ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: The rate at which a sum becomes four times of itself in 15 years at simple interest will be?

Solution:
Let, Sum = Tk. x.
Then, Simple interest, I = 4x - x = 3x.
We know, 
I = Pnr
⇒ r = I/Pn
⇒ r = {(3x × 100)/(x × 15)}%
∴ r = 20%

Question: At the rate of 8% simple interest, a sum of Tk. 2800 will earn how much interest in 2 years 6 months?

Solution:
Given,
Principal, P = 2800 Tk.
Rate of interest, r = 8% = 8/100 = 2/25.
Time, n = 2 years 6 months
⇒ n = 2 + (6/12) years
∴ n = 5/2 years.

We know,
I = Pnr
= 2800 × (5/2) × (2/25)
= 560 Tk.
Simple Interest Tk. 560.

Question: A sum of money amounts to Tk. 5200 in 5 years and to Tk. 5680 in 7 years at simple interest. The rate of interest per annum is?

Solution:
Simple interest for 2 years = (5680 - 5200) Tk.
= Tk. 480
∴ Simple Interest for 2 years =  Tk. 480
∴ Simple Interest for 5 years =  Tk. (480 × 5/2)
= Tk. 1200
∴ Principal = 5200 - 1200 = Tk. 4000.

We know, 
I = Pnr
⇒ r = I/Pn
 ⇒ r = (1200 × 100)/(4000 × 5)
∴ r = 6%

Question: Rahim, Karim, and Masum started a business by investing Tk.150000, Tk.120000, and Tk.135000 respectively. Find the share of Karim out of the annual profit of Tk. 56700?

Solution:
Ratio of the investments of Rahim, Karim and Masum = 150000 : 120000 : 135000
= 150 : 120 : 135
= 10 : 8 : 9
Sum of the ratio = 10 + 8 + 9
= 27

∴ Karim's share = 56700 × (8/27)
= 16,800 Tk.

Question: A and B invest in a business in the ratio 6 : 4. If 10% of the total profit goes to charity and A's share is Tk. 378, what is the total profit?

Solution:
Let,
The total profit be Tk. 100.
After paying 10% to charity,
A's share = 90 × (6/10)  = Tk. 54

If A's share is Tk. 54, total profit = Tk. 100.
If A's share is Tk. 1, total profit = Tk. 100/54
∴ If A's share is Tk. 378, total profit = Tk. (100 × 378)/54
= Tk. 700

Quesation: A, B and C are partners in a business. Their shares are in the proportion of 1/3 : 1/4 : 1/5. A withdraws half of his capital after 15 months and after another 15 months, a profit of Tk. 4340 is divided. The share of C is?

Solution:
Ratio of initial investments = 1/3 : 1/4 : 1/5
= 20 : 15 : 12

Let their initial investments be 20x, 15x and 12x respectively.

A : B : C = (20x × 15) + (10x × 15): (15x × 30) : (12x × 30)
= 450x : 450x : 360x
= 5 : 5 : 4

Sum of the ratio = 5 + 5 + 4 = 14.

C's share = 4340 × (4/14)
= 1240 Tk.

Question: Abir and Asif started a business investing Tk. 27500 and Tk. 35000 respectively. Out of a total profit of Tk. 14200, Asif's share is?

Solution:
Given,
Investment ratio = 27500 : 35000
= 11 : 14
Sum of the ratio's = 11 + 14 = 25

∴ Asif's share = 14200 × (14/25)
= 7952

Question: X, Y, and Z invested Tk. 90000, Tk. 70000, Tk. 45000 respectively to start a business. At the end of 1 year, they earned a profit of Tk. 164000. What will be the Z’s share?

Solution:
Investment ration of X, Y & Z = 90000 : 70000 : 45000
= 18 : 14 :  9

Sum of the ration = (18 + 14 + 9)
= 41

∴ Z’s share = 164000 x  (9/41) 
= 36000

Question: A man buys Tk. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is-

Solution:
Dividend on Tk. 20 = Tk. (9/100) × 20)
= Tk 9/5

Tk.12 is an income on Tk.100.
∴ Tk. 9/5 is an income on = Tk. (100/12 × 95)
= Tk.15

Question: A man deposits Tk. 500 in a Bank at 10% interest rate compounded annually. At the end of the second year, the total amount including interest will become?

Solution: 
Given,
Principal, P = 500 Tk.
Rate of interest, r = 10% = 10/100 = 1/10
Time, n = 2 years.

We know,
Compound Amount = P (1 + r)ⁿ
= 500 × (1 + 1/10)²
= 500 × (11/10)²
= 500 × (11/10) × (11/10)
= 605

Question: A sum of money amount to Tk. 720 in 2 years and Tk. 780 in 3 years. The rate per cent is?

Solution:
Simple interest for 1 year = Tk. (780 - 720) = Tk. 60
Simple interest for 2 year = Tk. (60 × 2) = Tk. 120
Sum = Tk. (720 - 120) = Tk. 600

We know, 
I = Pnr
⇒ r = I/Pn
= (120 × 100)/(600 × 2)
∴ r = 10%

Question: If 6 × A's capital = 8 × B's capital = 10 × C's capital, find the ratio of their capitals?

Solution:
Let,
6 × A's capital = 8 × B's capital = 10 × C's capital = x
Now,
A's capital = x/6
B's capital = x/8
C's capital = x/10

∴ Ratio of capitals of A, B, C = x/6 : x/8 : x/10
= 20 : 15 : 12

Question: Rakib obtained an amount of Tk. 8300 as simple interest on a certain amount at 8 p.c.p.a. after 5 years. What is the amount invested by Rakib?

Solution:
Suppose, Principal = Tk. 100
Then interest for 5 years at 8% = 5 × 8 = Tk. 40.

Now,
If interest is 40 taka then Principal = 100
∴ If interest is Tk. 8300 then Principal = (8300 × 100)/40 Tk.
= 20750 Tk.

Question: M and N enter into a partnership with capitals in the ratio 5 : 6 and at the end of 8 months, M withdraws. If they receive profit in the ratio of 5 : 9. Find how long N's capital was used?

Solution:
Let the capitals of N was used for X months.
According to the question,
(5 × 8)/(6 × X) = 5/9
⇒ X = 12 months

Hence capital of N was used for = 12 months.

Question: Simple interest on a certain sum is 16/25 of the sum. What is the rate percent & time, if both are equal.

Solution: 
Let.
The sum, P = Tk. x
Then, Simple interest, I = 16x/25
Rate of interest = r%
Since, rate percent = time
So r = n

We know,
I = Pnr
⇒ 16x/25 = x × r × r%
⇒ xr²/100 = 16x/25
⇒ r²/100 = 16/25
⇒ r² = 1600/25
⇒ r = 40/5
∴ r = 8

∴ Rate = 8% and Time = 8 years.

Question: A man invests in a 16% stock at 128. The interest obtained by him is?

Solution:
By investing Tk. 128, income derived = Tk. 16
By investing Tk. 100, income derived
= Tk. (16/128) × 100
= Tk. 12.5

∴ Interest obtained = 12.5%

Question: An amount of Tk. 4000 lent 5% per annum compounded interest for 2 years will become?

Solution:
Here,
Principal, P = Tk. 4000
Rate of interest, r = 5% = 5/100 = 1/20
Time, n = 2 years.

We know, 
C = P (1 + r)ⁿ
= 4000 × {1+ (1/20)}²
= 4000 × {(21/20) × (21/20)}
= 4000 × (441/400)
= 4410

∴ Compounded Interest Tk. 4410.

Question: A sum of money amounts to Tk. 735 in 3 years and Tk. 815 in 4 year. What's the sum?

Solution: 
Simple interest for 1 years = Tk. (815 - 735)
= Tk. 80
∴ Simple interest for 3 years = Tk.(80 × 3)
= Tk. 240

∴ Sum = (735 - 240)
= Tk. 495

Question: A man buys Tk. 40 shares in a company which pays 10% dividend. If the man gets 12.5% on his investment, at what price did he buy the shares?

Solution:
Dividend on 40 share = 10%
∴ Dividend on 1 share = (10 × 40)/100
= Tk. 4
Tk. 12.50 is an income on an investment of Tk. 100
Tk. 4 is an income on an investment of = (100 × 4)/12.50
= (100 × 4 × 10)/125
= Tk. 32

∴ Cost of 1 share = Tk. 32

Question: A started a business with Tk. 2100 and is joined afterwards by B with Tk. 3600. After how many months did B join if the profits at the end of the year are divided equally?

Solution:
Suppose,
B joined after x months.

Then,
2100 × 12 = 3600 × (12 - x)
⇒ 252 = 432 - 36x
⇒ 36x = 180
∴ x = 5

∴ B joined after 5 months.