Bank Math Master

Question: How much time will it take for an amount of Tk. 900 to yield Tk. 81 as interest at 9% per annum of simple interest?

Solution: 
I = Pnr
⇒ 81 = 900 × n × (9/100)
⇒ n = (81 × 100)/(900 × 9)
∴  n = 1 years.

Question: 4200 Taka is lent at compound interest of 10% per annum for 2 years. Find the amount after two years.

Solution:
Compound amount = P (1 + r)ⁿ
= 4200 {1 + (10/100)}²
= 4200 × (110/100) × (110/100)
= 42 × 11 × 11
= 5082

Question: The ratio of the ages of two boys is 5 : 6. After two years the ratio will be 7 : 8. The ratio of their age after 12 years will be = ?

Solution:
Ratio of ages of Boys A and B
Present age 5x : 6x
∴ After two years their ages are (5x + 2) and (6x + 2).

According to the question,
(5x + 2) : (6x + 2) = 7 : 8
⇒ 40x + 16 = 42x + 14
⇒ 2x = 2
∴ x = 1

∴ Present age A = 5 × 1 = 5
∴ Present age B = 6 × 1 = 6
After 12 years A = 5 + 12 = 17
After 12 years B = 6 + 12 = 18
∴ A/B = 17/18

Question: The ratio of three numbers is 3 : 4 : 5 and the sum of their squares is 1250. The sum of the numbers is-

Solution:
Let, the number be 3x, 4x, 5x

According to the question,
(3x)² + (4x)² + (5x)² = 1250
⇒ 9x² + 16x² + 25x² = 1250
⇒ 50x² = 1250
⇒ x² = 1250/50
⇒ x² = 25
∴ x = 5

∴ The sum of the numbers = 3x + 4x + 5x
= 12x
= 12 × 5
= 60

Question: In a school having roll strength 286, the ratio of boys and girls is 8 : 5. If 22 more girls get admitted into the school, the ratio of boys and girls becomes

Solution:
Boys : girls = 8 : 5
Let, the boys = 8x, girl = 5x

According to the 1st condition,
8x + 5x = 286
⇒ 13x = 286
⇒ x = 286/13
∴ x = 22
Boys = 8 × 22 = 176 and girls = 5 × 2 = 110

22 more girls get admitted then the number of girls become
(5x + 22) = 110 + 22 = 132

Now, new ratio of boys and girls = 176 : 132 = 4 : 3

Question: The cost of a table and a chair are in the ratio of 5 : 7. If the cost of a chair and table is increased by 20% and 10% respectively, then what will be the new ratio?

Solution:
Let, the cost of the table and chair be Tk. 5x and Tk. 7x respectively.

New cost of chair = 120% of 7x
= (120 × 7x)/100
= 42x/5

New cost of table = 110% of 5x
= (110 × 5x)/100
= 55x/10

∴ New ratio = 55x/10 : 42x/5
= 55 : 84

Question: Rana obtained an amount of Tk. 8376 as simple interest on a certain amount at 8 p.c.p.a. after 6 years. What is the amount invested by Rana?

Solution:
Simple interest, I = Tk. 8376
Rate of interest, r = 8%
Time, n = 6 years

We know,
I = Pnr
Or, P = I/nr
= (8376 × 100)/(6 × 8)
∴ P = 17450 Tk.

Question: If 0.75 : x :: 5 : 8, then x is equal to:

Solution:
0.75 : x :: 5 : 8
⇒ 0.75/x = 5/8
⇒ 5x = 0.75 × 8
⇒ 5x = 6
⇒ x = 6/5
∴ x = 1.2

Question: A sum of money lent out at simple interest amounts to Tk. 720 after 2 years and Tk. 1020 after a further period of 5 years. Find the principal?

Solution:
According to the question,
Principal + Simple interest for 2 year = Tk. 720 ------------- (1)
Principal + Simple interest for 7 year = Tk. 1020 ------------ (2)

Subtracting equation (1) from (2)
Principal + Simple interest for 7 year = Tk. 1020 
Principal + Simple interest for 2 year = Tk. 720
∴ Simple interest for 5 years = Tk. 300
⇒ Simple interest for 1 years = Tk. 300/5
⇒ Simple interest for 1 years = Tk. 60
⇒ Simple interest for 2 years = Tk. (60 × 2)
∴ Simple interest for 2 years = = Tk. 120

∴ Principal amount = (Amount after 2 years - 2 years Simple interest)
⇒ Principal amount = Tk. (720 - 120)
∴ Principal amount = Tk. 600

Question: The price of 2 pencils is less than 20% of the price of a pen. What is the ratio of the price of a pen to that of a pencil?

Solution:
Let, the price of pen = 100

20% less, price of 2 pencils = 100 - 20 = Tk. 80
20% less, price of 1 pencil = 80/2 = Tk. 40

∴ pen : pencil = 100 : 40
= 5 : 2

Question: A sum of money at simple interest amounts to Tk. 721 in 3 years and to Tk. 754 in 4 years. The sum is-

Solution:
Simple interest for 1 year = Tk. (754 - 721)
= Tk. 33

∴ Simple interest for 3 years = Tk.(33 × 3)
= Tk. 99

∴ Sum = (721 - 99)
= Tk. 622

Question: Tk. 800 becomes Tk. 956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4%. What amount will Tk. 800 become in 3 years?

Solution:
Here, I₁ = (956 - 800) = Tk. 156
P₁ = Tk. 800, n₁ = 3 years.

We know,
I₁ = P₁n₁r₁
Or, r₁ = I₁/P₁n₁
= (156 × 100)/(800 × 3)
= 6.5%

After interest rate increase of 4%
The new rate of interest r₂ = (6.5 + 4)%
= 10.5%

Now, amount = 800 + (800 × 3 × 10.5/100)
= 800 + 252
= Tk. 1052

Question: The ratio of third proportional to 12 and 30 and the mean proportional between 9 and 25 is-

Solution:
Let, the third proportional to 12 and 30 be x.

ATQ,
12 : 30 : : 30 : x
⇒ 12/30 = 30/x
⇒ 12x = 30 × 30
⇒ x = (30 × 30)/12
∴ x = 75

∴ Third proportional to 12 and 30 = 75.
Mean proportional between 9 and 25 = √(9 × 25) = 15
∴ Required ratio = 75/15 = 5 : 1 .

Question: An iron rod that weights 24 kg is cut into two pieces so that one of these pieces weights 16 kg and 34 m long. If the weight of each piece is proportional to its length, how long is the other one is-

Solution:
Total weight = 24 kg
1st piece weight = 16 kg and length = 34 m
2nd piece weight = (24 - 16) kg = 8kg 
Let, length = x m

According to the question,
16 : 8 = 34 : x
⇒ 34/x = 16/8
⇒ 34/x = 2
⇒ 2x = 34
∴ x = 17

Question: What annual rate was paid if Tk. 50000 earned Tk. 3000 in interest in two years?

Solution:
Tk. 50000 earned in 2 years Tk. 3000
∴ Tk. 100 earned in 1 year Tk. (3000 × 100)/(50000 × 2)
= 3%

Question: Find the number in the place of sign `?'.

Solution:
Let, the number be x
So,
9/x = x/81
⇒ x² = 81 × 9
⇒ x² = 729
⇒ x² = 27²
∴ x = 27

Question: If two times X is equal to three times of Y and also equal to four times of Z, then X : Y : Z is -

Solution:
2X = 3Y
Or, Y = 2X/3
and 2X = 4Z
Or, Z = X/2

Hence, X : Y : Z = X : 2X/3 : X/2
= 1 : 2/3 : 1/2
= 6 : 4 : 3

Question: Last year, the ratio between the salaries of A and B was 3 : 4. But the ratios of their individual salaries between last year and this year were 4 : 5 and 2 : 3 respectively. If the sum of their present salaries is Tk. 4160, then how much is the salary of A now?

Solution:
Let,
the salaries of A and B last year be Tk. 3x and Tk. 4x respectively.
Then,
A's present salary = Tk. (5/4) × 3x
= Tk. 15x/4

B's present salary = Tk.(3/2) × 4x
= Tk. 6x.

According to the question,
(15x/4) + 6x = 4160
⇒ 39x = 4160 × 4
⇒ x = (4160 × 4)/39

So, A's present salary = Tk. (15/4) × (4160 × 4)/39
= Tk.1600

Question: The average of the two numbers is 62. If 2 is added to the smaller number, the ratio between the numbers becomes 1 : 2. The larger number is -

Solution:
Let,
smaller number is x,
The larger number is y.

∴ (x + y)/2 = 62
⇒ x + y = 62 × 2
⇒ x + y = 124
∴ x = 124 - y .............. (1)

ATQ,
(x + 2)/y = 1/2
⇒ 2(x + 2) = y 
⇒ y = 2x + 4
⇒ y = 2(124 - y) + 4
⇒ y = 248 - 2y + 4
⇒ 3y = 252
⇒ y = 252/3
∴ x = 84

∴ The larger number is 84.