The correct sentence is - গ) The problem could be solved by them.
Active to Passive:
Passive Voice of Verbs preceded by can, may, should, would, etc.:
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Verb-এর আগে auxiliary verb হিসাবে can, could, should, would, must থাকলে passive গঠন হবে:
can/could/should/would/must + be + V(p.p.)
Examples:
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Act: I can do it. → Pass: It can be done by me.
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Act: You must eat the mango. → Pass: The mango must be eaten by you.
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Act: He would sing good songs in his boyhood. → Pass: Good songs would be sung by him in his boyhood.
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Act: She should love her husband. → Pass: Her husband should be loved by her.
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Act: They may use this tubewell. → Pass: This tubewell may be used by them.
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Act: Man can eat everything. → Pass: Everything can be eaten by man.
Other options:
ক) The problem could solved by them.
খ) The problem can be solved by them.
ঘ) The problem could be solving by them.
Source: A Passage to the English Language, S.M. Zakir Hussain.