correct answer is: b) \large\frac{4}{15}

Explanation

Here, two fractions LCM and HCF is \large\frac{4}{5} and \large\frac{2}{15}
And One fraction is \large\frac{2}{5}
Let, the other fraction is ‘x’
We know,
Product of two numbers = Their LCM \times Their HCF
So that,
\large\frac{2}{5}\times x=\large\frac{4}{5}\times\frac{2}{15}
\rightarrow\large\frac{2x}{5}=\large\frac{8}{75}
\rightarrow 150x=40
\rightarrow x=\large\frac{40}{150}
Or, \large\frac{4}{15}
\therefore The other fraction is \large\frac{4}{15}
Ans: The other fraction is \large\frac{4}{15}.

Other variants of this particular math question are:

1. If the least common multiple (LCM) and highest common factor (HCF) of two fractions are 4/5 and 2/15 respectively, and one of the fractions is 2/5, what is the other fraction?
2. If the LCM of two fractions is 4/5, the HCF is 2/15, and one of the fractions is 2/5, what is the other fraction?
3. Suppose one of the fractions is 2/5, and the LCM and HCF of two fractions are 4/5 and 2/15 respectively. What is the other fraction?
4. If the LCM of two fractions is 4/5, the HCF is 2/15, and one of the fractions is 2/5, what is the other fraction?