ISRO2018-47

Question

In a particular program, it is found that $1$% of the code account for $50$% of the execution time. To code a program in C++, it takes $100$ man-days. Coding in assembly language is $10$ times harder than coding in C++, but runs $5$ times faster. Converting an existing C++ program into an assembly language program is $4$ times faster.

To completely write the program in C++ and rewrite the $1$% code in assembly language, if a project team needs 13 days, the team consist of

1. $13$ programmers
2. $10$ programmers
3. $8$ programmers
4. $100/13$ programmers

Answer 1

see at first 100% work can be done in 100 days means 1% work in a man day.

now writing code in assembly language is 10 times harder means 10 times more time consuming.

also converting existing code form c++ is 4 times easier i.e less time consuming so overall by this scenario we can say 100% work can be done in 100*10/4 man days = 250 days.

So, 1% work will be done in 2.5 days.

NOW,99% work in C++ + 1% rewriting code will take = 99*1 + 1*2.5= 101.5 man days.

but we are given 13 days to complete so 101.5/13 = 8 programmer we need.

Ans-C

Comments

final answer will be 100*1+1*2.5=102.5 as first we write 100% code in C++ and then we rewrite 1%code.

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Why is it not 100+0.25(to convert 1% of work in c++ to assembly)=100.25/13=7.7 days

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@madhu02sai yes. first 100 days for writing full c++ program. then 0.25*1 day for converting into assembly language. total 100.25. So $\left \lceil \frac{100.25}{13} \right \rceil=8$