IPMAT 2025 Exam Solved Papers

$| a-b | + | b-c | = | c-a |$. This equation is only valid when $b$ lies between $a$ and $c$. Thus, there are two cases possible - $a b$. Thus, if we assume the value of $\mathrm{c}=99$ and $\mathrm{b}=98$ (which are the two maximum possible values), then -$\begin{aligned} & | a-98 | + | 98-99 | = | 99-a | \text {, and we assumed that } \mathrm{a} < \mathrm{b} \text {, thus } \mathrm{a} < 98 \text {. } \\ & \Rightarrow 98-a+1=99-a= > 0=0 \end{aligned}$Thus, any value of $a < 98$ is possible for this equation.Therefore, $\mathrm{c}=99, \mathrm{~b}=98$ and $\mathrm{a} < 98$Case -2:- $c b$. Thus, if we assume the value of $\mathrm{a}=99$ and $\mathrm{b}=98$ (which are the two maximum possible values), then -$\begin{aligned} & | 99-98 | + | 98-c | = | c-99 | \text {, and we assumed that } \mathrm{c} < \mathrm{b} \text {, thus } \mathrm{c} < 98 \text {. } \\ & \Rightarrow 1+98-c=99-c= > 0=0 \end{aligned}$Thus, any value of $\mathrm{c} < 98$ is possible for this equation.Therefore, $\mathrm{a}=99, \mathrm{~b}=98$ and $\mathrm{c} < 98$Thus, in both cases, the maximum value of $\mathrm{b}=98$.