Question

To find the present age of Rishi, which statements can be dispensed.
\[I.\] In ten years, Richard will be twice as old as Rishi was 10 years ago.
\[II.\] Richard is now 9 years older than Rishi.
\[III.\] Five years ago, Rishi was 9 years younger than Richard.
\[A\]) Only II
\[B)\] Only III
\[C)\] Either I or II
\[D)\] None of the three statements can be dispensed with

Answer 1

Hint: First we have to define what the terms we need to solve the problem are.
Since we need to find the present age of the Rishi using some given statements above like ten years ago, nine years older than Richard is the hint to find the Rishi present age. Also, either means maybe the first statement is correct or the second statement and if only means that statement only needs to be correct.

Complete step-by-step solution:
Let us fix some variables corresponding to the ages of Rishi and Richard so that we can convert the given problem into an equation and applying in any mathematical formula we get the required answer. Hence fix $x$ as the Rishi present age and $y$ as the Richard present age.
Now convert the statements into an equation as follows; for the statement \[I\] we get $y + 10 = 2x$ ( In ten years, Richard will be twice as old as Rishi was 10 years ago) and for statement II we get $y = x + 9$ ( Richard is now 9 years older than Rishi) and for statement III we get; $y - 5 = x - 5 + 9$ ( Five years ago, Rishi was 9 years younger than Richard)
The third statement can be also rewritten as $y - 5 = x - 5 + 9 \Rightarrow y = x + 9$; since statements II and III are similar,
Hence option I is a trivially correct option because we can get Rishi age using the information, also options II and III are the same and correct too.
Thus option \[C)\] Either I or II (can be dispensed) is correct (II and III are equal statements)

Note: Since II and III statements are the same; if the options contain all the three statement are correct then we must select that option only for the exceptional cases like this we can select \[C)\] Either I or II