a) \large\frac{7}{150} .

b) \large\frac{7}{100} .

c) \large\frac{8}{220} .

d) \large\frac{7}{120} .

correct answer is: d) \large\frac{7}{120} .

#### Explanation

The given quantity is \large\frac{7}{8}\normalsize,\large\frac{14}{15}\normalsize,\ 1\large\frac{1}{20} kg

Let us 1^{st} find the HCF of \large\frac{7}{8}\normalsize\ ,\large\frac{14}{15}\normalsize\ ,\ 1\large\frac{1}{20} or \large\frac{21}{20}

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 7,14 and 21.

\therefore The HCF of 7,14 and 21 is =7

And given denominators are 8,15 and 20.

\therefore The LCM of 8,15 and 20 are =120

So, the HCF of the quantity \large\frac{7}{8}\normalsize\ ,\large\frac{14}{15}\normalsize,\ 1\large\frac{1}{20} is =\large\frac{7}{120}

\therefore The greatest quantity is \large\frac{7}{120} . **Ans:** \large\frac{7}{120} is the greatest quantity.

###### This particular math question can also be formulated in the following manner:

**Finding the maximum weight divisor to deliver 7/8 kg, 14/15 kg, and 1 1/20 kg with integer outcomes.****What is the greatest common factor of weight for 7/8 kg, 14/15 kg, and 1 1/20 kg to ensure integer deliveries?****Determining the largest divisible weight for 7/8 kg, 14/15 kg, and 1 1/20 kg resulting in whole numbers.****Finding the maximum weight quantity for evenly distributing 7/8 kg, 14/15 kg, and 1 1/20 kg into integer amounts.**