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 situation and answer the question given.
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 Statement $1$ and Statement $2$ are true
• B. Both Statement $1$ 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

L.C.M of $15,24,10=120$

Comparing $\frac{2}{15},\frac{1}{24},\frac{3}{10}$, we get,

$\frac{16}{120},\frac{5}{120},\frac{36}{120}$

Among these, $\frac{5}{120}$ is the lowest, So Statement I is true.

Portion of the wall painted by all the three $=\frac{16}{120}+\frac{5}{120}+\frac{36}{120}=\frac{57}{120}$

Let, the whole wall to be painted be $1$

Portion of wall unpainted $=1-\frac{57}{120}=\frac{63}{120}=\frac{21}{40}$

Statement II is false.

Thus the correct answer is $C$