Bank Math Master

Question: If the price of a commodity is increased by 25% and its consumption is decreased by 20%, what will be the increase or decrease in expenditure on the commodity?

Solution:
Let the initial expenditure on the commodity be Tk. 100.

Price increases by 25%:
New Price = 100+ (25% of 100) = 100+ 25 = Tk. 125

Consumption decreases by 20%:
New Consumption = 125 (20% of 125) 125 - 25 = Tk. 100

So, the final expenditure remains Tk. 100, meaning there is no change in the expenditure on the commodity.

Question: Rahim purchased items worth Tk. 40, including a sales tax of 60 paisa on taxable purchases. If the tax rate was 8%, what was the cost of the tax-free items?

Solution:
Let the cost of taxable purchases be x taka.

According to the question,
0.08x = 60/100
⇒ x = 60/(100 × 0.08)
= 7.5 taka

∴ The cost of the tax-free items was = 40 - 7.5 - 0.6
= Tk. 31.9

Example: A, B, and C subscribe Tk. 45,000 for a business. A subscribes Tk. 6,000 more than B, and B subscribes Tk. 3,000 more than C. Out of a total profit of Tk. 30,000, how much does A receive?

Solution:
Let C subscribe x taka.
So, B subscribes x + 3000 taka,
and A subscribes x + 3000 + 6000 = x + 9000 taka.

x + x + 3000 + x + 9000 = 45000
⇒ 3x + 12000 = 45000
⇒ 3x = 33000
⇒ x = 11000 taka

A receives = {(x + 9000)/45000} × 30000
= (20000/45000) × 30000
= 13333.33 taka
≈ 13333 taka

Question: By selling 45 lemons for tk 40, a man loses 20%. How many should he sell for tk 24 to gain 20% in the transaction?

Solution:
The cost price of 45 lemons = (40 × 100)/80
= 50

Selling price of 45 lemons to gain 20% profit = (50 × 120)/100
= 60 tk

No. of lemons he should sell for tk 24 to gain 20% profit = (45 × 24)/60
= 18

Question: (75% of 320) + (40% of 150) - ? = 170

Solution:
Let,
(75% of 320) + (40% of 150) - x = 170
⇒ {(75 × 320)/100} + {( 40 × 150)/100} - x = 170
⇒ 240 + 60 - x = 170
⇒ - x = 170 - 300
∴ x = 130

Question: The marked price of a bag is Tk. 500, and a 15% discount is offered on it. Find the selling price.

Solution:
Discount = MP × 15%
= 500 × (15/100)
= Tk. 75

Selling price = MP - Discount
= 500 - 75
= Tk. 425.

Question: If the list price of a shirt is Tk. 800, and a Tk. 160 discount is offered on the shirt, then what is the discount percentage?

Solution:
Discount % = (Discount/marked Price) × 100
Marked Price = Tk. 800
Discount = Tk. 160

Discount (%) = (160/800) ×100%
= 20%

∴ Therefore, the discount percentage is calculated as 20%.

Question: A vendor buys mangoes at a score for Tk. 300 and retails them at a dozen for Tk. 240. Did he gain or lose in the transaction, and what percentage was his gain or loss?

Solution:
Cost Price (C.P) of 1 mango = Tk. 300/score
= 300/20 = 15 (Note: 1 score = 20)

Selling Price (S.P) of 1 mango = Tk. 240/dozen
= 240/12
= 20 

∴ Profit on 1 mango = 20 - 15 = 5

∴ % Profit = (5/15) × 100 % = 33.33%

Question: If the cost price of an item is 5/9 of its marked price and the profit is 20%, then the percentage of discount is =?

Solution:
let the Marked price of product = 900
∴ cost price will be = 900 × (5/9) = 500

Profit = 20%
Selling price will be = 500 + 20% of 500 = 600
Discounted value = 900 - 600 = 300

Discount % = (100 × 300)/900

Question: A reduction of 20% in the price of sugar enables a housewife to purchase 6 kg more for 240 Taka. What is the original price per kg of sugar?

Solution:
Reduction in the price of 20% amount of sugar will increase by 25%
It means, 25% = 6 Kg.

So, initially, total Sugar = 6 × 4 = 24 kg.

Thus, the original price of the sugar was = 240/24
= 10 Taka per kg.

Question: Amit, Priya, and Ravi enter into a partnership. Amit invests Tk. 40 lakh initially and adds Tk. 20 lakh after 2 years. Priya invests Tk. 50 lakh initially and withdraws Tk. 15 lakh after 1 year. Ravi invests Tk. 60 lakh throughout. In what ratio should the profit be divided at the end of 4 years?

Solution:
Amit : Priya : Ravi = (40 × 2 + 60 × 2) : (50 × 1 + 35 × 3) : (60 × 4)
= (80 + 120) : (50 + 105) : 240
= 200 : 155 : 240
= 40 : 31 : 48

Question: In an election, the winning candidate secured  70% of the total votes and won by a majority of 60,000 votes. What is the total number of votes polled?

Solution:
Let, The winning candidate secured  0.70x votes,
and the losing candidate secured  0.30x votes.

ATQ,
0.70x - 0.30x = 60,000
⇒ 0.40x = 60,000
⇒ x = 60,000 / 0.40
= 150,000

Thus, the total number of votes polled is 150,000.

Question: A student erroneously multiplied a number by 4/5 instead of 5/4. What is the percentage error in the calculation?

Solution:
Let the number be 100.

Now,
(5/4) × 100 = 125
and  (4/5) × 100 = 80
Difference = 125 - 80 = 45

∴ Percentage error = (45/125) × 100 = 36%

Question: A person buys goods worth tk 600. He sells half of it at a gain of 10%. At what gain % must he sell the remaining goods to achieve an overall gain of 15%?

Solution:
To gain 15% on the whole, he must sell all goods for = 600 + 15% of 600
= 690 tk

He sells half at a 10% gain = 300 + 10% of 300
= 330 tk
Required balance = 690 - 330 = 360 tk
He must gain tk 60 on the remaining tk 300.

∴ % gain on remainder goods= (60 × 100) / 300 = 20%

Question: A and B are two fixed points 5 cm apart and C is a point an AB such that AC is 3 cm. If the length of AC is increased by 6%, the length CB is decreased by-

Solution:

After increment of 6% new length of AC = 3 + {(3 × 6)/100}
= 3 + 0.18
= 3.18cm

Required % decrease = (0.18/2) × 100
= 9%

Question: A jacket is sold after providing two successive discounts of 15%. If the marked price of the jacket is Tk. 400, find the selling price.

Solution:
First Discount:
Discount 1 = 400 × (15/100) = Tk. 60
Selling Price after 1st Discount = 400 - 60 = Tk. 340

Second Discount:
Discount 2 = 340 × (15/100) = Tk. 51
Selling Price after 2nd Discount = 340 - 51 = Tk. 289

So, the selling price of the jacket after two successive discounts of 15% is Tk. 289.

Question: Azim sells an object to Belal at a profit of 15%, Belal sells that object to karim for Tk. 1012 and makes a profit of 10%. At what cost did Azim purchase the object?

Solution:
Let the actual cost price at which Azim bought the object be x
When Azim sells the object to Belal
Profit % = 15%
∴ selling price of object = [(100 + 15)/100] × x = 1.15x

Now, this cost price of the object for Belal
When Belal sells the object to karim
Selling Price = Tk. 1012
Profit % = 10%
∴ Selling price = [(100 + 10)/100] × 1.15x
⇒ 1012 = [(100 + 10)/100] × 1.15x
⇒ x = (1012 × 1000)/(11 × 115)
∴ x = 800
Therefore, the price at which Azim bought the object is Tk. 800.

Question: Two stories A and B mark the price of an item identically. A allows 3 successive discounts of 10% each. B allows 10% discount on the list price and a subsequent discount of 19%. Under the circumstances, which of the following is true?

Solution:
Let the M.P. of the item at each of the stories A and B be tk100.
The final price at A = 90% of 90% of 90% of tk 100 
= {(90/100) × (90/100) × (90/100) × 100} tk
= 72.9 tk

The final price at B = 81% of 90% of Rs. 100
= {(81/100) × (90/100) × 100} tk
= 72.9 tk

Hence, the price of the article is the same at A and B.

Question: Bimol started a business investing Tk. 9000. After five months, Sifat joined with a capital of Tk 8000. If at the end of the year, they earn a profit of Tk 6970, then what will be the share of Sifat in the profit?

Solution:
Bimol invested for 12 months and Sifat invested for 7 months.
So Bimol : Sifat = (9000 × 12) : (8000 × 7)
= 108 : 56
= 27 : 14

Sifat Ratio in profit will be = 6970 × (14/41)
= Tk 2380

Question: Which number is 25% less than 120?

Solution:
Let the number be x.
x = 120 - 120 × 0.25
⇒ x = 120 - 30
∴  x = 90

So, the number is 90.