Three children shared a basket of mangoes in such a way that the first child took 1/4 of the mangoes and the…

Analysis

To solve this problem, we need to determine the portion of the basket left after each child takes their share. We start with a whole basket, represented by the fraction $1$.

Concept

When dealing with "remainders" in fractions, we subtract the portion taken from the total to find what is left. We then apply the next fraction to that specific remainder.

Step-by-Step Solution

Step 1: Find the remainder after the first child. The first child took $\frac{1}{4}$ of the mangoes.

Step 2: Find the share of the second child. The second child took $\frac{3}{4}$ of the remainder.

Step 3: Find the share of the third child. The third child gets whatever is left after the first and second children have taken their portions.

To add these, find a common denominator (which is 16):

Now, subtract this total from the whole basket ($1$):

Conclusion

The third child took $\frac{3}{16}$ of the mangoes. This matches option A.

Exam Tip

Whenever you see the phrase "of the remainder," always calculate the remaining fraction first before multiplying. A common mistake is to multiply the second fraction by the original total instead of the remainder. Always check that your final fractions add up to $1$ ($\frac{4}{16} + \frac{9}{16} + \frac{3}{16} = \frac{16}{16} = 1$).