Question

A person bought $3\frac{1}{2}kg$ of apples, $2\frac{2}{3}kg$ of grapes, and $1\frac{1}{3}kg$ of oranges. He wants to divide them among $4$ people. Find the amount of fruits (in kg) that each person will receive.

• A. $2\frac{7}{8}kg$
• B. $1\frac{3}{8}kg$
• C. $1\frac{7}{8}kg$
• D. $1\frac{5}{8}kg$

Answer 1

The correct option is C

$1\frac{7}{8}kg$

First, let us do the conversion of mixed fractions into improper fractions.

i.e $3\frac{1}{2}=\frac{(2\times 3)+1}{2}=\frac{7}{2}$

$2\frac{2}{3}=\frac{(3\times 2)+2}{3}=\frac{8}{3}$, and

$1\frac{1}{3}=\frac{(3\times 1)+1}{3}=\frac{4}{3}$

$\text{Total quantity of fruits}=(\frac{7}{2}+\frac{8}{3}+\frac{4}{3})kg$

$=\frac{7}{2}+4$

$=\frac{7}{2}+\frac{8}{2}$

$=\frac{15}{2}kg$

When $\frac{15}{2}kg$ is divided among $4$ people,

each person's share $=\frac{\frac{15}{2}}{4}kg$

$=(\frac{15}{2}\times \frac{1}{4})kg$

$=\frac{15}{8}kg$

$=1\frac{7}{8}kg$

Hence, each person gets $\left(1\frac{7}{8}\right)kg$ of fruits.