JEE Mathematics 2024 Question with Solution

Given: The company initially planned to use $m$ computer systems for $17$ days. After the first day, $4$ systems crashed each day, and the work took $8$ extra days, so the total time became $25$ days.

Find: The value of $m$.

Without any crash, total work required is

computer-days.

With crashes, the work done day-wise forms an arithmetic progression:

because there are $25$ days in total.

Equating actual work to required work:

so

Now,

Substituting,

Therefore, the value of $m$ is $150$. The correct option is B.

Given: Planned work is $17m$ computer-days, but due to daily crashes of $4$ systems from day $2$ onward, the job finishes in $25$ days.

Find: The value of $m$.

Treat the actual daily working systems as an AP with first term $m$, common difference $-4$, and $25$ terms.

Using the compact form from the extracted working:

Therefore, the correct option is B.