Question

If a certain box contains \[200000\] medicine tablets each weighing $20$ mg, what will be the total weight of all the medicines in the box (in both grams as well as in kilograms) respectively?
(a) $4000$ and $4$
(b) $4$ and $4000$
(c) $4$ and $4$
(d) None of these

Answer 1

Hint: The given problem revolves around the concepts of standard measurements of calculations such as ‘m’, ‘cm’, ‘g’, ‘kg’, ‘km’, ‘ltrs’, ‘ml’, ‘milli’, etc. As a result, by considering the standard measurement for ‘milli’ i.e. $1m = {10^{ - 3}}$ and also, ‘g’ to ‘kg’ i.e. $1000$ g $ = $ $1$ kg respectively; multiplying the total value w.r.t. each term given, the desired values are obtained.

Complete step-by-step solution:
Since, we have given that,
Total of \[200000\] medicine tablets exhibits in the box, which weighs of $20$ mg per tablets (mg equals to milligrams, mathematically expressed as $1$ milli $ = $ \[{10^{ - 3}} = \dfrac{1}{{{{10}^3}}} = \dfrac{1}{{1000}}\] respectively) … (i)
Total weight of all the medicines (in mg) is,
$ = 200000 \times 20$ mg
$ = 4000000$ mg
As a result, converting the above value that is measurement in ‘g’ to ‘kg‘ or in ‘kg‘ to ‘g‘, we get
Here, we will first convert ‘mg‘ to ‘g‘ because the given measurement is in ‘milligrams’ noted as ‘mg’ from (i) i.e. $1m = {10^{ - 3}}$, we get
$ = 4000000$ mg $ = \dfrac{{4000000}}{{1000}}$ g
Hence, total weight of all the medicines (in g) is,
$ = 4000$ g
Similarly,
By converting the standard measurement in ‘g’ to ‘kg’ i.e. $1000$ g $ = $ $1$ kg, we get
Hence, (by solving mathematically) the equation becomes
$ = 4000$ g $ = \dfrac{{4000}}{{1000}}$ kg
Hence, total weight of all the medicines (in kg) is,
$ = 4$ kg
$\therefore$ The option (a) is correct.

Note: One must able to know all the basic standard measurement for the calculations such as $1000$ g $ = $ $1$ kg, $1$ milli $ = $ ${10^{ - 3}}$ , etc. required to convert the certain measurements from one standard to another say, ‘g’ to ‘kg’, etc. As a result, simplify the solution mathematically (algebraically) by given values or conditions, so as to be sure of our final answer.