ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: If the list price of a shirt is Tk. 800, and a Tk. 160 discount is offered on the shirt, then what is the discount percentage?

Solution:
Discount % = (Discount/marked Price) × 100
Marked Price = Tk. 800
Discount = Tk. 160

Discount (%) = (160/800) ×100%
= 20%

∴ Therefore, the discount percentage is calculated as 20%.

Question: If a man were to sell his chair for Tk. 720, he would lose 25%. To gain 25% he should sell it for:

Solution:
Let the Cost price of the Chair is x.
Selling price = x - 25% of x
⇒ 720 = x - (25x/100)
⇒ 720 = 75x/100
⇒ 75x = 72000
∴ x = 960

To gain 25% = 960 + 25% of 960
= Tk. 1200

Question: If a number is reduced by 40% it becomes two-thirds of another number. What is the ratio of the first number to the second number?

Solution:
Let the number be dx and y respectively.

ATQ,
60% of x = 2y/3
Or, 60x/100 = 2y/3
Or, 3x/5 = 2y/3
Or, x/y = (2/3) × (5/3)
Or, x/y = 10/9
x : y = 10 : 9

Question: Sixty-five percent of a number is 42 less than four-fifth of that number. What is the number?

Solution:
Let, the number = x.

ATQ,
65% of x = (4/5) of x - 42
⇒ 65x/100 = (4x/5) - 42
⇒ 13x/20 = (4x/5) - 42
⇒ (4x/5) - (13x/20) = 42
⇒ (16x - 13x)/20 = 42
⇒ 3x/20 = 42
⇒ 3x = 840
⇒ x = 840/3
∴ x = 280

So, the number is 280

Question: Mr. Anis is a trader. He mixes 26 kg of rice at Tk. 20 per kg with 30 kg of rice of other variety at Tk. 36 per kg and sells the mixture at Tk. 30 per kg. His profit percent is:

Solution: 
C.P. of 56 kg rice = (26 × 20 + 30 × 36)
= (520 + 1080)
= 1600 taka

S.P. of 56 kg rice = (56 × 30)
= 1680 taka

∴ Profit = 1680 - 1600
= 80 taka

∴ Profit percentage = (80/1600) × 100%
= 5%

Question: A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?

Solution:
Let, the number be x.
Then, error = (5/3)x - (3/5)x
= (25x - 9x)/15
= 16x/15

Error% = {(16x/15) × (3/5x) × 100}%
= 64%

Question: The monthly income of a person was Tk. 13500 and his monthly expenditure was Tk. 9000. Next year, his income increased by 14% and his expenditure by 7%. Find the percentage increase in his savings.

Solution:
Savings before increased income = Tk. (13500 - 9000)
= Tk. 4500

Increased income = 114% of 13500 = Tk. (114/100) × 13500
= Tk. 15390

Increased expenditure = 107% of 9000 = Tk. (107/100) × 9000
= Tk. 9630

Saving after Increased income = Tk. (15390 - 9630) = Tk. 5760

Increased Savings = Tk. (5760 - 4500)
= Tk. 1260

∴ Increase % in savings = (1260/4500) × 100 % 
= 28%

Question: A Hudi is sold for Tk. 2400 at a profit of 25%. What would have been the actual profit or loss if it had been sold at Tk. 1800?

Solution:
Firstly let us find the cost price of the same. C.P. = 2400 × (100/125) = 1920.
New selling price = 1800
Loss = 1920 - 1800 = 120

∴ Loss percentage = 100 × (120/1920)
= 6.25%.

Question: Three-fourths of a number is equal to 60% of another number and the difference between these two number is 20. What is the sum of these two numbers? 

Solution: 
Let the numbers be x and x + 20

Then, 
3x/4 = 60% of (x + 20)
⇒ 3x/4 = 60(x + 20)/100
⇒ 3x/4 = 3(x + 20)/5
⇒ x/4 = (x + 20)/5
⇒ 5x = 4x + 80
⇒ 5x - 4x = 80 
⇒ x = 80 

The sum of these two numbers = x + x + 20 
= 2x + 20
= 2 × 80 + 20
= 160 + 20 
= 180

Question: A book was sold for Tk. 144. If the percentage of profit was numerically equal to the cost price, the cost of the clock was -

Solution: 
Let, the percentage of profit be x% 
cost of the clock was x taka.

x + x × x/100 = 144 
⇒ x + (x²/100) = 144
⇒ (x² + 100x) = 14400
⇒ x² + 100x - 14400 = 0
⇒ x² + 180x - 80x - 14400 = 0
⇒ x(x + 180) - 80 (x + 180) = 0
⇒ (x + 180) (x - 80) = 0
∴ x = 80

Question: Mr. Jaman sold an article at 6% loss. Had he sold it for Tk. 64 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 

ATQ, 
0.94x + 64 = 1.1x
⇒ 1.1x - 0.94x = 64 
⇒ 0.16x = 64 
⇒ x = 64/0.16
∴ x = 400 taka 

Question: A reduction of 20% in the price of sugar enables a housewife to purchase 6 kg more for 240 Taka. What is the original price per kg of sugar?

Solution:
Reduction in the price of 20% amount of sugar will increase by 25%
It means, 25% = 6 Kg.

So, initially, total Sugar = 6 × 4 = 24 kg.

Thus, the original price of the sugar was = 240/24
= 10 Taka per kg.

Question: By Selling 45 lemons for Tk. 40, a man loses 20%. How many should he sell for Tk..24, to gain 20% in the transaction?

Solution: 
SP per Lemons = 40/45
= Tk. 0.88.
Let, CP was Tk. X per Lemons.
SP = CP - 20% of CP
⇒ 0.88 = 0.8X
⇒ X = Tk. 1.11

To get 20% profit,
SP = 1.11 + 20% of 1.11 = Tk.1.33

Thus, he can sell = 24/1.33
= 18 Lemons in Tk. 24.

Question:

Solution: 

Question: By selling 90 chocolets for Tk. 160 a person loses 20%. How many chocolets should be sold for Tk. 96 so as to have a profit of 20%?

Solution: 
S.P of 90 chocolets  = Tk. 160 
C.P of 90 chocolets  = Tk. {160×(100/80)}
= Tk. 200 

Desired  S.P of 90 chocolets = Tk. (120/100) × 200 
= Tk. 240

For Tk. 240 chocolets sold = 90 
For Tk. 96 chocolets sold = (90/240) × 96 
= 36

Question: It costs Tk. 1 to photocopy a sheet of paper. However, 2% discount is allowed on all photocopies done after the first 1000 sheets. How much will it cost to copy 5000 sheets of paper?

Solution: 
For the first 1000 sheets, cost = 1000 × 1 = Tk. 1000 

Cost for rest (5000 - 1000) or 4000 sheets = 4000 × (1 - 0.02)
= 4000 × 0.98
= Tk. 3920 

Total cost = 3920 + 1000 
= Tk. 4920 

Question: In an examination, 35% of total students failed in Bangla, 45% failed in English and 20% failed in both. Find the percentage of those students who passed in both the subjects?

Solution:
Failed students in Bangla = 35%
Failed students in English = 45%
Student failed in both subject Bangla and English = 20%

Student only fail in Bangla = (35 - 20)% = 15%
Student only fail in English = (45 - 20)% = 25%

Total fail students = (15 + 25 + 20)%
= 60%

Percentage of passed students in both subjects = (100 - 60)% 
= 40%

Question: 15% of 40% of a number is 120. What is 16% of that number? 

Solution:
Let, a number be x 

ATQm
x × 0.15 × 0.4 = 120 
⇒ x = 120/( 0.15 × 0.4) 
= 2000 

 16% of that number is = 2000 × 0.16
= 320 

Question: The profit earned after selling an article for Tk. 1754 is the same as loss incurred after selling the article for Tk. 1492. What is the cost price of the article?

Solution:
Let,
The cost price of the article be Tk. x.

ATQ,
x - 1492 = 1754 - x
⇒ 2x = 1754 + 1492
⇒ 2x = 3246
⇒ x = 3246/2
∴ x ​= 1623

∴ The cost price of the article is Tk. 1623.

Question: The sale price of an article including the Sales Tax is Tk. 616. The rate of Sales Tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is-

Solution:
Let,
The cost price be x.
Selling price = x + 12% of x
= x + (12x/100)
= 28x/25

ATQ,
(28x/25) + 10% of (28x/25) = 616
⇒ (28x/25) + (280x/2500) = 616
⇒ (28x/25) + (14x/125) = 616
⇒ (140x + 14x)/125 = 616
⇒ 154x = 77000
∴ x = 500

∴ Cost price tk. 500.

Question: A man bought some eggs of which 10% are rotten. He gives 80% of the remainder to his neighbors. Now he is left out with 36 eggs. Then he ate two eggs. How many eggs did he buy?

Solution:
let, the man bought  x eggs
10% are rotten

so eggs remained = x - x × 10%
= x - x/10
= 9x/10

80% of 9x/10
= (9x/10) × (80/100)
= 18x/25

he is left with = (9x/10) - (18x/25)
= (45x - 36x)/50
= 9x/50

So, (9x/50) = 36
⇒ 9x = 36 × 50
⇒ x = (36 × 50)/9
= 200

∴ He bought 200 eggs

Question: (75% of 320) + (40% of 150) - ? = 170

Solution:
Let,
(75% of 320) + (40% of 150) - x = 170
⇒ {(75 × 320)/100} + {( 40 × 150)/100} - x = 170
⇒ 240 + 60 - x = 170
⇒ - x = 170 - 300
∴ x = 130