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Mathematics
1.

A man sells an article at a profit of 25% . If he had bought it at 20% less and sold it for Tk. 10.50 less, he would have gained 30% . Find the cost price of the article.
Created: 3 months ago | Updated: 14 hours ago

একজন একটি দ্রব্য 25% লাভে বিক্রয় করে। সে যদি দ্রব্যটি 20% কম দাম দিয়ে কিনতো এবং তা যদি 10.50 টাকা কমে নিত্রনা করতো, তবে সে ঐ দ্রব্যটি বিক্রয় করে 30% লাভ করতো।  দ্রব্যটির ক্রয়মূল্য কত?

 

Let, cost price of the article is Tk. x 

At, 25% profit. Then first selling price is Tk. 125% of x=TK.125x100=TK. 5x4

At, 20% less price, New cost price = Tk. 80% of x= TK. 80x100=TK.4x5

At 30% profit, New selling price = TK. 130% of 4x5=Tk.130×4x5×100=Tk.26x25

According to question,

5x4-26x25=10.50⇒125x-104x100=10.50⇒21x=10.50×100∴x=50 

So, cost price of the article is Tk. 50

Mathematics
2.

A and B can do a piece of work in 18 days; B and C can do it in 24 days; A and C can do it in 36 days. In how many days will A, B and C finish it, working together and separately?
Created: 3 months ago | Updated: 14 hours ago

A ও B একটি কাজ 18 দিনে, B ও C 24 দিনে এবং A ও C 36 দিনে করতে পারে। ঐ কাজটি তারা একত্রে আলাদাভাবে কয়দিনে করবে?

 

(A+B) take 18 days to complete= 1 work

(A + B) take 1 day to complete = (118) part of work

Similarly, (B+C) take 1 day to complete =124 part of work

And (A+C) take 1 day to complete = 136 part of work

On adding, [(A+B)+(B+C)+(A+C)] take 1 day to complete

=118+124+136=4+3+272=972 Part of work

2(A+B+C) take 1 day to complete =18 Part of work

⇒(A+B+C) take 1 day to complete =18×2=116 Part of work

116 Part of work is done by (A+B+C) in 1 day

∴ 1 or complete part of work is done by (A+B+C) in =1×161=16 days

Only A can do the work (A+B+C)-(B+C)

Or, 116-136=5144 part in 1 day.

So, A can complete the whole work in 48 days

Now, Only B can do the work (A+B+C)-(A+C)

or, 116-118=5144 

So, B can complete the whole work in 28.8 or 29 days.

And only C can do the work (A+B+C)-(A+B)

or, 116-118=1144 part in I day. 

So, C can complete the whole work in 144 days

 

ans. Working together A, B and C finish the work in 16 days and separately A, B and C finish the we in 48 days, 29 days & 144 days respectively 

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