a) \large\frac{12}{147}

b) \large\frac{10}{147}

c) \large\frac{19}{147}

d) \large\frac{11}{147}

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:

**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?****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.****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.****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.**