Question

Three pieces of cakes of weights \( 4 \frac{1}{2} \) lb, \( 6 \frac{3}{4} \) lb and \( 7 \frac{1}{5} \) lb respectively are to be divided into parts of equal weight. Further, each part must be as heavy as possible. If one such part is served to each guest, then what is the maximum number of guests that could be entertained?

• A. 54
• B. 72
• C. 20
• D. None of these

Hint:

Use the GCD and LCM method to calculate the largest common portion when dividing items into equal parts.

Answer 1

The Correct Option is B

First, convert the mixed fractions into improper fractions: \[ 4 \frac{1}{2} = \frac{9}{2}, \quad 6 \frac{3}{4} = \frac{27}{4}, \quad 7 \frac{1}{5} = \frac{36}{5}. \] Now, find the greatest common divisor (GCD) of \( \frac{9}{2}, \frac{27}{4}, \frac{36}{5} \). To do this, find the GCD of the numerators and the LCM of the denominators. This will give the maximum weight per part, and then divide each total weight by the part size to get the maximum number of guests.