Question

Raj, Gaurav and Amit are fast friends. They started painting a wall. Raj paints $\frac{2}{15}$ of the wall, Gaurav paints $\frac{1}{24}$ of the wall and Amit paints $\frac{3}{10}$ of the wall. Read the statements related to above situation and answer the question given below.

Statement $1:$ Gaurav painted least portion of the wall.

Statement $2:$ $\frac{1}{18}$ portion of the wall is unpainted.

Which of the following option holds?

• A. Both statements $1$ and statement $2$ are true.
• B. Both statements $1$ and statement $2$ are false.
• C. Statement $1$ is true but statement $2$ is false.
• D. Statement $1$ is false and statement $2$ is true.

Answer 1

The correct option is C

Statement $1$ is true but statement $2$ is false.

Given,

Raj paints $\frac{2}{15}$ of the wall.

Gaurav paints $\frac{1}{24}$ of the wall.

Amit paints $\frac{3}{10}$ of the wall.

Convert the fractions into like fraction for comparing,

LCM of $15,24,10=120$

$\frac{2}{15}=\frac{2\times 8}{15\times 8}=\frac{16}{120}$

$\frac{1}{24}=\frac{1\times 5}{24\times 5}=\frac{5}{120}$

$\frac{3}{10}=\frac{3\times 12}{10\times 12}=\frac{36}{120}$

$\because \frac{1}{24}<\frac{2}{15}<\frac{3}{10}$

$\Rightarrow$Gaurav painted the least, Statement $1$ is true.

Total portion painted by all the three$=\frac{16}{120}+\frac{5}{120}+\frac{36}{120}=\frac{57}{120}$

Unpainted portion$=1-$Total painted portion

$=1-\frac{57}{120}=\frac{63}{120}=\frac{21}{40}$

$\Rightarrow$The unpainted portion is $\frac{21}{40}$, statement $2$ is false.

Hence, the correct option is C.