000 mg).

Step2: Analyze option 1.

For 100 mg : 1 tablet = 500 mg : X tablets, cross - multiplying gives $100X=500\times1$, so $X = 5$ tablets.

Step3: Analyze option 2.

100 mg : 2 tablets. Convert 100 mg to g (100 mg=0.1 g). So we have 0.1 g : 2 tablets. If we set it equal to X g : 2 tablets, then X = 0.1 g.

Step4: Analyze option 3.

10 mg : 1 tablet. Convert 10 g to mg (10 g = 10000 mg). The proportion 10 mg : 1 tablet = 10000 mg : X tablets. Cross - multiplying gives $10X=10000\times1$, so $X = 1000$ tablets.

Step5: Analyze option 4.

500 g = 500000 mg. 500 g : 2 tablets = 1 tablet : X g. Convert 500 g to mg for cross - multiplying. 500000 mg : 2 tablets = 1 tablet : X g (convert X g to mg say Y mg). Cross - multiplying gives $500000\times X=2\times1\times1000$ (since we convert X g to mg), $X = 4$ mg or 0.004 g.

Let's check the ratios more formally.
For a proportion $a:b=c:d$, $ad = bc$.
For the first option:
The first ratio is $\frac{100\text{ mg}}{1\text{ tablet}}$ and the second is $\frac{500\text{ mg}}{X\text{ tablets}}$. Cross - multiplying: $100X=500\times1$, $X = 5$ tablets.
For the second option:
The first ratio is $\frac{100\text{ mg}}{2\text{ tablets}}=\frac{0.1\text{ g}}{2\text{ tablets}}$, and the second is $\frac{X\text{ g}}{2\text{ tablets}}$. Cross - multiplying gives $0.1\times2=X\times2$, so $X = 0.1$ g.
For the third option:
The first ratio is $\frac{10\text{ mg}}{1\text{ tablet}}$ and the second is $\frac{10\text{ g}}{X\text{ tablets}}$. Since 10 g = 10000 mg, cross - multiplying gives $10X=10000\times1$, $X = 1000$ tablets.
For the fourth option:
500 g = 500000 mg. The first ratio is $\frac{500000\text{ mg}}{2\text{ tablets}}$ and the second is $\frac{1000X\text{ mg}}{1\text{ tablet}}$. Cross - multiplying gives $500000\times1=2\times1000X$, $X = 250$ mg or 0.25 g.

The correct proportion is 100 mg : 1 tablet = 500 mg : 5 tablets. But among the given options, if we assume the question is about correct set - up of proportion and unit - handling, the proportion 100 mg : 1 tablet = 500 mg : X tablets (where we solve for X) is a valid proportion set - up.

Answer:

100 mg : 1 tablet = 500 mg : X tablets (first option)