ব্যাংক নিয়োগ বিষয়ভিত্তিক প্রস্তুতি

Question: What percent of a is equal to 3a?

Solution:
Let x% of a = 3a
⇒ (x/100) × a = 3a
⇒ x/100 = 3a/a
⇒ x/100 = 3
⇒ x = 100 × 3
∴ x = 300

Question: Arif bought a ticket of a cricket match for Tk. 25 and later sold the ticket to Rafi for Tk. 75. What was the percent increase in the price of the ticket?

Solution:
ক্রয়মূল্য = 25 টাকা
বিক্রয়মূল্য = 75 টাকা
লাভ = 75 - 25 = 50 টাকা

25 টাকায় লাভ হয় = 50 টাকা
1 টাকায় লাভ হয় = 50 / 25 টাকা
100 টাকায় লাভ হয় = (50 × 100)/25 টাকা = 200 টাকা

শতকরা লাভ 200%

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

Solution:
ধরি, শুরুতে দুধ ছিল = 5x লিটার,
পানি ছিল = 3x লিটার।

এখন ৪ লিটার পানি যোগ করলে,
নতুন পানি = 3x + 4 লিটার

ATQ,
5x/(3x + 4) = 5/4
⇒ 4 × 5x = 5 × (3x + 4)
⇒ 20x = 15x + 20
⇒ 5x = 20
⇒ x = 4

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

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 man bought a book for Tk. 360 after getting a 20% discount. What was the original catalog price of the book?

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. 360, the catalog price = (100 × 360)/80
= Tk. 450

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: A man paid tax on 12000 Taka at the rate of 20%. He paid the tax in 10 equal payments. what is the amount of each payment?

Solution:
100 টাকায় কর দেয় = 20 টাকা
∴ 1 টাকায় কর দেয় = 20/100 = 1/5 টাকা
∴ 12000 টাকায় কর দেয় (20× 12000)/100 = 2400 টাকা

∴ মোট কর = 2400 টাকা

10টি সমান কিস্তিতে পরিশোধ করে।

∴ প্রতি কিস্তিতে পরিশোধ = 2400/10 = 240 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: A sum of Tk. 2500 amounts to Tk. 2809 in 2 years at compound interest. Find the rate of interest per annum.

Solution:
Here,
Principal, P = 2500 Tk.
Final amount, A = 2809 Tk.
Time, n = 2 years
Interest rate, r = ?

প্রশ্নমতে,
A = P × (1 + r/100)ⁿ
⇒ 2809 = 2500 × (1 + r/100)²
⇒ (1 + r/100)² = 2809/2500
⇒ (1 + r/100) = √(2809/2500)
⇒ 1 + r/100 = 53/50
⇒ r/100 = (53/50) - 1
⇒ r/100 = 3/50
⇒ r = (3/50) × 100
⇒ r = 6

∴ The annual rate of interest is 6%.

Question: A and B started a business with investments in the ratio 2:3. After 4 years, A withdrew his capital. B continued alone for 2 more years. If the total profit after 6 years is Tk. 39,000, what is A's share of the profit?

Solution:
Let A's capital = 2x
Let B's capital = 3x

A's investment for 4 years = 2x × 4 = 8x
B's investment for 6 years = 3x × 6 = 18x

Ratio of profits = 8x : 18x = 4 : 9

∴ Total contribution units = 4 + 9 = 13

Here, total profit = Tk. 39,000
∴ A's share = (4/13) × 39000
= (4 × 39000)/13
= Tk. 12,000

Question: Mr. Khan's salary is Tk. 5000.00 and he gets 10% commission of his salary. If his salary increased by 10%, by what percent his commission will increase?

Solution:
পূর্বের কমিশন:
= 5000 এর 10% টাকা
= 5000 × 10/100
= 500 টাকা

১০% বৃদ্ধিতে বর্তমান বেতন = 5000 + 5000 এর 10%
= 5000 + 5000 × 10/100
= 5000 + 500 = 5500 টাকা

নতুন কমিশন = 5500 এর 10% = 5500 × 10/100 = 550 টাকা

কমিশন বৃদ্ধি পায় = 550 - 500 = 50 টাকা

শতকরা কমিশন বৃদ্ধি পায় = (50/500) × 100% = 10%

Question: A machine is sold at a profit of 20%. Had it been sold for Tk. 60 less, there would have been a loss of 20%. What was the cost price?

Solution:
ধরি, মেশিনটির ক্রয়মূল্য = x টাকা

20% লাভে বিক্রয়মূল্য = x + x এর 20%
= x + 20x/100
= 12x/10

20% ক্ষতিতে বিক্রয়মূল্য = x - x এর 20%
= x - 20x/100
= 8x/10

প্রশ্নমতে,
(12x/10) - (8x/10)= 60
⇒ 4x/10 = 60
⇒ 4x = 60 × 10
⇒ x = (60 × 10)/4
∴ x = 150

∴ মেশিনটির ক্রয়মূল্য = 150 টাকা

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: 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 man borrowed some money for 90 days. He paid Tk. 270 as interest at the rate of 8% per annum. What was the amount he borrowed?

Solution:
এখানে,
সময়, n = 90 দিন
= 3 মাস = 3/12 বছর
= 1/4 বছর

মুনাফা, I = 270 টাকা
মুনাফার হার, r = 8% = 8/100 = 2/25
আসল, P = ?

আমরা জানি,
I = P × n × r
⇒ P × n × r = I
⇒ P = I/(n × r)
= 270/{(1/4) × (2/25)}
= 270/(1/50)
= 270 × 50
= 13500 টাকা

Question: The marked price of a watch was Tk. 1500. A customer bought it for Tk. 1080 after getting two successive discounts. The first discount was 20%. What was the second discount rate?

Solution:
Price after first discount (20%),
= 1500 - (20% of 1500)
= 1500 - (1500 × 0.20)
= 1500 - 300
= Tk. 1200

Amount of second discount
= 1200 − 1080
= Tk. 120

∴ Second discount rate
= (Second discount amount/Price after first discount) × 100
= (120/1200) × 100
= 0.10 × 100
= 10%

∴ The second discount rate is 10%.

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: A buys a product for Tk. 500 and sells it to B at a profit of 25%. B then sells it to C at a profit of 20%. How much does C pay to B?

সমাধান:
A এর 25% লাভে বিক্রয়মূল্য = 500 + 500 এর 25%
= 500 + (500 × 25 / 100)
= 500 + 125
= 625

A এর বিক্রয়মূল্য = B এর ক্রয়মূল্য

B এর 20% লাভে বিক্রয়মূল্য = 625 + 625 এর 20%
= 625 + (625 × 20 / 100)
= 625 + 125
= 750

সুতরাং, B এর বিক্রয়মূল্য = C এর ক্রয়মূল্য = Tk. 750

Question: A certain principal amount, invested at simple interest, grows to Tk. 920 after 2 years and Tk. 1010 after 5 years. What is the original principal amount?

Solution:
Given,
Amount after 2 years = Tk. 920
Amount after 5 years = Tk. 1010

∴ Interest for (5 - 2) = 3 years = 1010 - 920 
= Tk. 90
∴ Interest for 1 year = 90/3 = Tk. 30
∴ Interest for 2 years = 30 × 2 = Tk. 60

∴ Principal = 920 - 60 = Tk. 860

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.

Question: What will be the difference between simple and compound interest at 5% on a sum of Tk. 8000 after 2 years?

Solution:

দেওয়া আছে,
Principal, P = 8000 টাকা
Rate of interest, r = 5%
Time, n = 2 বছর

Simple Interest (SI):
SI = (P × r × n) / 100 = (8000 × 5 × 2) / 100 = 800 টাকা

Compound Interest (CI):
CI = P × (1 + r/100)ⁿ - P
= 8000 × (1 + 5/100)² - 8000
= 8000 × (1.05)² - 8000
= 8000 × 1.1025 - 8000
= 8820 - 8000 = 820 টাকা

∴ Difference between CI and SI:
= 820 - 800 = 20 টাকা

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%