ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: 25% of 30% Is equal to-

Solution:
25% of 30%
= (25/100) × (30/100)
= (1/4) × (3/10)
= 3/40
= 0.075

Question: An item is sold at 25% discount making a profit of 20%. If the discount is reduced to 15%, what will be the new profit percentage?

Solution:
Let,
the cost price is 100
So, the selling price is 120

Giving 25% discount, then
⇒ x - 25% of x = 120
⇒ x - (x/4) = 120
⇒ 3x/4 = 120
∴ x = 160 

Now,
giving 15% discount,
160 - 15% of 160 = 160 - 24 = 136
So the new selling price is 136 taka.

So profit = 136 - 100 = 36

When the discount is reduced to 15%, the profit becomes 36%.

Question: An agent sells goods worth Tk. 22000. If his commission rate was 15.5​%, what was the amount of his commission?

Solution:
Commission = 15.5% of 22000
= (155/10) × (1/100) × 22000
= (155/1000) × 22000
= 3410

Question: If 25% of a = b, then b% of 16 is equal to- ?

Solution:
Given that,
⇒ 25% of a = b
⇒ (25/100) × a = b
⇒ a/4 = b
∴ b = a/4

Now,
b% of 16
= (b/100) × 16
= (a/4) × (16/100)
= 4a/100
= 4% of a

Question: Rina bought 8 mangoes for Tk. 40. She sold 5 mangoes for Tk. 40. What is her profit percentage?

Solution:
৮ টি আমের ক্রয়মূল্য ৪০ টাকা
১ টি আমের ক্রয়মূল্য ৪০/৮ = ৫ টাকা

আবার,
৫ টি আমের বিক্রয়মূল্য ৪০ টাকা
১ টি আমের বিক্রয়মূল্য ৪০/৫ = ৮ টাকা

∴ লাভ = ৮ - ৫ = ৩ টাকা

∴ ৫ টাকায় লাভ হয় ৩ টাকা
১ টাকায় লাভ হয় ৩/৫ টাকা
১০০ টাকায় লাভ হয় ৩০০/৫ = ৬০ টাকা

∴ লাভ ৬০%

Question: The sum of two numbers is 456. If the bigger number is decreased by 20% and the smaller number is increased by 10%, then the numbers obtained are equal. The smaller number is-

Solution:
Let,
Larger number = x and smaller number = 456 - x

According to the question
⇒ 80x/100 = {(456 - x)/100} × 110
⇒ 80x = (456 - x) × 110
⇒ 80x = 456 × 110 - 110x
⇒ 110x + 80x = 456 × 110
⇒ 190x = 456 × 110
⇒ x = (456 × 110)/190
⇒ x = 264

∴ Smaller number = 456 - 264 = 192

Question: 45% of 750  -  25% of 480 = ?

Solution:
Given that,
= 45 × (750/100) - 25 × (480/100)
= (45 × 7.5) - (25 × 4.8)
= 337.5 - 120
= 217.50

Question: The marked price of a watch was Tk. 720. A man bought the same for Tk. 550.80 after getting two successive discounts. the first being 10%. then the second discount rate is-

Solution:
Marked price = 720
Actual price = 550.80
First discount = 10%
Let the second discount be x%
Then, we can write
⇒ 720(1 - 0.1)(1 - x/100) = 550.80
⇒ 720 × 0.9(1 - 0.01x) = 550.8
⇒ 648(1 - x/100) = 550.8
⇒ 1 - x/100 = 550.8/648
⇒ x/100 = 1 - 0.85
⇒ x/100 = 0.15
⇒ x = 0.15 × 100
∴ x = 15

∴ Second discount = 15%

Question: What Percentage of 20 kg is 70 grams?

Solution:
Required Percentage = {(70gm/20kg) × 100}%
= {(70/20000) × 100}%    ;[1kg = 1000gm]
= (7000/20000)%
= 0.35%

Question: A person spends 30% of his income on food, 20% on transportation, and 50% of the remaining amount on house rent. What percentage of his income is left?

Solution:
Let, total income = 100
Total expense food and transportation = 30 + 20 = 50
∴ Remaining = (100 - 50) = 50

∴ Expense on house rent = 50 × (50/100) = 25
∴ Remaining after all expense = 50 - 25 = 25

The person is left with 25% of his income.

Question: One-half percent, written as a decimal, is-

Solution:
As we know,1% =1/100
Hence,
(1/2)% = (1/2) × (1/100)
= 1/200
= 0.005

Question: The Cost Price of an article is 40% of the Selling Price. The percent that the Selling Price is of Cost Price is-

Solution:
ধরি, বিক্রয়মূল্য = x টাকা

∴ ক্রয়মূল্য = x এর 40%
= 40x/100 = 2x/5

∴ ক্রয়মূল্য 2x/5 টাকা হলে বিক্রয়মূল্য = x টাকা
∴ ক্রয়মূল্য 1 টাকা হলে বিক্রয়মূল্য = 5x/2x = 5/2 টাকা
∴ ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য = (100 × 5)/2 = 250 টাকা

∴ বিক্রয়মূল্য 250% ক্রয়মূল্যের

Question: In an election with three candidates, Candidate A received 30% of the valid votes, and Candidate B received 45%. If 15% of the total votes were invalid and 8,000 votes were cast in total, how many valid votes did Candidate C receive?

Solution:
Invalid votes = 15% of 8000 = (15/100) × 8000 = 1200

∴ Valid votes = 8000 - 1200 = 6800
Now,
Votes for A and B = 30% + 45% = 75% of 6800 = (75/100) × 6800 = 5100

∴ Votes for C = 6800 - 5100 = 1700

∴ So Candidate C received 1700 valid votes.

Question: If Amina’s salary is 60% more than Bina’s salary, then Bina’s salary is what percent less than Amina’s salary?

Solution:
Let,
Bina’s Salary is Tk. 100. Then,
Amina’s Salary = (100 + 60% of 100)
= 100 + (60× 100)/100
= 100 + 60
= 160

Difference between Amina’s Salary and Bina’s Salary = 160 - 100 = 60

∴ lower = (60/160) × 100 = 37.5%

∴ Bina’s salary is 37.5% lower than Amina’s salary.

Question: If the list price of a mobile phone is Tk. 10000, and a Tk. 1500 discount is offered on the mobile phone, then what is the discount percentage?

Solution:
Marked Price = Tk. 10000
Discount = Tk. 1500

Discount % = (Discount/marked Price) × 100%
Discount (%) = (1500/10000) × 100%
= 15%

∴ So the discount percentage is 15%.

Question: Ratio of the income of A and B is 6 : 5 and the ratio of the savings of A and B is 3 : 1. If the expenditure of A and B is Tk. 12000 and Tk.16000 respectively, then find the difference between the income of A and B?

Solution:
Let,
Income of A = 6x and Income of B = 5x
And
Savings of A = 3y and Savings of B = y

We know,
Income = Savings + Expenditure

ATQ,
6x = 3y + 12000 ......(1)   (for A)
5x = y + 16000    (for B)
⇒ y = 5x - 16000 ...... (2)

Puting this value in (1) then we get,
⇒ 6x = 3y + 12000
⇒ 6x = 3(5x - 16000) + 12000
⇒ 6x = 15x - 48000 + 12000
⇒ 6x = 15x - 36000
⇒ 15x - 6x = 36000
⇒ 9x = 36000
∴ x = 4000
(2) ⇒ y = 5x - 16000 = 20000 - 16000 = 4000

∴ Income of A = 24000
∴ Income of B = 20000

∴ Difference = 24000 - 20000 = Tk. 4000

Question: If a woman sells her table for Tk. 2,400, she loses 20%. To gain 20%, at what price should she sell it?

Solution:
Let the Cost price of the Table is x.
Selling price = x - 20% of x
⇒ 2400 = x - (20x/100)
⇒ 2400 = 80x/100
⇒ 80x = 240000
∴ x = 3000

To gain 20% = 3000 + 20% of 3000
= 3000 + 600
= Tk. 3600

To gain 20%, she should sell the table for Tk. 3600.

Question: Seventy-two percent of a number is 30 less than three-fourths of that number. What is the number?

Solution:
Let, the number = x.

ATQ,
72% of x = (3/4) of x - 30
⇒ 72x/100 = (3x/4) - 30
⇒ 18x/25 = (3x/4) - 30
⇒ (3x/4) - (18x/25) = 30
⇒ (75x - 72x)/100 = 30
⇒ 3x/100 = 30
⇒ 3x = 3000
⇒ x = 3000/3
∴ x = 1000

So, the number is 1000

Question: Mr. Ali 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. 32 per kg. His profit percent is-

Solution:
Cost Price of 56 kg rice = {(26 × 20) + (30 × 36)}
= (520 + 1080)
= 1600 taka

Selling Price of 56 kg rice = (56 × 32)
= 1792 taka

∴ Profit = 1792 - 1600
= 192 taka

∴ Profit percentage = (192/1600) × 100%
= 12%

Question: A shirt is sold for Tk. 1500 at a profit of 20%. What would have been the actual profit or loss if it had been sold for Tk. 1200?

Solution:
Firstly let us find the cost price of the same. C.P. = 1500 × (100/120) = 1250.
New selling price = 1200
Loss = 1250 - 1200 = 50

∴ Loss percentage = 100 × (50/1250)
= 4%.

If sold at Tk. 1200, there would be a loss of 4%.

Question: There is a ratio of 5 : 4 between two numbers. If 40% of the first number is 12, then what would be 50% of the second number is ?

Solution: 
Let the numbers be 5x and 4x respectively

According to the question,
⇒ 5x × (40/100) = 12
⇒ 2x = 12
∴ x = 6

Now,
50% of the second number is,
= 4x of 50%
= 4 × 6 × (50/100)
= 12

So 50% of the second number is 12.

Question: A reduction of 25% in the price of sugar enables a housewife to purchase 5 kg more for 600 Taka. What is the original price per kg of sugar?

Solution:
Let original price per kg = p Taka
Reduced price = p - p of 25% = 0.75p
Original quantity for 600 Taka
Q₁ = 600/p kg

And
New quantity for 600 Taka
Q₂ = 600/0.75p = 800/p kg

Now, quantity difference,
Q₂ - Q₁ = 5
(800/p) - (600/p) = 5
200/p = 5
p = 200/5
p = 40 

∴ Original price per kg = Tk. 40

Question: The ratio between Karim's age and Rahim's age is 10 : 11. What is the age of Rahim in percentage of Karim's age ?

Solution: 
Given that,
The ratio of Karim's age to Rahim's age = 10 : 11

Let, Karim's age = 10x
and Rahim's age = 11x

Now, we find Rahim's age as a percentage of Karim's age,

∴ Percentage = (Rahim’s age/Karim’s age​) × 100
= (11x/10x) × 100
= 110

So, Rahim's age is 110% of Karim's age.