ব্যাংক নিয়োগ বিষয়ভিত্তিক প্রস্তুতি

Question: If b is equal to 20% of a, then what is b% of 20 equal to?

Solution:
20% of a = b    
⇒ 20a/100 = b

∴ b% of 20
= (b/100) × 20
= (20a/100) × (1/100) × 20
= 4a × (1/100)
= 4% of a

Question: A worker union contract specifies a 6% salary increase plus a Tk. 450 bonus for each worker. For a worker, this is equivalent to an 8% salary increase. What was this worker's salary before the new contract?

Solution:
ধরি, কর্মীর পূর্বের বেতন = x টাকা।

6% বৃদ্ধিতে বেতন = x + x এর 6%
= x + (6x/100) = 106x/100

বোনাস হিসেবে 450 টাকা যোগ করলে মোট বেতন = (106x/100) + 450

8% বৃদ্ধিতে বেতন = x + x এর 8%
= x + (8x/100) = (108x/100)

প্রশ্নমতে,
(106x/100) + 450 = (108x/100)
⇒ 450 = (108x/100) - (106x/100)
⇒ 450 = (2x/100)
⇒ x = (450 × 100)/2
∴ x = 22500

অর্থাৎ, কর্মীর পূর্ববর্তী বেতন ছিল 22500 টাকা।

Question: Rafi weighs 72 kg. If he reduces his weight in the ratio 6 : 5, find his new weight​ in kg.

Solution:
ধরি, রাফির পূর্বের ওজন = 6x
রাফির পরের ওজন = 5x

প্রশ্নমতে,
6x = 72
⇒ x = 72 / 6 = 12

∴ ওজন কমে যাওয়ার পর হবে = 5x = 5 × 12 = 60 kg

Question: How many years will it take for an investment of Tk. 7500 to earn Tk. 2250 in simple interest rate of 6%?

Solution:
Given that,
Principal, P = 7500
Simple Interest, SI = 2250
Rate of interest, r = 6%
Time, n = ?

We know,
SI = Pnr/100
⇒ n = (S × 100)/(P × r)
= (2250 × 100)/(7500 × 6)
= 5 years

So, it will take 5 years for the investment to earn Tk. 2250 at 6% simple interest.

Question: A sum of money is to be divided among P, Q, R, S in the ratio 7 : 3 : 5 : 2. If R gets Tk. 2000 more than S, what is Q's share?

Solution:
Let their shares be 7x, 3x, 5x, and 2x respectively.

ATC,
5x - 2x = 2000
⇒ 3x = 2000
⇒ x = 2000/3

Therefore,
Q's share = 3x
= 3 × (2000/3)
= 2000 taka.

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: The marked price of a shirt was Tk. 2400. A customer bought it for Tk. 1620 after getting two successive discounts. The first discount was 25%. What was the second discount rate?

Solution:
Price after first discount (25%),
= 2400 - (25% of 2400)
= 2400 - (2400 × 0.25)
= 2400 - 600
= Tk. 1800

Amount of second discount = 1800 - 1620 = Tk. 180

∴ Second discount rate = (Second discount amount/Price after first discount) × 100
= (180/1800) × 100
= 0.10 × 100
= 10%

∴ The second discount rate is 10%.

Question: Ms. Rahman's monthly salary is Tk. 8000.00 and she gets 15% commission on her salary. If her salary increased by 20%, by what percent will her commission increase?

Solution:
পূর্বের কমিশন = 8000 এর 15% টাকা
= 8000 × 15/100
= 1200 টাকা

২০% বৃদ্ধিতে বর্তমান বেতন = 8000 + 8000 এর 20%
= 8000 + 8000 × 20/100
 = 8000 + 1600
=9600 টাকা

নতুন কমিশন = 9600 এর 15%
= 9600 × 15/100 = 1440 টাকা

কমিশন বৃদ্ধি পায় = 1440 - 1200 = 240 টাকা

শতকরা কমিশন বৃদ্ধি পায় = (240/1200) × 100%
= 20%

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: A car is sold at a profit of 25%. Had it been sold for Tk. 15,000 less, there would have been a loss of 15%. What was the cost price?

Solution:
ধরি, গাড়িটির ক্রয়মূল্য = x টাকা

25% লাভে বিক্রয়মূল্য = x + x এর 25%
= x + 25x/100
= x + x/4
= 5x/4

15% ক্ষতিতে বিক্রয়মূল্য = x - x এর 15%
= x - 15x/100
= x - 3x/20
= 17x/20

প্রশ্নমতে,
(5x/4) - (17x/20) = 15000
⇒ (25x/20) - (17x/20) = 15000
⇒ 8x/20 = 15000
⇒ 2x/5 = 15000
⇒ 2x = 15000 × 5
⇒ 2x = 75000
⇒ x = 75000/2
∴ x = 37500

∴ গাড়িটির ক্রয়মূল্য = 37,500 টাকা

Question: Two numbers P and Q are such that the sum of 10% of P and 15% of Q is three-fourths of the sum of 20% of P and 18% of Q. Find the ratio of P : Q.

Solution:
10% of P + 15% of Q = 3/4 × (20% of P + 18% of Q)
⇒ 10P/100 + 15Q/100 = 3/4 × (20P/100 + 18Q/100)
⇒ P/10 + 3Q/20 = 3/4 × (P/5 + 9Q/50)
⇒ 2P/20 + 3Q/20 = 3/4 × (10P + 9Q)/50
⇒ (2P + 3Q)/20 = (30P + 27Q)/200
⇒ 10(2P + 3Q) = 30P + 27Q
⇒ 20P + 30Q = 30P + 27Q
⇒ 30Q - 27Q = 30P - 20P
⇒ 3Q = 10P
⇒ P/Q = 3/10
∴ P : Q = 3 : 10

Question: A sum of Tk. 4000 amounts to Tk. 4840 in 2 years at compound interest. Find the rate of interest per annum.

Solution:
Here, Principal, P = 4000 Tk.
Final amount, A = 4840 Tk.
Time, n = 2 years
Interest rate, r = ?

Now,
A = P × (1 + r/100)ⁿ
⇒ 4840 = 4000 × (1 + r/100)²
⇒ (1 + r/100)² = 4840/4000
⇒ (1 + r/100)² = 121/100
⇒ 1 + r/100 = √(121/100)
⇒ 1 + r/100 = 11/10
⇒ r/100 = 11/10 - 1
⇒ r/100 = 1/10
⇒ r = (1/10) × 100
⇒ r = 10

∴ The annual rate of interest is 10%.

Question: A bank offers 10% compound interest calculated half-yearly. A customer deposits Tk. 2000 on 1st January and another Tk. 2000 on 1st July of the same year. How much interest will he earn at the end of the year?

Solution:
Here,
Half-yearly interest rate = 10% ÷ 2 = 5%
Now,
The first deposit of Tk. 2000 was made on 1st January.
It stays for 12 months, so it earns interest twice (i.e., 2 half-years).   
∴ A₁ = P(1 + r/100)ⁿ
= 2000 × {1 + 5/100}²
= 2000 × (1.05)²
= 2000 × 1.1025
= 2205

Now,
The second deposit of Tk. 2000 was made on 1st July.
It stays for 6 months, so it earns interest only once (1 half-year).
∴ A₂ = P(1 + r/100)ⁿ
= 2000 × (1 + 5/100)¹
= 2000 × 1.05
= 2100

Total amount = 2205 + 2100 = 4305
Total money deposited = 2000 + 2000 = 4000

∴ Interest earned = 4305 - 4000 = Tk. 305

∴ The customer would have gained Tk. 305 by way of interest.

Question: The marked price of a ceiling fan is Tk. 1250 and the shopkeeper allows a discount of 6% on it. Find the selling price of the fan.

Solution:
Marked price = Tk. 1250 and discount = 6%. 

Discount = 6% of Marked Price 
= (6% of Tk. 1250) 
= Tk. {1250 × (6/100)} 
= Tk. 75 

Selling price = (Marked Price) - (discount) 
= Tk. (1250 - 75) 
= Tk. 1175. 

∴ Hence, the selling price of the fan is Tk. 1175. 

Question: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school?

Solution:
Given,
20% of students are below 8 years of age
Number of students of 8 years of age = 48
Number of students above 8 years = 2/3 of students of 8 years

∴ Students above 8 years = 2/3 × 48 = 32
∴ Students of 8 years or above = 48 + 32 = 80

Since 20% are below 8 years, then 80% are of 8 years or above.
So, 80% of total students = 80

Let, total number of students = x
80% of x = 80
⇒  (80/100) × x = 80
⇒ x = 80 × (100/80)
∴ x = 100

Question: A wholesaler buys a television for Tk. 18,000 and sells it to a retailer at a profit of 30%. The retailer then sells it to a customer at a profit of 25%. How much does the customer pay to the retailer?

সমাধান:
পাইকারের 30% লাভে বিক্রয়মূল্য = 18,000 + 18,000 এর 30%
= 18,000 + (18,000 × 30/100)
= 18,000 + 5,400 = 23,400 টাকা

পাইকারের বিক্রয়মূল্য = খুচরা বিক্রেতার ক্রয়মূল্য = 23,400 টাকা

খুচরা বিক্রেতার 25% লাভে বিক্রয়মূল্য = 23,400 + 23,400 এর 25%
= 23,400 + (23,400 × 25/100)
= 23,400 + 5,850 = 29,250 টাকা

সুতরাং, খুচরা বিক্রেতার বিক্রয়মূল্য = ক্রেতার ক্রয়মূল্য = Tk. 29,250

Question: A sum of money becomes 4 times itself in 20 years at simple interest. What is the annual interest rate?

Solution:
Let, Principal amount = P
Sum of amount = 4P
∴ Interest, I = 4P - P = 3P
Time, n = 20 years
Rate of interest = r

We know, I = Pnr/100
⇒ Pnr/100 = 3P
⇒ nr/100 = 3
⇒ 20 × r/100 = 3
⇒ 20r = 300
⇒ r = 300/20
⇒ r = 15

∴ The annual interest rate is 15%.

Question: The investment ratio of two partners, P and Q, is 7 : 9, while their profit ratio is 14 : 27. Given that P invested his funds for 6 months, determine the duration of Q's investment.

Solution:
Let P invested Tk 7x for 6 months
Q invested Tk 9x for y months

Now,
(7x × 6) : (9x × y) = 14 : 27
⇒ (7x × 6)/(9x × y) = 14/27
⇒ 42x/9xy = 14/27
⇒ 42 × 27 = 14 × 9y
⇒ 1134 = 126y
⇒ y = 1134/126
∴ y = 9

So, Q invested for 9 months.

Question: What will be the difference between simple and compound interest at 6% on a sum of Tk. 15000 after 2 years?

Solution:
দেওয়া আছে, Principal, P = 15000 টাকা
Rate of interest, r = 6%
Time, n = 2 বছর

Simple Interest (SI):
SI = (P × r × n) / 100
= (15000 × 6 × 2) / 100
= 180000 / 100
= 1800 টাকা

Compound Interest (CI):
CI = P × (1 + r/100)ⁿ - P
= 15000 × (1 + 6/100)² - 15000
= 15000 × (1.06)² - 15000
= 15000 × 1.1236 - 15000
= 16854 - 15000
= 1854 টাকা

∴ Difference between CI and SI:
= 1854 - 1800
= 54 টাকা

Question: In a mixture of milk and water, the ratio is 4 : 3. If 5 liters of water is added, the new ratio becomes 4 : 4. What was the original amount of milk in the mixture?

Solution:
ধরি, শুরুতে দুধ ছিল = 4x লিটার,
পানি ছিল = 3x লিটার।

এখন 5 লিটার পানি যোগ করলে, নতুন পানি = 3x + 5 লিটার

ATQ,
4x/(3x + 5) = 4/4
⇒ 4x/(3x + 5) = 1
⇒ 4x = 1 × (3x + 5)
⇒ 4x = 3x + 5
⇒ 4x - 3x = 5
⇒ x = 5

∴ দুধের পরিমাণ = 4x = 4 × 5 = 20 লিটার

Question: In January, the value of a stock increased by 50%; and in February, it decreased by 20%. In March, it increased by 25%; and in April, it decreased by 10%. If a person invested Tk. 200 in the stock on January 1 and sold it at the end of April, what was the percentage change in the price of the stock?

Solution:
At the end of January,
The value of the stock is = Tk. 200 + 50% of (Tk. 200)
= Tk. 200 + Tk. 100 = Tk. 300.

At the end of February,
The value of the stock is = Tk. 300 - 20% of (Tk. 300)
= Tk. 300 - Tk. 60 = Tk. 240.

At the end of March,
The value of the stock is = Tk. 240 + 25% of (Tk. 240)
= Tk. 240 + Tk. 60 = Tk. 300.

At the end of April,
The value of the stock is = Tk. 300 - 10% of (Tk. 300)
= Tk. 300 - Tk. 30 = Tk. 270.

Now, the percentage change in price is,
= (Change in price/Original price) × 100%
= (270 - 200)/200 × 100%
= (70/200) × 100%
= 35%

Question: Population of a town increase 2.5% annually but is decreased by 0.5% every year due to migration. What will be the percentage increase in 2 years?

Solution:
Net percentage increase in Population = (2.5 - 0.5) = 2% each year.
Assuming initial population = 100

Population of Town after 1st year = (100 + 2% of 100)
= 100 + 2 = 102

Population of Town after 2nd year = (102 + 2% of 102)
= 102 + 2.04 = 104.04

Increase = 104.04 - 100 = 4.04
∴ Percentage increase = (4.04/100) × 100% = 4.04%

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

সমাধান:
ধরি, শার্টের ক্রয়মূল্য = x টাকা

20% লাভে বিক্রয়মূল্য = x + x এর 20%
= x + (x × 20/100)
= x + x/5 = 6x/5

প্রশ্নমতে,
6x/5 = 1500
⇒ 6x = 1500 × 5
⇒ 6x = 7500
⇒ x = 7500/6
⇒ x = 1250

∴ শার্টের ক্রয়মূল্য = Tk. 1250

বিক্রয়মূল্য = Tk. 1200 ক্রয়মূল্য = Tk. 1250

যেহেতু বিক্রয়মূল্য < ক্রয়মূল্য, তাই ক্ষতি হবে।

ক্ষতি = ক্রয়মূল্য - বিক্রয়মূল্য
= 1250 - 1200 = 50 টাকা

শতকরা ক্ষতি = (ক্ষতি/ক্রয়মূল্য) × 100%
= (50/1250) × 100%
= 5000/1250
= 4%

∴ 4% ক্ষতি হবে

Question: In your wallet, there are Tk 1000, Tk 500, and Tk 100 notes in the ratio 3 : 5 : 2, amounting to Tk 22,800. Find the number of each note respectively.

Solution:
Let,
The number of Tk 1000 notes is 3x
The number of Tk 500 notes is 5x
The number of Tk 100 notes is 2x

ATQ,
1000 × 3x + 500 × 5x + 100 × 2x = 22800
⇒ 3000x + 2500x + 200x = 22800
⇒ 5700x = 22800
⇒ x = 22800 / 5700
⇒ x = 4

Number of Tk 1000 note = 3x = 3 × 4 = 12
Number of Tk 500 note = 5x = 5 × 4 = 20
Number of Tk 100 note = 2x = 2 × 4 = 8

Therefore, the number of Tk 1000, Tk 500, and Tk 100 notes are respectively 12, 20, and 8.