Bank Math Master

Question: A sum of money at simple interest amounts to Tk. 715 in 4 years and to Tk. 754 in 5 years. The sum is:

Solution: 
১ বছরের সুদ = ৭৫৪ - ৭১৫ টাকা
= ৩৯ টাকা 

∴ ৪ বছরে সুদ = (৩৯ × ৪) টাকা
= ১৫৬ টাকা 

∴ আসল = ৭১৫ - ১৫৬ টাকা 
= ৫৫৯ টাকা

Question: Find the compound interest on Tk. 2000 at 15% interest per annum for 2 years, compounded annually-

Solution:
Compound Principal for 2 years = 2000(1 + 15/100)²
= 2000(115/100)²
= (2000 × 115 × 115)/(100 × 100)
= 2645 tk.

Question: The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is 10 taka. The sum is:

Solution: 
ধরি,
আসল x টাকা 

সরল সুদ = x × 2 × 4/100
= 2x/25
= 0.08 x

চক্রবৃদ্ধি সুদ = x (1 + 0.04)² - x
= x × 1.04 × 1.04 - x
= 1.0816 x - x
= 0.0816 x 

প্রশ্নমতে,
0.0816 x - 0.08 x = 10
⇒ 0.0016 x = 10
⇒ x = 10/0.0016
∴ x = 6250

Question: 100 taka is doubled in 5 years when compounded annually. How many more years will it take to get another 200 taka compound interest-

Solution:
100 taka invested in compound interest becomes 200 taka in 5 years.
The amount will double again in another 5 years.

i.e., the amount will become 400 taka in another 5 years.
So, to earn another 200 taka interest, it will take another 5 years.

Question: The compound interest on 300 tk. at 7% per annum is 21 taka. The period is:

Solution: 
চক্রবৃদ্ধি সুদাসল = P (1 + r)ⁿ
= 300 + 21
= 321 tk.

321 = 300 × (1 + 7/100)ⁿ
⇒ (1 + 7/100)ⁿ = 321/300
⇒  (107/100)ⁿ = 107/100
⇒  (107/100)ⁿ = (107/100)¹
∴ n = 1 year

Question: A sum of Tk. 10,000 amounts to Tk. 12,000 in 4 years at the rate of simple interest. What is the rate of interest?

Solution: 
সুদ = ১২০০০ - ১০০০০ টাকা 
= ২০০০ টাকা 

ধরি, সুদের হার r%  

I = pnr
⇒ 2000 = 10000 × 4 × r/100
⇒ r = 5

সুদের হার ৫%

Question: If ratio of three numbers is 3 : 2 : 5 and their sum is 150, what is the largest number?

Solution:
let the numbers be 3x, 2x, 5x 

3x + 2x + 5x = 150 
⇒ 10x = 150 
∴ x = 15 

largest number = 5 × 15
= 75 

Question: A sum of money at compound interest doubles itself in 15 years. It will become four times of itself in-

Solution: 
let the sum P 

2P = P (1 + r)¹⁵
⇒ (1 + r)¹⁵ = 2

let, sum will 4 times in n years
4P = P(1 + r)ⁿ
⇒ 4 = (1 + r)ⁿ
⇒ 2² = (1 + r)ⁿ
⇒ ((1 + r)¹⁵)² = (1 + r)ⁿ
⇒ (1 + r)³⁰ = (1 + r)ⁿ
∴ n = 30 years 

Question: Rafi invested 1/3 of his capital at 7%, 1/4 at 8% and the remainder at 10%. If his total simple interest is 561 taka after 1 year then the capital is - 

Solution: 
ধরি, আসল x টাকা

আমরা জানি,
I = Pnr
561 = x ×7/(100 × 3) + x 8/(100 × 4) + (5x × 10)/(12 × 100)
⇒ 561 = (7x/300) + (x/50) + (x/24)
⇒ 561 = 102x/1200
⇒ 561 = 51x/600
∴x = 6600 টাকা

Question: What must be added to each term of the ratio 7 : 11 so as to make it equal to  5 : 6?

Solution: 
let, the number be x

(7 + x) : (11 + x) = 5 : 6
⇒ (7 + x) / (11 + x) = 5/6
⇒ 6 (7 + x) = 5 (11 + x)
⇒ 42 + 6x = 55 + 5x
⇒ 6x - 5x = 55 - 42
∴ x = 13

Question: A sum of money becomes 4/3 of itself in 3 years at a certain rate of simple interest. What is the rate of interest per annum?

Solution: 
আসল = 3y
সুদাসল = 3y × 4/3 = 4y
সুদ = 4y - 3y
= y

৩ বছরে, 
y = 3yr × 3/100 [r = rate of simple interest]
or, r = 100/9

Question: A jar contains white, red and green marbles in the ratios 2 : 3 : 5. Six more green marbles are added to the jars and then the ratio becomes 2 : 3 : 7. How many green marbles are there in the jar?

Solution: 
A jar contains white, red and green marbles in the ratios 2 : 3 : 5
let there are 2x white, 3x red and 5x green marbles.

Six more green marbles are added to the jars and then the ratio becomes 2 : 3 : 7
let there are 2y white, 3y red and 7y green marbles.
2x = 2y
⇒ x = y 

7y - 6 = 5x
⇒ 7x - 6 = 5x
⇒ 7x - 5x = 6
∴ x = 6/2
= 3

green marbels = 7 × 3
= 21

Question: (3/4) : (1/2) :: 9y : ?

Solution: 
(3/4) : (1/2) :: 9y : p
⇒ (3/4) / (1/2) = 9y / p
⇒ 3/2 = 9y/p
⇒ p = 9y × 2/3
∴ p = 6y 

Question: 7^3.04 : 7^2.03 is equal to-

Solution: 
7^3.04 : 7^2.03
= 7^2.03 × 7 : 7^2.03
= 7 : 1

Question: If m : 5 = n : 7 = r : 8, then (m + n + r)/m =?

Solution: 
m : 5 = n : 7
⇒ m/5 = n/7
⇒ n = (7/5)m

m : 5 = r : 8
⇒ m/5 = r/8
∴ r = 8m/5

(m + n + r)/m = {m + (7/5)m + 8m/5}/m
= 1 + (7/5) + (8/5)
= 20/5
= 4

Question: 1050 tk are divided among P, Q and R. The share of Q is 2/5 of the combined share of P and R. Q gets-

Solution: 
let, combined share of P and R is x
share of Q is 2x/5 

x + 2x/5 = 1050
⇒ (5x + 2x)/5 = 1050
⇒ 7x/5 = 1050
⇒ x = 1050 × 5/7
∴ x = 750 tk

Q gets - 750 × 2/5
= 300 tk

Question: A person takes a loan of 200 taka at 5% simple interest.  He returns 100 taka at the end of 1 year. In order to clear his dues at the end of 2 years, he would pay- 

Solution: 
১ বছরে সুদ = ২০০ × ৫/১০০ টাকা
= ১০ টাকা 

১ বছর শেষে সে ১০০ টাকা ফেরত দেয়। 

বাকি আছে = ২১০ - ১০০ টাকা
= ১১০ টাকা 

১১০ টাকা এক বছরে সুদাসলে হয় = ১১০ + ১১০ × ৫/১০০
= ১১৫.৫ টাকা 

অতএব, ২য় বছর শেষে তাকে ১১৫.৫ টাকা দিতে হবে। 

Question: If X and Y are in the ratio 3 : 4, and Y and Z in the ratio 12 : 13, then X and Z will be in the ratio-

Solution: 
X : Y = 3 : 4
⇒ X/Y = 3/4

Y : Z = 12 : 13
⇒ Y/Z = 12/13

 X/Y ×  Y/Z = 3/4 × 12/13
⇒ X/Z = 9/13
∴ X : Z = 9 : 13 

Question: What is the profit of Tk. 650 in 6 years at the simple rate of profit Tk. 7 percent per annum?

Solution: 
profit = Pnr
= 650 × 6 × 7/100
= 273 tk.