ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: A shopkeeper marks his goods 30% above the cost price, but allows a 20% discount for cash purchase. What percent profit does he make?

Solution:
At 30% above,
The market price of goods = (100 + 30)
= Tk. 130

At 20% discount,
Selling price = 130 - 20% of 130
= 130 - 26
= Tk. 104

∴ Profit = (104 - 100) = Tk. 4
Profit % = (4/100) × 100
= 4%

Question: If the selling price is tripled, the profit becomes eight times. Find the profit percent.

Solution:
Let,
The cost price be Tk.100 and sell price be Tk. x,

Then,
The profit is = (x - 100)

Now, The sell price is doubled, then the new sell price is 3x
New profit is = (3x - 100)

ATQ,
8(x - 100) = 3x - 100
⇒ 8x - 800 = 3x - 100
⇒ 8x - 3x = 800 - 100
⇒ 5x = 700
∴ x = 140

Then, the Profit = (140 - 100) = 40
Hence the profit percentage is = (40/100) × 100%
= 40%

Question: A machine making cost is Tk 25,000, sold with two successive discounts of 25% and 20%. An additional discount of 10% is offered for cash payment. What is the total loss in the selling price of the machine at cash payment?

Solution:
Making price = 25000 Tk
Selling Price after first Discount of 25% = 25000 - 25% of 25000
= 25000 - {(25/100) × 25000}
= 18750 Tk

The selling price after the second Discount of 20% = 18750 - 20% of 18750
= 18750 - {(20/100) × 18750
= 15000 Tk

∴ The final selling price at cash = 15000 - 10% of 15000
= 15000 - {(10/100) × 15000}
= 13500 Tk

Total loss = (25000 - 13500) = 11500 Tk

Question: The cost price of 60 articles is the same as the selling price of 'q' articles. If the profit is 20%, then the value of 'q' is -

Solution:
Let,
The cost price of each article be = Tk. 1
The cost price of 'q' articles = Tk. q
The selling price of 'q' articles = Tk. 60

∴ Profit = Tk. (60 - q)

According to the question,
(60 - q)/q = 20%
⇒ 100(60 - q)/q = 20
⇒ 6000 - 100q = 20q
⇒ 120q = 6000
⇒ q = 6000/120
∴ q = 50

Question: The marked price of a shirt and trousers are in the ratio 1 : 2. The shopkeeper gives 40% discount on the shirt. If the total discount in the set of the shirt and trousers is 30%, the discount offered on the trousers is:

Solution:
Let,
the price of shirt and trouser be Tk. 100 and Tk. 200 respectively.
Then, price of set of shirt and trouser = Tk. 300.

After giving 30% discount on the set,
Selling Price = 300 - 30% of 300
= 210.

∴ Total Discount on Set = Original price × Discount percentage
= 300 × (30/100)
= 300 × 0.30
= Tk. 90

And Discount on shirt is 20% alone,
SP of shirt alone = 100 - 40% of 100 = 60.
Tk. 40 is the discount on shirt then Tk. 50 must be the discount on the trouser.
So, discount on trouser = (50 × 100)/200 = 25%

Question: A trader mixes 26 kg of fertilizer at Tk. 20 per kg with 30 kg of fertilizer of other variety at Tk. 36 per kg and sells the mixture at Tk. 30 per kg. His profit percent is:

Solution:
Cost price of 56 kg fertilizer = Tk. (26 × 20) + (30 × 36) 
= Tk. (520 + 1080) 
= Tk. 1600 

∴ Selling price of 56 kg rice = Tk. (56 × 30) 
= Tk.1680 

Profit = Tk. (1680 - 1600) = Tk. 80 
∴ Gain = {(80/1600) × 100}
= 5%

Question: A sells an article to B at gain of 25% B sells it to C at a gain of 20% and C sells it to D at a gain 10%. If D pays Tk. 330 for it, how much did it cost to A?

Solution:
Let,
Cost Price for A was = 100

Then, CP for B = (100 + 25% of 100) = 125
CP for C = (125 + 20% of 125) = 150
CP for D = (150 + 10% of 150 ) = 165

But, D pay Tk. 660. Then it must be equal to,
165 = 330
1 = 330/165
∴ 100 = {330 × (100/165)} = 200

So, CP for A = Tk. 200

Question: There is a shopkeeper whose claim is that he sells a certain product at a cost of Tk 23/kg, which actually costs him Tk 25/kg. The shopkeeper says that he is taking the loss to let his customers get a better deal. When examined thoroughly, the constabulary find that the shopkeeper is actually using an 800 gms weight in place of a 1 kg weight. How much does he gain or lose?

Solution:
Selling price of 0.8 kg = 23 taka

Now,
Selling price of 1 kg = 23/0.8 taka
= 115/4 taka
= 28.75 taka

∴ Percentage profit = {(28.75 - 25)/25} × 100%
= (3.75/25) × 100%
= 15%

Question: A student bought a bag for Tk. 3500 and later sold it for Tk. 4000. Find the profit percentage he earned.

Solution:
Here,
CP = 3500, and SP = 4000
As SP > CP,

∴ Profit = SP - CP
= (4000 - 3500)
= 500

Profit% = (500/3500) ×100%
= 100/7 %
= 14.29%

Question: Chocolates are bought at 10 for Tk 20 and sold at 12 for Tk 30. The gain percent is-

Solution:
Cost per chocolate = 20/10 Tk.
= 2 Tk.

Sell per chocolate = 30/12 Tk.
= 2.5 Tk.

So, gain percentage = {(2.5 - 2)/2} × 100
= 25 Tk. or 25%

Question: If an article is sold for Tk. 540 at a loss of 10%, what should be its selling price in order to earn a profit of 15%?

Solution:
Selling Price of the article = Tk. 540
Loss % = 10%

∴ Cost Price = {100/(100 - 10)} × 540
= (540 × 100)/90 = 600

Now, Cost Price = Tk. 600 and Profit% = 15%
∴ New Selling Price = {(100 + 15)/100} × 600 = (115 × 600)/100
= 690 Tk.

Therefore, the article should be sold at Tk. 690

Question: On selling 12 balls at Tk. 720 there is a loss equal to the cost price of 4 balls. The cost price of a ball is-

Solution:
Let,
The cost price of 1 ball is = Tk. x
The cost price of 12 balls is = Tk. 12x

We know,
Cost price - Selling price = Loss
⇒ 12x - 720 = 4x
⇒ 8x = 720
⇒ x = 720/8
∴ x = 90

∴ The cost price of 1 ball is Tk. 90