Question

Given, $1<s+t<r$

Column A: $\frac{r+s+t}{r-s-t}$

Column B: $0$

• A. The quantity in Column A is greater
• B. The quantity in Column B is greater
• C. The two quantities are equal
• D. The relationship cannot be determined from the information given

Answer 1

The correct option is A The quantity in Column A is greater

Given $1<s+t<r$.

Consider $\frac{r+s+t}{r-s-t}$

Now apply component and dividend rule, we get $\frac{r+s+t+r-s-t}{r+s+t-(r-s-t)}=\frac{2r}{2(s+t)}=\frac{r}{s+t}$.

Given that $r>s+t$, so $\frac{r}{(s+t)}>1$.

Therefore the quantity in $1$st column is greater.

So, the correct option is $A$.