Question

Given that $24$ carat gold is pure gold, $18$ carat gold \[3/4\] gold and \[20\] carat gold is \[5/6\] gold. Find the ratio of the pure gold in \[18\] carat gold to the pure gold in \[20\] carat gold.

A. $5:8$
B. $9:10$
C. $15:24$
D. $8:5$

Answer 1

Hint- In order to deal with this question we will use the concept as $18$ carat gold is \[3/4\]of pure gold and \[20\] carat gold is \[5/6\] of pure gold as it is given that $24$ carat gold is pure gold by putting the values and further by taking the ratio we will get the required ratio easily.

Complete step-by-step answer:
Given that $24$ carat gold is pure gold, $18$ carat gold \[3/4\] gold and \[20\] carat gold is \[5/6\] gold.
We have to find the ratio of the pure gold in $18$ carat gold to the pure gold in \[20\] carat gold.
So first we will individually calculate both of them
Now, According to question $18$ carat gold = \[3/4\] of pure gold
As pure gold = $24$ (given)
Substitute the value in above equation we have
$3/4 \times 24 = 18$
$18$ carat gold = $18$
Similarly, \[20\] carat gold = \[5/6\] of pure gold
As pure gold = $24$ (given)
Substitute the value in above equation we have
$5/6 \times 24 = 20$
\[20\] carat gold = \[20\]
Now we will find the ratio by dividing $18$ carat gold and \[20\] carat gold, so we get
$18:20 = 9:10$
Further simplifying it we have $9:10$
Hence the required ratio is $9:10$

Note- A ratio is a way to measure two quantities, using division as we measure miles and hours in miles per hour. On the other hand, a proportion is an equation which states that two ratios are equal. When one number is unknown in a proportion the number can be identified by solving the proportion.