ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: A sold a watch to B at a gain of 20% and B sold it to C at loss of 10%. If C bought the watch for TK. 432 at what price did A purchase it?

Solution:
A purchase at x taka
Selling price of A = purchasing price of B = x + 20% of x = 1.2x

Buying price of C = 1.2x - 10% of 1.2x = 1.2x - 0.12x = 1.08x

1.08x = 432
⇒ x = 432/1.08 = Tk. 400

Question: If selling price is doubled, the profit sextuples. 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 2x
New profit is (2x - 100)

ATQ,
6(x - 100) = 2x - 100
⇒ 6x - 600 = 2x - 100
⇒ 6x - 2x = 600 - 100
⇒ 4x = 500
∴ x = 125

Then the Profit = (125 - 100) = 25
Hence the profit percentage is = (25/100) × 100 %
= 25%

Question: A merchant selling 44 meters of cloth obtains a profit equal to the selling price of 11 meters of cloth, the profit is = ?

Solution:
Profit = selling price of 11 m of cloth = 1/4 selling price of 44 m of cloth

Let the selling price of 44 meters of cloth = 4x
∴ profit = (1/4) × (4x) = x

So, cost price = selling price - profit = 4x - x = 3x

% Profit = (x/3x) × 100% = 33.33%

Question: A shopkeeper marks his goods 20% above the cost price, but allows 10% discount for cash purchase. What percent profit does he make?

Solution:
At 20% above,
The market price of goods = 100 + 20 = Tk. 120

At 10% discount,
Selling price = 120 - 10% of 120
= 120 - 12
= Tk. 108

∴ Profit = 108 - 100 = Tk. 8
Profit % = (8/100) × 100
= 8%

Question: Zayed sold an article at 6% loss. Had he sold it for Tk. 32 more, he would have made a profit of 10%. Then the cost of the article is =?

Solution:
Let, the cost of the article is x taka

Selling price = 0.94x

According to the question,
0.94x + 64 = 1.1x
⇒ 1.1x - 0.94x = 32
⇒ 0.16x = 32
⇒ x = 32/0.16
∴ x = 200 taka

Question: The cost price of 40 articles is the same as the selling price of 'p' articles. If the profit is 25%, then the value of 'p' is -

Solution:
Let,
The cost price of each article be Tk. 1
The cost price of 'p' articles = Tk. p
The selling price of 'p' articles = Tk. 40

∴ Profit = Tk. (40 - p)

According to the question,
(40 - p)/p = 25%
Or, 100(40 - p)/p = 25
Or, 4000 - 100p = 25p
Or, 125p = 4000
∴ p = 32

Question: If a man was to sell his table for Tk. 750, he would lose 25%. To gain 25% he should sell it for:

Solution:
Let the Cost price of the table be x.

Selling price = x - 25% of x
⇒ 750 = x - (25x/100)
⇒ 750 = 75x/100
⇒ 75x = 75000
∴ x = 1000

To gain 25% = 1000 + 25% of 1000
= 1000 + 250
= Tk. 1250

Question: Mr. Anis marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price. What is his profit or loss percent?

Solution:
Let the cost price of goods = Tk. 100
The market price of goods = 110% of 100
= (110/100)×100
= Tk. 110

After the discount, the selling price of the goods
= 90% of 110
= (90/100) × 110
= Tk. 99

Loss = 100 - 99 = Tk. 1

∴ Loss % = (1/100) × 100 = 1%

Question: On selling 17 balls at Tk. 840 there is a loss equal to the cost price of 5 balls. The cost price of a ball is-

Solution:
Let,
The cost price of 1 ball is = Tk. x
The cost price of 17 balls is = Tk. 17x

We know,
Cost price - Selling price = Loss
17x - 840 = 5x
⇒ 12x = 840
⇒ x = 840/12
∴ x = 70

∴ The cost price of 1 ball is Tk. 70

Question: A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of 784 Tk, what was his profit?

Solution:
Given,
Selling price = 784 Tk.

For a gain of 22.5%,
The cost price can be = 122.5

Cost price = (100/122.5) × 784 Tk.
= (1000/1225) × 784 Tk.
= 640 Tk

Therefore, Profit = 784 - 640 Tk.
= 144 Tk.

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: 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: If an article is sold for Tk. 356 at a loss of 11%, what should be its selling price in order to earn a profit of 11%?

Solution:
Selling Price of the article = Tk. 356
Loss % = 11%

∴ Cost Price = {100/(100 - 11)} × 356
= (356 × 100)/89 = 400

Now Cost Price = Tk. 400 and Profit% = 11%
∴ New Selling Price = {(100 + 11)/100} × 400 = (111 × 400)/100 = 444 Tk.

Therefore, the article should be sold at Tk. 444

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

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%