correct answer is: d) \large\frac{11}{147}

Explanation

To find the required greatest quantity we need to HCF the given amounts.
Here, the given amounts are = Rs 1\large\frac{4}{7}, Rs 1\large\frac{1}{21} and Rs \large\frac{33}{49}.
Or, Rs \large\frac{11}{7},\frac{22}{21} and \large\frac{33}{49}. _{[covert mixed to improper]}
The formula we use to get the HCF of two or more fractions is:
\large\frac{The\ HCF\ of\ Numerator}{The\ LCM\ of\ Denominator}

Here, given numerators are 11,22 and 33.
\therefore The HCF of 11,22 and 33 is =11
And given denominators are 7,21 and 49.
\therefore The LCM of 7,21 and 49 is =7\times3\times7=147
So that, the HCF of Rs \large\frac{11}{7},\frac{22}{21} and \large\frac{33}{49} is =\large\frac{11}{147}
\therefore Rs \large\frac{11}{147} is the greatest quantity that must be divided into Rs 1\large\frac{4}{7}, Rs 1\large\frac{1}{21} and Rs \large\frac{33}{49} so that the quotients are integers.
Ans: Rs \large\frac{11}{147} is the greatest quantity.

Other ways to ask this same math question are:

1. What is the largest number by which Rs 1 4/7, Rs 1 1/21, and Rs 33/49 must be divided to obtain whole-number quotients?
2. Calculate the greatest divisor by which Rs 1 4/7, Rs 1 1/21, and Rs 33/49 must be divided to yield integer quotients.
3. Determine the largest quantity by which Rs 1 4/7, Rs 1 1/21, and Rs 33/49 must be divided so that the resulting quotients are integers.
4. Find the maximum amount by which Rs 1 4/7, Rs 1 1/21, and Rs 33/49 must be divided to ensure that the quotient is an integer.