Question

The ratio of weights of copper and tin in bronze is 22:3. Find the weight of tin in a bronze article weighing 500 gm.

Answer 1

Hint: Let $k$ be the common factor of 22 and 3. From the given ratio, the amount of copper in bronze is \[22k\] and the amount of tin in bronze is \[3k\]. Then, total bronze is \[25k\] which is given as 500 gram. Solve the equation and find the value of $k$. Substitute the value of $k$ to find the amount of tin in the bronze.

Complete step-by-step answer:
We are given the ratio of weights of copper and tin in bronze is 22:3.
 Write the given ration in terms of fraction.
$\dfrac{{{\text{Weight of copper}}}}{{{\text{Weight of tin}}}} = \dfrac{{22}}{3}$
Let the weight of copper in the bronze=\[22k\]
And weight of tin in the bronze=\[3k\]
From here, the weight of bronze will be \[22k + 3k = 25k\]
Also, the given weight of bronze is 500 gram.
So, we have
 \[\begin{gathered}
  25k = 500 \\
  k = \dfrac{{500}}{{25}} \\
  k = 20{\text{gram}} \\
\end{gathered} \]
But the weight of tin in bronze is \[20k = 20\left( 3 \right) = 60{\text{ gram}}\]
Hence, the weight of tin in bronze is 60 gram.

Note: Ratio is a method of relating objects. If the ratio is given as $a:b$, then there exists a common factor of $a$ and $b$. When that common factor is multiplied with $a$ and $b$, it gives the real amount of that object. Ratios do not have any units but the objects of which ratio is calculated can have a unit.