Bank Math

Question: If the simple interest on Tk. N at N% per annum for 5 years is Tk. N, what is the value of N?

Solution:
Given,
P = N
r = N% = N/100
n = 5 years
I = N

We know,
I = Prn
⇒ N = N × (N/100) × 5
⇒ N = (N² × 5)/100
⇒ N = N²/20
⇒ N² = 20N
⇒ N²/N = 20
∴ N = 20

সুতরাং, N এর মান হলো 20

Questions: What is the greatest number of 3 digits which when divided by 6, 9 and 12 leaves a remainder of 3 in each case?

Solution: 
৬, ৯, ১২ এর ল.সা.গু = ৩৬ 

তিন অঙ্কের বৃহত্তম সংখ্যা = ৯৯৯ 
 ৯৯৯ কে ৩৬ দ্বারা ভাগ করলে অবশিষ্ট থাকে ২৭ 
৯৯৯ - ২৭ = ৯৭২ ; ৩৬ দ্বারা নিঃশেষে বিভাজ্য। 

নির্ণেয় সংখ্যা = ৯৭২ + ৩ = ৯৭৫ 

We Know
Total work = rate × Time

therefore
30 = Rate × 6
or Rate = 30/6 = 5

Now we need to find the number of computers
total work given = 80 and total time = 3 hrs

therefore
80 = 5 × 3 × No. of computers
or No. of computers = 80/15 = 5.333 , but no. of computers cannot be fraction i.e , so we have to consider as 1.

Total no. of computers = 5 + 1 = 6.

Speed of the boat in still water = 8 km/hr
Speed upstream = 1/1 = 1 km/hr.
Speed of the stream = 8 - 1 = 7 km/hr.
Speed downstream = (8 + 7) = 15 km/hr.
Time is taken to travel 1 km downstream = (1/15) hr
= (1 × 60)/15
= 4 minutes.

LCM of 4, 5, and 6 is 60.
So the number is = 60 + 3 = 63

দেয়া আছে, 3x + 4y = 12 এবং kx + 12y = 30 
যদি, 3/k = 4/12 হয় তাহলে সমীকরণ জোটটির অসংখ্য সমাধান থাকবে।
এখন, 3/k = 4/12
⇒ 4k = 12 × 3
⇒ k = 36/4
⇒ k = 9

Question: If 6 men can build a wall in 8 days, how many days will 12 men take to build the same wall?

Solution:
6 জন লোক একটি দেয়াল 8 দিনে তৈরি করতে পারে।
1 জন লোক সেই দেয়াল তৈরি করতে লাগবে = (8 × 6) দিন
12 জন লোক সেই দেয়াল তৈরি করতে লাগবে = (8 × 6)/12 দিন
= 4 দিন

Question: If a 44 meter ladder is placed against a 22 meter wall such that it just reaches the top of the wall, the angle of elevation of the wall is-

Solution:
Given that,
Ladder's length = 44 m
Wall's height = 22 m

Perpendicular = Wall's height = 22 m
Hypotenuse = Ladder's length = 44 m

We know,
Sinθ = Perpendicular/Hypotenuse
⇒ Sinθ = 22/44
⇒ Sinθ = 1/2
⇒ Sinθ = sin30º
∴ θ = 30º

Question: Find the area of a triangle whose sides are 15 cm, 8 cm, and 17 cm.

Solution:
ত্রিভুজের তিন বাহু যথাক্রমে,
a = 15 cm, b = 8 cm, c = 17 cm

অর্ধপরিধি, S = (a + b + c)/2
= (15 + 8 + 17)/2
= 40/2 = 20 cm

আমরা জানি,
ত্রিভুজের ক্ষেত্রফল = √{S(S - a)(S - b)(S - c)}
= √{20(20 - 15)(20 - 8)(20 - 17)}
= √{20 × 5 × 12 × 3}
= √3600
= 60 cm²

অতএব, ত্রিভুজের ক্ষেত্রফল = 60 cm²

Question: A water tank contains 24 liters of water. Rahim uses 1/4 of the total water. Then Karim uses 1/2 of the remaining water. How many liters of water are left in the tank?

Solution:
Total water = 24 liters
Water used by Rahim = (1/4) × 24 = 6 liters

∴ Remaining water = 24 - 6 = 18 liters

Water used by Karim = (1/2) × 18 = 9 liters

∴ Water left in the tank = 18 - 9 = 9 liters

Question: 600 grams of sugar solution has 30% sugar in it. How much sugar should be added to make 75% in the solution?

Solution:
Amount of sugar =600 × 30/100
=180 grams
Let,
x gram sugar to be added

ATQ,
(180 + X)/(600 + X) = 75%
⇒ (180 + X)/(600 + X) = 75/100
⇒ (180 + X)/(600 + X) = 3/4
⇒ 4(180 + X) = 3(600 + X)
⇒ 4X + 720 = 3X + 1800
⇒ 4X - 3X= 1800 - 720
∴ X = 1080 grams

Question: A can complete 1/5 of a task in 4 days, while B can complete 1/10 of the same task in 5 days. If they work together and receive a total payment of Tk 900, what amount should A receive?

Solution:

Whole work is done by A in (5 × 4) = 20 days
∴ A's 1-day work = (1/5) ÷ 4 = 1/20

Whole work is done by B in (5 × 10) = 50 days
∴ B's 1-day work = (1/10) ÷ 5 = 1/50

Ratio of A's and B's 1-day work = 1/20 : 1/50
= 50 : 20 = 5 : 2

∴ A's share of payment = (5/(5+2)) × 900 
= (5/7) × 900
= 643 Tk

Question: If a : b : c = 2 : 3 : 4 and 2a - 3b + 4c = 33, then the value of c is-

Solution:
Let,
 a = 2x, b = 3x and c = 4x  ; (since a : b : c = 2 : 3 : 4)

Now substitute into the equation,
2a - 3b + 4c = 33
⇒ 2(2x) - 3(3x) + 4(4x) = 33 
⇒ 4x - 9x + 16x = 33 
⇒ 11x = 33
∴ x = 3

Since c = 4x = 4 × 3 = 12

Let AB be the tower
then∠ACB=30º
AB=100 meter
AB/AC= tan30º
=>100/AC= 1/√3
=>AC= √3/100
=>AC= 1.73×100
=>AC= 173meter

Question: The area of a square is equal to the area of a parallelogram. If the base of the parallelogram is 45 meters and its height is 5 meters, what is the length of one side of the square?

Solution:
Area of the parallelogram = Base × Height
= 45 × 5
= 225 square meters

Let,
Side of the square = k meters
∴ Area of the square = k² square meters

ATQ,
k² = 225
⇒ k = √225
∴ k = 15
Therefore, the length of one side of the square = 15 meters

Question: A merchant sells an item at a 20% discount, but still makes a gross profit of 20 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?

Solution:
Let the Market Price of the product be MP.
Let the Original Cost Price of the product be CP.

Selling Price (Discounted Price) = 100%of MP - 20%MP = 80% of MP ....... (1)
Profit made by selling at discounted price = 20% of CP ....... (2)

Now,  Profit = Selling Price - Original Cost Price
⇒ 20% of CP = 80% of MP - 100% CP
⇒ MP = 120CP/80 = 3/2 (CP)

Now if Product is sold without any discount, then,
​
Profit = Selling Price (without discount) - Original Cost Price
= Market Price - Original Cost Price
= MP - CP
= (3/2)CP - CP
= 1/2 CP
= 50% of CP

Question: A train that is 300 meters long takes 30 seconds to pass a stationary pole. At the same constant speed, how much time will the train take to completely pass a platform that is 500 meters long? 

Solution:
Length of the train = 300 m
Time taken to pass a pole = 30 seconds

So, speed of the train
= 300/30
= 10 m/s

Length to be covered while passing the platform
= Length of train + Length of platform
= 300 + 500
= 800 m

Time taken to pass the platform
= Total distance/Speed
= 800/10
= 80 seconds

Therefore, the train will take 80 seconds to pass the platform.

Question: Tk. 8000 becomes Tk. 9600 in 2 years at a certain rate of simple interest. If the rate becomes double, what will be the total amount in 5 years on the same principal?
​
​Solution:
Principal = Tk. 8000
Amount after 2 years = Tk. 9600
∴ Interest in 2 years = 9600 - 8000 = Tk. 1600
∴Interest per year = 1600/2 = Tk. 800

Since the interest rate doubles, the yearly interest also doubles,
∴ Interest per year = 800 × 2 = Tk. 1600
⇒ Interest for 5 years = 1600 × 5 = Tk. 8000
⇒ New total amount = 8000 + 8000 = Tk. 16000

Question: Three partners, X, Y, and Z, invest Tk. 90000 in a business. X invests Tk. 12000 more than Y, and Y invests Tk. 6000 more than Z. If the total profit is Tk. 45000, how much does X receive?

Solution:
Let Z's investment be Tk. x.
∴ Y's investment = Tk. (x + 6000)
∴ X's investment = Tk. (x + 6000 + 12000) = Tk. (x + 18000)

Since the total investment is Tk. 90000,
∴ X + Y + Z = 90000
⇒ (x + 18000) + (x + 6000) + x = 90000
⇒ 3x + 24000 = 90000
⇒ 3x = 90000 - 24000
⇒ 3x = 66000
⇒ x = 22000

So, Z's investment = Tk. 22000
Y's investment = Tk. (22000 + 6000) = Tk. 28000
X's investment = Tk. (28000 + 12000) = Tk. 40000

Total profit = Tk. 45000
∴ X's share of profit = (X's investment/Total investment) × Total profit
= (40000/90000) × 45000
= Tk. 20000

∴ X receives Tk. 20000