Question

In a game, the person who takes the least amount of time to finish the tasks comes first. Nana takes $\frac{2}{5}$ minutes, the carpenter takes $\frac{2}{3}$ minutes, and Lobo takes $\frac{4}{5}$ minutes. Out of all three, who came second?

• A. Nana
• B. Lobo
• C. All of them take the same time
• D. Carpenter

Answer 1

The correct option is D Carpenter

Just as we compare fractions by making the denominators equal, we can also do it by making the numerators equal.

The first fraction has $2$ as its numerator, the second fraction has $2$ as its numerator, and the third fraction has $4$ as its numerator. Let's make all the numerators the same.

Calculate the equivalent fraction of $\frac{2}{5}$ with $4$ as the numerator.

$=\frac{2\times 3}{5\times 2}=\frac{4}{10}$

Calculate the equivalent fraction of $\frac{2}{3}$ with $4$ as the numerator.

$=\frac{2\times 2}{3\times 2}=\frac{4}{6}$

The third fraction is $\frac{4}{5}$. Now, all the fractions have the same numerators.

If fractions have the same numerator, the fraction having the smallest denominator has the highest value.

So, $\frac{4}{5}>\frac{4}{6}>\frac{4}{10}\text{or}\frac{4}{5}>\frac{2}{3}>\frac{2}{5}.$

So, the time taken by the carpenter is less than the time taken by Lobo, but more than the time taken by Nana.
Thus, the carpenter came second.