Question

Find the third proportional to 1kg250g, 500g.

Answer 1

Hint: Proportion means equal ratios. So when a certain number of quantities are in proportion it means they are in equal ratios with each other. So if a,b and c are in proportion then $\dfrac{a}{b} = \dfrac{b}{c}$ with b as the mean ratio.


Complete step by step solution:
Now Since we are given the measures of weights as a mix of kg(kilogram) and g(gram) so we will convert the bigger unit kg to smaller unit g and make the given measures of weights uniform first.
Now let $a = 1kg250g$, $b = 500g$ and c be the unknown third proportion we need to find.
Now, $1kg = 1000g$ then 1kg250g will become:
$1kg250g = (1000 + 250)g$
Therefore $a = 1250g$
Now, it is given that, a, b and c are in proportion , then we can say that the following relation holds true:
$\dfrac{a}{b} = \dfrac{b}{c}$,
So, putting the values of $a = 1250g$ and $b = 500g$ in this proportion we will get:
$\dfrac{{1250}}{{500}} = \dfrac{{500}}{c}$
Which will give us c as:
$
  c = \dfrac{{500 \times 500}}{{1250}} \\
   \Rightarrow c = 200 \\
$
That is, the value of c = 200g, which means the third proportional will be c = 200g.
So 1kg250g : 250g : 200g
All the three quantities are proportional to each other.

Therefore, the third proportional to 1kg250g, 500g is 200g.


Note: For such problems it is important to convert the quantities and bring them all to one standard form and then start calculating.Do not have the quantities in different units