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বাংলাদেশ সিকিউরিটিজ এন্ড এক্সচেঞ্জ কমিশন || সহকারী পরিচালক (19-06-2021) || 2021

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1.

Working alone at their respective constant rates, A can complete a task 'a' days and B in "b" days. They take turns in doing the task with each working 2 days at a time. starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?
Created: 3 months ago | Updated: 12 hours ago

As, A starts the work

So, A works for = 6 days

B works for = 4 days

that means = 6a+4b=1.......(i)

If, B starts the work, they take 1012 days to complete work. So, B works for = 6 days ∴A works for = 412 days That mean's =4.5a+6b=1............(ii) Multiplying (i) by 3 and (ii) by 2 and subtracting (ii) from (i). we get

18a+12b=3 9a+12b=218a-4b=1 =18-9a=1 =9a=1 ∴a=9 

putting the value of a in (i), we get

6a+4b=1 =69+4b=1 =4b=1-23=3-23=13 ∴b=12

so, A can complete the work in = 9 days

& B can complete the work in = 12 days

∴They together can do the woek in 1 day = 19+112=4+336=736

736 part of work in done by them in = 1 day ∴ 1 or complete work is done by them in = 367 day


2.

The cost of operating a toy company in the first year is $10,000 plus $2 for each toy. Assuming the company sells every toys it makes in the first year for $7, how many toys must the company sell to break even? 
Created: 3 months ago | Updated: 12 hours ago

মনে করি, নির্ণেয় পণ্য সংখ্যা ক টি

∴ক টি পণ্যের মূল্য ২ক ডলার

এবং ক টি পণ্যের উৎপাদন বিক্রয়মূল্য ৭ক ডলার 

প্রশ্নমতে, ৭ক-২ক=১০০০০

=৫ক=১০০০০

∴ক=১০০০০৫=২০০০.


3.

The posted weight limit for a wooden bridge in Bandarban is 6,000 kg. A delivery truck that is carrying x identical boses each weighting 14 Ag will pass over the bridge. If the combined weight of the empty delivery truck and its driver is 4.500 kg, what is the maximum possible value of x that will keep the combined weight of the truck, driver and boxes below the bridge's weight limit?
Created: 3 months ago | Updated: 10 hours ago

Give, the weight of 1 box is = 14kg

∴The weight of x box is = 14kg

According to question

4500+14x=6000

=14x=6000-4500=1500

∴x=15004=107.14

∴maximum number of boxes is 107.

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