correct answer is: c) 56\large\frac{1}{4}

Explanation

Here given Rupees =3\large\frac{3}{4}\normalsize,5\large\frac{5}{4}\normalsize,4\large\frac{11}{16}
Or, Rupees \large\frac{15}{4},\large\frac{25}{4},\large\frac{75}{16} _{[covert mixed to improper fraction]}
To find the required least quantity we need to LCM the given Rupees.
We know,
The formula we use to get the LCM of two or more fractions is:
\large\frac{The\ LCM\ of\ Numerator}{The\ HCF\ of\ Denominator}

\rightarrow LCM of Numerators 15,25,75 is =5\times5\times3\times3=225
\rightarrow HCF of Denominators 4,4,16 is =4
So that, the LCM of 3\large\frac{3}{4}\normalsize,5\large\frac{5}{4}\normalsize,4\large\frac{11}{16} is =\large\frac{225}{4} or 56\large\frac{1}{4}
\therefore Rs 56\large\frac{1}{4} is the least quantity which, when divided by Rs 3\large\frac{3}{4}, Rs 5\large\frac{5}{4} and Rs 4\large\frac{11}{16}, yields integral quotients.
Ans: Rupees 56\large\frac{1}{4} is the least quantity.

Another form of this specific math question exists:

1. Finding the minimum amount for evenly dividing by Rs 3 ¾, Rs 5 5/4, and Rs 4 11/16 into whole numbers.
2. Determining the lowest common multiple for Rs 3 ¾, Rs 5 5/4, and Rs 4 11/16 to ensure integer outcomes.
3. What is the smallest amount divisible by Rs 3 ¾, Rs 5 5/4, and Rs 4 11/16 to ensure integer results?
4. Finding the minimum whole number dividend for evenly dividing by Rs 3 ¾, Rs 5 5/4, and Rs 4 11/16