ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: If Profit = 25 Taka and Cost Price = 150 Taka, what is the profit percentage?

Solution:
Here,
Cost Price = 150 Tk
Profit = 25 Tk

Now,
Cost Price is 150 and Profit is 25 Taka.
∴ When cost Price is 1 Taka then the Profit is = 25/150 Taka
∴ When cost Price is 100 Taka then the Profit is = (25× 100)/150 Taka
 = 16.6 %

Question: A man sells a watch for Tk. 960 at a loss of 20%. What was the original cost price of the watch?

Answer:
Here,
Selling Price = 960 Tk. 
and Loss 20 %,
Now we can write,
The Selling Price is 80 Tk. and the cost price is = 100 Tk.
∴ The Selling Price is 1 Tk. then the cost price is = 100/80 Tk.
∴ The Selling Price is 960 Tk. then the cost price is = (100×960)/80 Tk.
 = 1200 Tk.

Question: The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:
 
Answer:
Let,
The cost price of each article is Taka 1
∴ Cost Price of x articles = x Taka

Selling Price of x articles = 20 Taka
∴ Profit = (20 - x) Taka

x টাকায় লাভ হয় 20 - x টাকা
∴ 1 টাকায় লাভ হয় (20 - x)/ x টাকা
∴ 100 টাকায় লাভ হয় = [(20 - x) × 100]/x টাকা
    
প্রশ্নমতে,
[(20 - x) × 100]/x = 25
⇒ 100(20-x) = 25x
⇒ 125x = 2000
∴ x = 2000/125
= 16

আরেকভাবে,
মনে করি, প্রতিটি আর্টিকেলের ক্রয়মূল্য (cost price) = ১০০ টাকা।
তাহলে ২০টি আর্টিকেলের ক্রয়মূল্য = ২০ × ১০০ = ২০০০ টাকা।

প্রশ্ন অনুসারে, এই ২০০০ টাকা x টি আর্টিকেলের বিক্রয়মূল্য (selling price) এর সমান।

লাভ ২৫% হলে,
ক্রয়মূল্য (cost price) = ১০০ টাকা। হলে,
অর্থাৎ, প্রতি আর্টিকেলের বিক্রয়মূল্য (SP) = ১২৫ টাকা।

তাহলে x টি আর্টিকেলের SP = x × ১২৫
ATQ,
 x × ১২৫  = ২০০০
⇒ x = ২০০০/১২৫
∴ x = ১৬ টাকা

Question: If a shopkeeper buys eggs at Tk. 42 per sext (six eggs) and sells them at Tk. 56 per two quads (eight eggs), what percentage profit does he make?

Solution:
Cost price of 6 eggs = Tk. 42
Cost price of 1 egg = 42/6
= 7 Tk.

Cost price of 8 eggs = 8 × 7
= 56
Selling price of 8 eggs = Tk. 56

∴ Profit = 56 − 56
= 0 

∴ As the selling and cost prices are the same, there is no profit. 

Question: The cost prices of a book and a notebook are in the ratio 3 : 7, while their selling prices are in the ratio 1 : 4. If the loss incurred on selling each item is the same, find the ratio of the cost price to the selling price of the notebook.

Answer: 
Let,
cost price of
a book = 3x
a notebook = 7x

Selling price of
a book = y
a notebook = 4y

According to the question,
3x - y = 7x - 4y
⇒ 4y - y = 7x - 3x
⇒ 3y = 4x
∴ y = 4x/3

∴ The ratio of the cost price of a notebook : the selling price of a notebook = 7x : [4 × (4x/3)]
= 21 : 16

Question: A man sells a watch for Tk. 550 and makes a profit of 10%. What was the cost price of the watch?

Answer:
Selling Price = 110% of Cost Price
⇒ Cost Price = 550 ÷ 1.1 
= 500

Another Method,
With 10% gain,
The selling price is 110 Taka when the cost price is 100 Taka
∴ The selling price is 1 Taka when the cost price is = 100/110 Taka
∴ The selling price is 550 Taka when the cost price is (100 × 550)/110 Taka 
= 500 Taka

Question: A shopkeeper marks an article 40% above the cost price and allows a discount of 10%. What is his profit percentage?

Answer:
Cost Price 100 Taka
Then Mark Price = 140, (40% above the cost price)

10% discount
If marked price is 100, then discount is 10 taka
If marked price is 1, then discount is 10/100 taka 
If marked price is 140, then discount is 140/10 = 14 taka

Selling Price = 140 - 14 = 126,
As the Cost Price = 100
Then, the Profit percentage is = 26%

Question: Any sold her bicycle for Taka. 5000 while making a profit of Taka. 70. Then what is the price at which she bought that cycle?

Solution:
Given,
Selling Price (SP) = Taka. 5000
Profit = 70 Taka

Thus,
Cost Price = Selling Price - Profit
⇒ Cost Price = 5000 - 70
⇒ Cost Price = 4930 Taka

Thus, cost price of the bicycle is Taka 4930

Question: A vendor purchased 200 books for Taka 150 each and sold them for Taka 200 each. Calculate the total profit.

Solution:
Cost Price of 200 books = 200 × Taka 150 = Taka 30,000
Selling Price of 200 books = 200 × Taka 200 = Taka 40,000
∴ Total Profit = Selling Price - Cost Price 
= Taka 40,000 - Taka 30,000
= Taka 10,000

Question: A retailer marked the price of a television at Taka 12000 and gave a discount of 15%. Calculate the selling price and the amount of discount.

Solution:
Marked Price of the television = Taka 12000
Discount Percentage = 15%

∴ Discount Amount = Discount Percentage × Marked Price
= 15% × Taka 12000
= Taka 1800

∴ Selling Price = Marked Price - Discount Amount
= Taka 12000 - Taka 1800 
= Taka 10200

Question: Rafiq bought 120 storybooks at Tk. 250 each and sold them at a profit of 15%. Find the total profit he made.

Solution:
Cost Price of 120 storybooks = 120 × Taka 250
= Taka 3,0000

Profit Percentage = 15%
∴ Profit Amount = Profit Percentage × Cost Price 
= 15% × Taka 3,0000
= Taka 4500

∴ Total Profit = Profit Amount = 4500

Question: A man sells a watch at a 5% loss. If he had sold it for Tk. 56.25 more, he would have made a 10% profit. What was the cost price of the watch?

Solution:
Let,
the price of watch x taka

According to the question,
x(100% - 5%) + 56.25 = x(100% + 10 %)
→ 95%x + 56.25 = 110% x
→ 15%x = 56.25
→ x = (5625/15)
∴ x = 375 taka

∴ the cost of the watch is 375 taka.

Question: A bicycle is purchased for Tk. 200 and sold at a 10% loss. Find the selling price and the total loss incurred.

Solution:
Cost Price of the bicycle = Taka 200
Loss Percentage = 10%

∴ Loss Amount = Loss Percentage × Cost Price
= 10% × Taka 200
= Taka 20

∴ Selling Price = Cost Price - Loss Amount
= Taka 200 - Taka 20
= Taka 180

Total Loss Incurred: Tk. 20

Question: The fourth proportional to 5, 6, and 15 is- 

Solution: 
Let, The fourth proportional is x.

So, 5/6 = 15/x
⇒ 5x = 90
∴ x = 18

Question: Jalal bought a bicycle for Tk. 8000 and then sold it at a loss of Tk. 1200. What was the selling price of the bicycle?

Answer:
Given,
Cost Price (CP) = 8000 Taka
Loss = 1200 Taka
Using Formula
Selling Price (SP) = Cost Price - Loss
⇒ Selling Price (SP) = Tk. 8000 - Tk. 1200
⇒ Selling Price (SP) = Tk. 6800

Therefore, the selling price of the bicycle is Tk. 6800.