ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: If 45% of A = 15% of B, what percentage of A is B?

Solution: 
45% of A = 15% of B
⇒ (45/100) × A = (15/100) × B
⇒ 9A/20 = 3B/20
⇒ 9A = 3B
⇒ B = 9A/3
∴ B = 3A

Required percentage = (B/A) × 100%
= (3A/A) × 100%
= 3 × 100%
= 300%

Question: If the list price of a pair of shoes is Tk. 1500, and a discount of Tk. 375 is offered, then what is the discount percentage?

Solution:
Given,
Marked Price = Tk. 1500
Discount = Tk. 375

We know,
Discount % = (Discount/marked Price) × 100
Discount (%) = (375/1500) ×100%
= 25%

∴ Therefore, the discount percentage is calculated as 25%

Question: If a man sells a chair for Tk. 600 and he would loss 20%, then at what price should he sell it to gain 20%?
 
Solution:
Let
the cost price of the chair be x.

Selling price = x - 20% of x
⇒ 600 = x - (20x/100)
⇒ 600 = x - (x/5)
⇒ 600 = 4x/5
⇒ 4x = 3000
∴ x = 750
 
To gain 20%, the selling price should be = 750 + 20% of 750
= 750 + {(20/100) of 750}
= 750 + 150
= Tk. 900

Question: A t-shirt marked at Tk. 400 is sold for Tk. 320. The rate of discount is-

Solution:
Given,
Marked price = Tk. 400
Selling price = Tk. 320

Discount = Tk. (400 - 320)
= Tk. 80
∴ Discount Rate = (80/400) × 100
= 20%

Question: A student erroneously multiplied a number by 7/10 instead of 7/5. What is the percentage error in the calculation?

Solution:
Let
the number be 100.

ATQ,
Actual calculation be: (7/5) × 100 = 140
and error calculation be: (7/10) × 100 = 70

∴ Difference = 140 - 70 = 70

∴ Percentage error = (70/140) × 100 = 50%

Question: A shopkeeper marks his goods 20% above cost price, but allows a 20% discount for cash payment. His net loss is?

Solution:
Let
The cost price of goods = Tk. 100
Market price of goods = 120% of 100  
= 120/100 × 100
= Tk. 120

At 20% discount for cash payment, real price = (100 - 20)%
= 80%

After discount selling price of goods = 80% of 120
= Tk. 96
Loss = Tk. (100 - 96) = Tk. 4

∴ Loss % = (4/100) × 100 = 4%

Question: 60% of 500 is what percent of 400?

Solution:
Let
60% of 500 be x percent of 400.

That means,
60% of 500 = x% of 400.
⇒ 60 × 500/100 = 400x/100
⇒ 300 = 4x
⇒ 4x = 300
⇒ x = 75

Question: What is the discount rate percentage on a gift whose selling price is Tk. 440 after a reduction of Tk. 60 on its marked price?

Solution: 
Given,
SP of the gift = Tk. 440
Discount = Tk. 60

MP of the gift = Tk. (440 + 60) = Tk. 500

∴ Discount percentage = (60/500) × 100 = 12%

Question: A bike originally cost Tk. 1000 and was discounted 10%. After three months it was sold after being discounted another 15%. How much was the bike sold for?

Solution:
Given
Original price = Tk. 1000
10% discounted price = 1000 - (10% of 1000)
= 1000 - (10/100 of 1000)
= Tk. 900

The bike was sold after another 15% discount.
∴ 15% of Tk. 900 = Tk. (15/100 of 900)
= Tk. 135

∴ Selling price= Tk. (900 - 135)
= Tk. 765

Question: If 7% more is gained by selling a phone for Tk. 25000 then by selling it for Tk. 23600. The cost of the phone is?

Solution: 
Given,
1st selling price = Tk. 25000
2nd selling price = Tk. 23600

∴ Selling price more = (25000 - 23600) = Tk. 1400

If tk. 7 more gained then the cost price Tk. 100
If tk. 1 more gained then the cost price Tk. (100/7)
If tk.1400 more gained then the cost price Tk. {(100 × 1400)/7}
= Tk. 20000

Question: In an election between two candidates, winner got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 80,000, the number of valid votes that the loser candidate got, was-

Solution:
Given,
20% of the votes were invalid
∴ the valid votes = (100 - 20) = 80%

∴ Number of valid votes = (80% of 80,000)
= (80/100 of 80,000)
= 64,000

∴ Winner candidates got = (55% of 64,000)
= (55/100 of 64,000)
= 35,200

So, the loser got = (64,000 - 35,200)
= 28,800

Question: A man bought 40 shares of Tk. 50 at 5tk discount, the rate of dividend being 27%. The rate of interest obtained is-

Solution:
Given,
Total investment = Tk. [40 × (50 - 5)] = Tk. 1800.
Face value = Tk. (50 × 40) = Tk. 2000.

∴ Dividend = (27/100) × 2000
= Tk. 540

∴ Interest obtained = (540/1800) × 100%
= 30%

Question: A hat seller had some hats. He sells 55% hats and still has 90 hats. Originally, he had:

Solution:
Let,
The hat seller had = x hats.

ATQ,
(100 - 55)% of x = 90
⇒ 45% of x = 90
⇒ 45x/100 = 90
⇒ 9x/20 = 90
⇒ x = (90 × 20)/9
∴ x = 200

∴ Originally, he had 200 hats

Question: A discount of 10% on one article is equal in amount to a discount of 25% on a second article. What can be the ratio of their marked prices?

Solution:
Let
the marked prices of the two articles be X and Y

ATQ,
10% of X = 25% of Y
⇒ 10X/100 = 25Y/100
⇒ 10X = 25Y
⇒ X/Y = 25/10
∴ X : Y = 5 : 2

The ratio of their marked prices is = 5 : 2

Question: A student scores 70% marks in 10 papers of 100 marks each. He scores 14% of the total marks in Math. How much does he score in Math?

Solution:
Here,
Total marks in 10 subjects = 10 × 100
= 1000

∴ He scores = 70% of 1000
= (70/100) of 1000
= 700

∴ He scores in Math = 14% of 700
= (14/100) of 700
= 98