db={"Result":[{_id:ObjectId("6010664ac5c4f77f26f5d005"),questions:[{_id:ObjectId("5d2627c94bb703bfcc910763"),correct:false},{_id:ObjectId("5d2627c94bb703bfcc910764"),correct:true},{_id:ObjectId("5d2627c94bb703bfcc910765"),correct:true}]},{_id:ObjectId("6010664ac5c4f77f26f5d006"),questions:[{_id:ObjectId("5d2627c94bb703bfcc910763"),correct:false},{_id:ObjectId("5d2627c94bb703bfcc910764"),correct:false},{_id:ObjectId("5d2627c94bb703bfcc910766"),correct:true}]},{_id:ObjectId("6010664ac5c4f77f26f5d007"),questions:[{_id:ObjectId("5d2627c94bb703bfcc910764"),correct:false},{_id:ObjectId("5d2627c94bb703bfcc910765"),correct:true},{_id:ObjectId("5d2627c94bb703bfcc910766"),correct:true},{_id:ObjectId("5d2627c94bb703bfcc910764"),correct:true}]}],"Question":[{_id:ObjectId("5d2627c94bb703bfcc910763")},{_id:ObjectId("5d2627c94bb703bfcc910764")},{_id:ObjectId("5d2627c94bb703bfcc910765")},{_id:ObjectId("5d2627c94bb703bfcc910766")},{_id:ObjectId("5d2627c94bb703bfcc910767")}]}

db.Question.aggregate([{/** lookup documents in Result that match _id*/"$lookup":{"from":"Result","localField":"_id","foreignField":"questions._id","as":"results"}},{/** unwind everything*/"$unwind":"$results"},{/** more of everything*/"$unwind":"$results.questions"},{/** only keep answers that match question*/"$match":{"$expr":{"$eq":["$_id","$results.questions._id"]}}},{/** reassemble and count correct/wrong answers*/"$group":{"_id":"$_id","correct":{"$sum":{"$cond":[{"$eq":["$results.questions.correct",true]},1,0]}},"wrong":{"$sum":{"$cond":[{"$eq":["$results.questions.correct",false]},1,0]}}}},{/** project what you want as output*/"$project":{newField:{correctAnswers:"$correct",wrongAnswers:"$wrong"}}}])