Bank Math Master

Question: After a 10% reduction in the price of cooking oil, a family is able to purchase 4 liters more oil for Tk. 720. What was the original price per liter?

Solution:
Let
Original price of cooking oil = x Tk/liter.
Original quantity = 720/x​ litre

New price = 0.90x Tk/litre
New quantity = 720/0.90x = 720/(9x/10) = (720 × 10)/9x = 800/x​ liters

ATQ,
(800/x​) - (720/x) = 4
⇒ (800 - 720)/x = 4
⇒ 80/x = 4
⇒ x = 80/4
∴ x = 20

 ∴ Original price of cooking oil = 20 Tk/liter.

Question: Find the simple interest on BDT 12000 at 4% per annum for 8 months.

Solution:
Principal, P = 12000 Taka
Time, n = 8 months = 8/12 = 2/3 years
Rate of interest, r = 4% = 4/100

Simple Interest, I = P × n × r
= 12000 × (2/3) × (4/100)
= 40 × 2 × 4
= 320

∴ The simple interest is Tk. 320.

Question: A mixture of milk and water has a total volume of 42 liters, where milk and water are mixed in the ratio 3 : 4. How many liters of milk must be added so that the quantities of milk and water become equal?

Solution:
The ratio of milk to water is 3 : 4
Total portion = 3 + 4 = 7

Quantity of milk = 42 × (3/7) = 18 liters.
Quantity of water = 42 × (4/7) = 24 liters.

Let,
Quantity of milk to be added = x liters

According to the question,
(18 + x) : 24 = 1 : 1
⇒ (18 + x)/24 = 1/1
⇒ 18 + x = 24
⇒ x = 24 - 18
⇒ x = 6

∴ Quantity of milk to be added = 6 liters

Question: Rina and Shila started a business by investing Tk. 85,000 and Tk. 15,000 respectively. If the business runs for 2 years, what will be the ratio of profit earned by Rina and Shila?
 

Solution:
Given,
Rina's investment = Tk. 85,000
Shila's investment = Tk. 15,000
Time = 2 years for both

The ratio of profit earned after 2 years between Rina and Shila respectively = (85000 × 2) : (15000 × 2)
= 170000 : 30000
= 17 : 3

Question: In a business, the ratio of the capitals of Arun and Babul is 2 : 1, that of Babul and Chandan is 4 : 3, and that of Dipu and Chandan is 6 : 5. What is the ratio of the capitals of Arun and Dipu?

Solution:
Given,
Arun : Babul = 2 : 1
⇒ Arun/Babul = 2/1

Babul : Chandan = 4 : 3
⇒ Babul/Chandan = 4/3

Dipu : Chandan = 6 : 5
⇒ Chandan/Dipu = 5/6

Now,
Arun/Dipu = (Arun/Babul) × (Babul/Chandan) × (Chandan/D)
= (2/1) × (4/3) × (5/6)
= 20/9

∴ Arun/Dipu = 20 : 9

Question: If the price of an article is increased by 20% and then decreased by 20%, the net change in the price is -

Solution: 
Let,
The price of an article is 100 Tk.

If the price increased by 20%,
So, the new price will be after increase = 100 + {100 × (20/100)} Tk.
= 100 + 20 Tk.
= 120 Tk.

Then the new price decreased by 20%,
So, the new price will be after decrease = 120 - {120 × (20/100)} Tk.
= 120 - 24 Tk.
= 96 Tk.

∴ The net change in the price of the article is = (100 - 96) 
= 4 Taka

So, there is a 4% decrease in the price

Question: A train takes 50 seconds to cross a platform 300 meters long and 35 seconds to cross another platform 150 meters long. Find the length of the train.

Solution:
Let the length of the train = x meters

Then,
For the first platform, the distance covered by the train = (x + 300) meters
And,
For the second platform, the distance covered by the train = (x + 150) meters

According to the question,
(x + 300)/50 = (x + 150)/35
⇒ 50(x + 150) = 35(x + 300)
⇒ 50x + 7500 = 35x + 10500
⇒ 50x - 35x = 10500 - 7500
⇒ 15x = 3000
⇒ x = 3000/15 
⇒ x = 200

∴ The length of the train is 200 meters

Question: A merchant mixes two types of sugar costing Tk. 250/kg and Tk. 350/kg in the ratio 3:2. If he sells the mixture at Tk. 360/kg, what is his profit percentage?

Solution: 
Cost of first variety = 250 Taka/kg
Cost of second variety = 350 Taka/kg
Ratio = 3:2

Cost price of mixture = {(3×250) +(2×350)}/(3+2)
= 1450/5
= 290 Taka/kg

Profit = Selling price - Cost price
= 360 - 290 
= 70 Taka/kg

Profit percentage = (70/290) × 100%
= 24.13% ≈ 24%

Question: A shopkeeper marks his items 40% above the cost price and then gives a 20% discount on the marked price. What is his gain percentage?

Solution:
Let,
the cost price (CP) be Tk. 100

Marked Price = 40% more than cost price
= 100 + 40
= 140 Tk.

Discount = 20% of 140
= (20/100) ​× 140
= 28 Tk.

Selling Price (SP)= 140 - 28 = 112 Tk.

∴ Profit = SP - CP = 112 - 100 = 12 Tk.

∴ Gain percent = 12%

Question: What is the compound amount of Tk. 16000 for 2 years at a rate of interest of 5% per annum?

Solution:
Given,
Principal, P = 16000
Rate, r = 5% = 5/100 = 1/20
Time, n = 2 years

We know,
A = P(1 + r)ⁿ
= 16000 × (1 + 1/20)²
= 16000 × (21/20)²
= (16000 × 21 × 21)/(20 × 20)
= (16000 × 441)/400
= 40 × 441
= 17640

∴ The compound amount is Tk. 17640.

Question: The ratio of milk to water in a mixture is 6 : 3. When adding 6 liters of water, the ratio becomes 5:5. What was the quantity of milk in the original mixture? 

Solution:
Let the initial quantity of 
Milk = 6x liters
Water = 3x liters

When 6 liters of water are added, the new quantity of water becomes = (3x + 6) liters
The new ratio becomes 5 : 5, which simplifies to 1 : 1. This means the amount of milk and water are now equal. 
6x = 3x + 6
3x = 6 
∴ x = 2

So, the initial quantity of Milk = 6 × 2 = 12 liters

Question: A swimmer can swim at a speed of 4 km/h in still water. If the river current flows at 2 km/h, how long will it take to swim 12 km downstream and then return to the starting point?

Solution: 
Speed of the swimmer in still water = 4 km/h
Speed of the current = 2 km/h
Distance one way = 12 km

Downstream Speed = 4 + 2 = 6 km/h
Upstream Speed = 4 - 2 = 2 km/h 

Time taken downstream = 12/6 = 2 hours
Time taken upstream = 12/2 = 6 hours

∴ Total time = 6 + 2 
= 8 hours

Question: A and B are business partners. A invests Tk. 20,000 for 4 months, while B invests Tk. 30,000 for 6 months. If the total profit at the end of the year is Tk. 65,000, what is B’s share of the profit?

Solution: 
A’s Contribution = 20000 × 4 = 80000 Taka
B’s Contribution = 30000 × 6 = 180000 Taka

The ratio of A's and B's investment = 80000 : 180000
= 4 : 9

So, B's share in profit = {9/(4+9)} × 65000
= 45000 Taka

Question: A retailer buys a TV from a wholesaler at a 25% discount. He then marks up the price by 50% on the discounted price and offers a 20% discount to the customer. What is the retailer’s profit percentage?

Solution: 
Let the original price of the TV be 1000 Taka.

Wholesaler’s discount = 25%
Retailer’s purchase price:
1000 − 25% of 1000 = 1000−250 = 750 Taka

Retailer’s markup = 50% on Taka 750
New marked price:
750 + 50% of 750 = 750 + 375 = 1125 Taka

Customer’s discount = 20% on Taka 1125
Selling price:
1125 − 20% of 1125 = 1125 − 225 = 900 Taka

So, Profit = {(900 - 750)/750} × 100%
= 20%

Question: A certain sum of money becomes 2.5 times itself in 5 years at simple interest. What is the rate of interest per annum? 

Solution: 
Let the principal amount be P.
The sum becomes 2.5 times itself in 5 years.

So, A = 2.5P
∴ Simple Interest, I = 2.5P - P = 1.5 P

We know, I = Pnr/100
⇒ 1.5 P = (P × 5 × r)/100
⇒ 5r = 150
∴ r = 30%

Question: What is the difference between simple and compound interest at 10% per annum on a sum of Tk. 3000 at the end of 2 years?

Solution:
Principal (P) = Tk. 3000
Rate (r) = 10% per annum
Time (n) = 2 years

Simple Interest (SI):
SI = (P × R × T)/100
= (3000 × 10 × 2)/100
= 60000/100
= Tk. 600

Compound Interest (CI):
Amount (A) = P × (1 + r/100)ⁿ
= 3000 × (1 + 10/100)²
= 3000 × (1.1)²
= 3000 × 1.21
= Tk. 3630

∴ CI = A - P = 3630 - 3000
= Tk. 630

∴ Difference between CI and SI = 630 - 600
= Tk. 30

Question: An F‑7 BGI fighter jet covers a certain distance at a speed of 1200 km/h in 5 hours. What speed must it maintain to cover the same distance in 250 minutes?

Solution:
Total distance = Speed × Time
= (1200 × 5) km
= 6000 km

Given time = 250 minutes = (250/60) hours
= 25/6 hours

∴ Required speed = Distance/Time
= {6000/(25/6)} km/h
= {6000 × (6/25)} km/h
= (240 × 6) km/h
= 1440 km/h

Question: A person who has a rice storage has two types of rice costing Tk. 50 per kg and Tk. 70 per kg. In what ratio should he mix them to make a mixture worth Tk. 58 per kg?

Solution: 
Cheaper variety price, a = Taka 50 per kg
Expensive variety price, b = Taka 70 per kg
Mixture price, c = Taka 58 per kg

Ratio = (b - c)/(c - a)
= (70 - 58)/(58 - 50)
= 12/8
= 3 : 2

Question: A fruit seller sells 20 pomegranates for Tk. 900 and incurs a loss equal to the cost of 5 pomegranates. What is the cost price of one pomegranate?

Solution:

Selling price of 20 pomegranates for Tk. 900

Let,
cost price of 1 pomegranate is = Tk. x
∴ cost price of 20 pomegranates is = Tk. 20x
∴ cost price of 5 pomegranates is = Tk. 5x

We know,
∴ Loss = Cost price - Selling price 
⇒ 5x = 20x - 900 
⇒ 20x - 5x = 900
⇒ 15x = 900
⇒ x = 900/15
∴ x = 60

∴ The cost price of 1 pomegranate is Tk. 60

Question: In a map, 4 cm represents 80 km. The distance between two cities is 9 cm on the map. The actual distance between the cities is - 

Solution: 
Since 4 cm = 80 km,
Actual Distance = (80/4) × 9
= 20 × 9 km
= 180 km