ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: A lead ore mine contains 50% metal. Of this metal, 4/5% is gold and the remainder is lead. If 6000 kg of ore is extracted, what is the mass of the lead?

Solution:
Given mass of lead ore = 6000 kg 

The mass of metal is 50% of 6000 = 3000 kg 
∴ Mass of gold is 4/5% of 3000
= (4 × 3000)/(5 × 100)
= 24 kg 

∴ Mass of lead = Mass of metal - Mass of gold
= 3000 - 24 
= 2976 kg

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: 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 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: 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 toaster machine is priced at Tk. 25,000 and sold with two successive discounts of 15% and 10%. What is its final selling price?

Solution: 
Given,
Marked Price = Tk. 25000
Price after 15% discount
= 25000 - (15% of 25000)
= 25000 - 3750
= Tk. 21,250

Price after 10% discount
= 21250 - (10% of 21250)
= 21250 - 2125
= Tk. 19,125

∴ Final Selling Price = Tk. 19,125

Question: Every 2 minutes, 5 litres of water are poured into a 1,500 litre tank. After 3 hours, what percent of the tank will be full?

Solution:
In 2 minutes, 5 liters is poured
In 180 minutes = (180 × 5)/2 = 450 liters

So, percentage filled = (450 × 100)/1500
= 30%

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

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

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

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

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

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

Question: A girl bought a Nepenthes plant for Tk. 1600 after getting a 20% discount. What was the original catalog price of the plant?

Solution:
20% discount,
If the catalog price is Tk. 100 then the purchased price = (100 - 20)
= Tk. 80

Now,
If the purchase price is Tk. 80, the catalog price = 100 taka.
∴ If the purchase price is Tk. 1, the catalog price = 100/80 taka
∴ If the purchase price is Tk. 1600, the catalog price = (100 × 1600)/80
= Tk. 2000

∴ the original catalog price of the plant is  Tk. 2000

Question: By what percentage must 40 be increased to become 70?

Solution: 
Let,
x% should be added.

Therefore,
40 + x% of 40 = 70
⇒ 40 + 40x/100 = 70
⇒ 40x/100 = 30
⇒ 2x/5 = 30
⇒ 2x = 150
⇒ x = 75

Therefore, 75% should be added to 40 to make it 50.

Question:

Solution: 

Question: If a student of the mathematics department sells all his books for Tk. 7,500, he loses 25%. To gain 10%, at what price should he sell the books?

Solution:
Let,
The cost price of the books x.
Selling price = x - 25% of x
⇒ 7500 = x - (25x/100)
⇒ 7500 = 75x/100
⇒ 75x = 750000
∴ x = 10000

To gain 10% = 10000 + 10% of 10000
= 10000 + 1000
= Tk. 11000

To gain 10%, he should sell the books for Tk. 11000.

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

Solution:
Let the cost price (CP) be Tk. 100

With 20% profit:
Selling Price (SP) = CP + 20% profit
= 100 + 20
= Tk. 120

This SP is after 25% discount on Marked Price (MP).
∴ SP = 75% of MP 
⇒ 120 = 0.75 × MP
⇒ MP = 120 / 0.75
= Tk. 160

Now, with reduced discount of 15%:
New Selling Price = 85% of Marked Price
= 0.85 × 160
= Tk. 136

∴ New profit = New Selling Price – Cost Price 
= 136 – 100
= Tk. 36

∴ New profit percentage = (36 / 100) × 100% = 36%

Question: What percentage of numbers from 1 to 50 has 2 or 9 in the unit digits?

Solution:
Numbers from 1 to 50 has 2 or 9 in the unit digits
= 2, 9, 12, 19, 22, 29, 32, 39, 42, 49
= 10 Numbers

∴ Amount in percentage
= 10/50 × 100%
= 20%

Question: A shop offers a ‘Buy 2, Get 1 Free’ deal. What is the equivalent percentage discount?

Solution:
Assume the price of each item = 1 Taka.
Then,
Cost of 2 items = 2 Taka
Since 1 item is received for free, total items = 2 + 1 = 3

After the discount,
Cost of 3 items = 2 Taka
∴ Cost per item = 2/3 Taka

Actual price per item = 1 Taka
∴ Discount per item = 1 − (2/3) = 1/3 Taka

So, discount on 1 Taka = 1/3 Taka
∴ Discount on 100 Taka = 100 × (1/3) = 33.33 Taka

Therefore, in a “Buy 2, Get 1 Free” offer, the equivalent discount is 33.33%.

Question: The bus fare was recently raised from Tk. 3.70 to Tk. 4.00 per kilometer. What is the approximate percentage increase?

Solution: 
বাস ভাড়া বাড়ে = (4.00 - 3.70) টাকা
= 0.30 টাকা

বাস ভাড়া শতকরা বাড়ে = (0.30/3.70) × 100%
= 8.1 %
≈ 8%

Question: If both the length and the breadth of a rectangle are increased by 20%, what is the percentage increase in its area?

Solution: 
মনে করি,
দৈর্ঘ্য = x একক এবং
প্রস্থ = y একক
∴ ক্ষেত্রফল = xy বর্গ একক

২০% বৃদ্ধিতে,
নতুন দৈর্ঘ্য = x + x এর ২০%
                 = ১২x /১০ একক

২০% বৃদ্ধিতে,
প্রস্থ = y + y এর ২০%
        = ১২y /১০ একক

∴ নতুন ক্ষেত্রফল = (১২x/১০) ×( ১২y/১০) = ১৪৪xy/১০০ বর্গ একক

∴ ক্ষেত্রফল বৃদ্ধি =১৪৪xy/১০০ - xy
                      =(১৪৪xy - ১০০xy)/১০০
                      = ৪৪xy/১০০
∴ শতকরা ক্ষেত্রফল বৃদ্ধি = {(৪৪xy/১০০) × (১/xy) × ১০০}%
= ৪৪% 

 Question: A dozen Bombay peppers are purchased for Tk. 37.50 and sold for Tk. 39.75. What is the profit percentage?

Solution:
∴ লাভ = ৩৯.৭৫ - ৩৭.৫০ = ২.২৫ টাকা

∴ ৩৭.৫০ টাকায় লাভ হয় = ২.২৫ টাকা
∴ ১ টাকায় লাভ হয় = ২.২৫/৩৭.৫০ টাকা
∴ ১০০ টাকায় লাভ হয় = (২.২৫ × ১০০)/৩৭.৫০ টাকা
= (২২৫ × ১০০)/৩৭৫০ টাকা 
= ৬ টাকা বা ৬% 

Question: Akmal multiplied a number by 2/5 instead of 5/2. What is the percentage error in the calculation? 

Solution:
Let the number be x

∴ Error = (5x/2) - (2x/5)
= (25x - 4x)/10
= 21x/10

∴ percentage Error = {(21x/10)/(5x/2) × 100}% 
= 84% 

Question: A shirt with a list price of Tk. 150 is sold for Tk. 105 after two successive discounts. If the second discount is 12.5%, what was the rate of the first discount?

Solution:
Let the first discount be x%.

∴ After the first discount,
∴ the price = (100 − x)% of 150 
= (100 − x)/100 × 150

After the second discount of 12.5%,
the selling price = 87.5% of the first discounted price
= 87.5/100 × (100 − x)/100 × 150

Given selling price = 105,
ATQ,
87.5/100 × (100 − x)/100 × 150 = 105
⇒ 100 − x = (105 × 100 × 100) / (87.5 × 150)
⇒ 100 − x = 80

∴ x = 100 − 80
= 20

∴ The first discount is 20%.

Question: 70 grams is what percentage of 20 kilograms?

Solution:
We know,
20 kg = 20 × 1000 
= 20000 grams

∴ Percentage = (70 ÷ 20000) × 100
= 0.35%

∴ 70 grams is 0.35% of 20 kg.

Question: The population of Gotham City increases from 175,000 to 262,500. What is the percentage increase in the population?

Solution:
জনসংখ্যা বৃদ্ধি পেয়েছে 
 = (262500 - 175000) = 87500

175000 জনে বৃদ্ধি পায় = 87500 জন
∴ 1 জনে বৃদ্ধি পায় = 87500/175000 জন
∴ 100 জনে বৃদ্ধি পায় = (87500 × 100)/175000 = 50 জন

∴ জনসংখ্যা বৃদ্ধির শতকরা হার = 50%

Question: If the cost price of 15 books is equal to the selling price of 20 books, what is the loss percentage?

Solution:
Let C.P. of each books Tk. 1
Cost Price of 20 books Tk. 20
Selling Price of 20 books Tk. 15

∴ Loss  = TK. (20 - 15)
= Tk.5

∴ Percentage of loss = {(5/20) × 100}%
 = 25%

Question: If Adnan’s salary is 60% higher than Bina’s salary, by what percentage is Bina’s salary less than Adnan’s?

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

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

∴ lower = (60/160) × 100 = 37.5%

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