Question

There are some coins and rings of either gold or silver in a box. $60\%$ of the objects are coins and $40\%$ of the rings are of gold and $30\%$ of the coins are of silver. What is the percentage of gold articles?
A) 16
B) 27
C) 58
D) 70

Answer 1

Hint: To solve this question we have to know the concept of percentage. To make the calculation easy the percentage is converted into fraction like $a\%$ in fractional form is written as$\dfrac{a}{100}$ . Each condition given in the question demands for the number of certain objects. TO find the percentage of certain material formula used is $\dfrac{\text{no}\text{.of certain material}}{\text{total no}\text{.of material}}\times 100$.

Complete step by step solution:
The given question asks to find the percentage of the gold articles among the coins and rings which are either gold or silver. To find the percentage we will have to calculate the percentage formulas. To solve the question we will consider the total number of coins and rings of both the gold and silver will be$x$. Mathematically it will be written as
$\text{No}\text{.of coins+No}\text{.of rings}=x$
Let us start with each condition given, so to start with no. of coins is $60\%$of the total. So the number of coins are:
$\text{No}\text{.of coins=60 }\!\!\%\!\!\text{ }\times x$
To change the percentage the value is divided by and percentage sign is removed, so on doing this we get the below equation:
$\text{No}\text{.of coins=}\dfrac{60}{100}\times x$
$\Rightarrow \dfrac{3x}{5}$
Second condition given in the question is that the $40\%$ of the rings are gold, mathematically it means:
$\text{No}\text{.of rings =Total objects- No}\text{.of coins}$
$\Rightarrow \text{No}\text{.of rings = x-}\dfrac{3x}{5}$
$\Rightarrow \text{No}\text{.of rings = }\dfrac{2x}{5}$
The condition says that the gold rings are $40\%$of the total rings, so it is presented mathematically as:
\[\text{No}\text{.of gold rings = 40 }\!\!\%\!\!\text{ }\times \dfrac{2x}{5}\]
On calculating, we get:
\[\Rightarrow \text{No}\text{.of gold rings = }\dfrac{40}{100}\times \dfrac{2x}{5}\]
$\Rightarrow \text{No}\text{.of gold rings = }\dfrac{4x}{25}$
The last condition given in the question is, the number of silver coins are \[30\%\] of the whole coins present:
\[\text{No}\text{.of silver coins = 30 }\!\!\%\!\!\text{ }\times \text{Total coins}\]
\[\Rightarrow \text{No}\text{.of silver coins = }\dfrac{30}{100}\times \dfrac{3x}{5}\]
\[\Rightarrow \text{No}\text{.of silver coins = }\dfrac{9x}{50}\]
We are asked to find the percentage of the total silver objects
\[\text{No}\text{.of gold rings+ No}\text{.of gold coins = }\dfrac{4x}{25}+\left( \text{No}\text{.of coins-No}\text{.of silver coins} \right)\]
\[\Rightarrow \text{No}\text{.of gold objects = }\dfrac{4x}{25}+\dfrac{3x}{5}-\dfrac{9x}{50}\]
\[\Rightarrow \dfrac{8x+30x-9x}{50}\]
\[\Rightarrow \dfrac{29x}{50}\]
Percentage of the gold objects among the total objects is:
\[\Rightarrow \dfrac{\text{No}\text{.of gold objects}}{\text{No}\text{.of total objects}}\times 100\]
Putting the values in the above formula:
\[\Rightarrow \dfrac{\dfrac{29x}{50}}{x}\times 100\]
\[\Rightarrow \dfrac{29x}{50x}\times 100\]
On cancelling out $x$ we get:
\[\Rightarrow 29\times 2\]
\[\Rightarrow 58\%\]
\[\therefore \] The percentage of gold objects is \[58\%\].

Note: The above question could be solved more easily if the total objects is considered to be\[100\] .
No. of coins +No. of rings = \[100\]
No. of coins =\[60\]
No. of Rings =\[100-60=40\]
No. of Ring of gold = \[\dfrac{40\times 40}{100}=16\]
No. of Ring of gold = \[\dfrac{30\times 60}{100}=18\]
No. of Coins of Golds = \[60-18=42\]
No. of (Ring+Coins) of gold = \[16+42=58\]
Hence the percentage of gold articles =\[58\%\]