Question

A $5$ metre long piece of cloth is cut into three smaller pieces. How long is the longest of the three pieces? Given that:
I. One piece is $2.90$ metre long.
II. One piece is $90cm$ longer than another piece and the remaining piece is $20cm$ long

• A. Statement I alone but not statement II alone is sufficient to answer the problem
• B. Statement II alone but not statement I alone is sufficient to answer the problem
• C. Statement I and II both are needed to answer the problem
• D. Statement I alone suffices and also statement II alone suffices to answer the problem

Answer 1

The correct option is B Statement II alone but not statement I alone is sufficient to answer the problem

From statement II :

One piece is $20cm$ long, so other two pieces together will be $480cm$ long.

Suppose length of first piece is $x$ and of second piece is $y$.

$\therefore$ $x+y=480$ .............. $\left(1\right)$

And $x+90=y$

Substitute the value of y in $\left(1\right)$ and we get,

$x+x+90=480$ $⟹$ $2x=390$

$\therefore$ $x=195$

Substituting $x$ in $x+90=y$ we get

$y=285$.

So, the longest piece is of $285cm$.

Thus, from statement II only we can get the longest piece.

But from only I we can't get the required result.

Hence, option B is correct.