which option is correct and why?

First, which options do you choose, sundarnaz—and why?

For first sentence both options seems to me correct.
1) You have solved first sum. Similarly (using the same method) you can do the whole exercise.
2) You have solved first sum. Hence ( as you learn the method or you are now able enough) you can do the whole exercise.
For second sentence option one seems to me correct
They love one another so they shared the sufferings of the victi

Actually, I find both questions hopeless, sundarnaz. If you have transcribed them accurately, they were written by a non-native with a limited understanding of English.

1) You have solved the first sum, so you can do the whole exercise.-- This is the native sentence. 'Hence,' is an adequate synonym, but it is overly formal and little used nowadays. 'Similarly,' als

Thank you so much. Realy great informations. It means, I must expand my research to make my English more reasonable.

sundarnazI must expand my research to make my English more reasonable.

Do you mean that you wrote those questions?

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No, I didn't write those questions. Those question are included in the exercise book that I use to practice my English. Now I must get some other books that are more reliable.