Bank Math Master

Question: Which of the following is the 350% of 1?

Solution:
Let,
350% of 1 = x
or, (350/100) × 1 = x
∴ x = 3.5
So, 350% of 1 is 3.5

Question: The population of a town increases every year by 4%. If its present population is 50,000, then after 2 years it will be-
Solution:
Here we can use the compound interest based formula,
Population after n years
= P × [1 + (r/100)]ⁿ

∴ Population after 2 years,
= 50000 × [1 + (4/100)]²
= 50000 × [1 + 0.04]²
= 50000 × (1.04)²
= 54080

∴ Population after 2 years = 54080

Question: Asif bought 5 apples at Taka 15 and sold 3 apples at Taka 15. What will be the rate of profit-

Solution:
5 টি আপেলের ক্রয়মূল্য 15 টাকা
1 টি আপেলের ক্রয়মূল্য 15/5 = 3 টাকা

আবার,
3 টি আপেলের বিক্রয়মূল্য 15 টাকা
1 টি আপেলের বিক্রয়মূল্য 15/3 = 5 টাকা

∴ লাভ = 5 - 3 = 2 টাকা

∴ 3 টাকায় লাভ হয় 2 টাকা
1 টাকায় লাভ হয় 2/3 টাকা
100 টাকায় লাভ হয় 200/3 = 66.67 টাকা

∴  লাভ 66.67%

Question: The cost of an article was Tk.75. The cost was first increased by 20% and later on it was reduced by 20%. The present cost of the article is?

Solution:
Initial Cost = Tk. 75
After 20% increase in the cost, it becomes,
= (75 + 20% of 75)
= 75 + (20 ×75)/100
= 75 + 15
= 90

Now, Cost is decreased by 20%, So cost will become,
(90 - 20% of 90)
= 90 - (20 × 90)/100
= 90 - 18
= 72

So, present cost is Tk. 72

Question: If books bought at prices ranging from Tk. 200 to Tk.350 are sold at prices ranging from Tk.300 to Tk. 425, what is the greatest possible profit that might be made in selling ten books?

Solution:
সর্বনিম্ন ক্রয়মূল্য = 10 × 200  = 2000 টাকা
সর্বোচ্চ বিক্রয়মূল্য = 10 × 425 =4250 টাকা

∴ সর্বোচ্চ লাভ = 4250 - 2000 = 2250 টাকা

Question: The sum of two numbers is 520. If the bigger number is decreased by 4% and the smaller number is increased by 12%, then the numbers obtained are equal. The smaller number is-

Solution:
Let,
Larger number = x and smaller number = 520 – x

According to the question
⇒ 96x/100 = {(520 - x)/100} × 112
⇒ 96x = (520 - x) × 112
⇒ 96x = 520 × 112 - 112x
⇒ 112x + 96x = 520 × 112
⇒ 208x = 520 × 112
⇒ x= (520×112)/208
⇒ x = 280

∴ Smaller number = 520 - 280 = 240

Question: Ajay and Vijay started a business together with an investment of Tk. (1400 + x) and (1800 + 2x). After a year, Vijay received a profit of
Tk. 3200 out of total profit of Tk.5600. What is the initial investment of Ajay?

Solution:
Ratio of profit share = Ajay : Vijay
⇒ (1400 + x) : (1800 + 2x) = (5600 - 3200) : 3200
⇒ (1400 + x) /(1800 + 2x) = (5600-3200)/3200
⇒ (1400 + x) /(1800 + 2x) = 2400 / 3200
⇒ (1400 + x) /(1800 + 2x) = 3 / 4
⇒ 5600 + 4x = 5400 + 6x
⇒ 6x - 4x = 5600 - 5400
⇒ 2x = 200
∴ x= 100

∴ Initial investment of Ajay = 1400 + 100 = Tk.1500

Question: Rajib purchased a car for Tk. 2,60,000 and sold it for Tk. 3,50,000. What is the percent profit she made on the car?

Solution:
Profit = Selling Price - Cost Price = 3,50,000 - 2,60,000 = 90,000 Tk.

We know that,
Percent Profit = (Profit/​Cost Price) × 100
= (90000/260000) × 100
= (9 × 100)/26
= 34.615
= 34.62%

∴ Rajib made a 34.62% profit on the car.

Question: In an examination 77% candidates passed in English and 87% candidates passed in Mathematics. If 69% candidates passed in both these subjects, then what percent of candidates failed in both the subjects?

Solution:
Given that,
Students passed in English = 77%
Students passed in Math's = 87%
Students passed in both subjects = 69%
Then, number of students passed in at least one subject
= (77 + 87) - 69
= 95%

Thus, students failed in both subjects = 100 - 95 = 5%

Question: If 25 is 25 percent of 40 percent of a certain number, what is the number?

Solution:
Let, The number be x then
25 = 25% of 40% of x
or, 25 = (25/100) × (40/100) × x
or, x = (25 × 100 × 100)/(25 × 40)
or, x = 250

So the number is 250.

Question: One-fourth percent, written as a decimal, is-

Solution:
As we know,1% =1/100
Hence,
(1/4)% = (1/4) × (1/100)
= 1/400
= 0.0025

Question: Polash and Hasan started a business with the investment of Tk.6000 and Tk.5000 respectively and after 6 months, Mehedi joined with the investment of Tk.3000. At the end of the year, the total profit is Tk.5000. Find the Hasan’s profit share?

Solution:
Polash invest = 6000 × 12 =72,000
Hasan invest = 5000 × 12 = 60,000
Mehedi invest = 3000 × 6=18,000

The ratio of their investments is = 72,000 : 60,000 : 18,000
= 12 : 10 : 3

The total profit is Tk. 5000

Now,
Hasan’s share of the profit is = (10/25) × 5000 = 2000

∴ Hasan’s share of the profit is Tk. 2000

Question: If the cost price of 20 books is the same as selling price of 25 books, then the loss percentage is-

Solution:
Let, the cost price of 1 book be  x
So, the cost price of 20 books is = 20x

Let, the selling price of 1 book be  y
So, the selling price of 25 books is = 25y

Given that the cost price of 20 books is equal to the selling price of 25 books.
⇒ 20x = 25y
⇒ y = (20/25)x = 4x/5

∴ Loss = cost price - selling price = x - y = x - (4x/5)
∴ Loss = x/5

∴ The loss percentage is = {(x/5)/x} × 100
= (1/5) × 100
= 20%

Question: If Kamal's salary is 25% more than Jamal's salary, then Jamal's salary is how much lower than Kamal's salary?

Solution:
Let Jamal's Salary is Tk. 100. Then,
Kamal's Salary = (100 + 25% of 100)
= 100 + (25× 100)/100
= 125

Difference between Kamal's Salary and Jamal's Salary = 125 - 100 = 25

∴ lower = (25/125) × 100 = 20%

∴ Jamal's salary is 20% lower than Kamal's salary.

Question: After paying 10% tax on all income over 2000. Rahman had a net income of Tk 20000. Rahman's income before tax was?

Solution:
Let,  Rahim’s income was = x
Taxable Income = x - 2000
Tax paid = 10% × (x - 2000)

According to the question,
⇒ x - 10% × (x - 2000) = 20000
⇒ x - {10 × (x - 2000)}/100 = 20000
⇒ x - (x - 2000)/10 = 20000
⇒ 10x - (x - 2000) = 200000
⇒ 10x - x + 2000 = 200000
⇒ 9x = 200000 - 2000
⇒ x = 198000/9
⇒ x = 22000

∴ Rahim's income before tax was Tk 22,000

Question: A, B and C started a business with the investment of Tk.4000, Tk.3000 and Tk.2000 respectively. At the end of the year, the profit received by B and C together is Tk.1500 more than the profit received by A. What is the total profit of the business?

Solution:
 বিনিয়োগের অনুপাত, A : B : C = 4000 : 3000 : 2000 = 4 : 3 : 2

ধরি, মোট লাভ = x টাকা
সুতরাং,
A এর লাভ = 4​x/9
B এবং C এর একত্রে লাভ = (3x/9) + (2x/9) = 5x/9

প্রশ্নমতে,
⇒ 5x/9 = (4​x/9) + 1500
⇒ (5x/9) - (4​x/9) = 1500
⇒ (5x - 4x)/9 = 1500
⇒ x/9 = 1500
⇒ x = 1500 × 9
⇒ x = 13500

∴ মোট লাভ 13500

Question:  If the profit on selling an article for Tk. 425 is the same as the loss on selling it for Tk. 355, then the cost price of the article is?

Solution:
Let the cost price of the article be x
Profit = 425 - x 
And, Loss = x - 355

According to the question,
425 – x = x – 355
⇒ 2x = 425 + 355 = 780
⇒ x = 780/2 = 390

∴ The cost price of the article is Tk. 390.

Question: A trader sold a cycle at a loss of 10%. If the selling price had been increased by Tk. 200, there would have been a gain of 6%. The cost price of the cycle is-

Solution:
Let the Cost price of cycle be x

Case I,
Selling Price of cycle = 90x/100 = 9x/10 = 0.9x

Case II,
106% of x = (9x/10) + 200
⇒ (106x/100) - (9x/10) = 200
⇒ (106x - 90x)/100 = 200
⇒ 16x/100 = 200
⇒ x = (200 × 100)/16
⇒ x = 1250

∴ The cost price of the cycle is Tk. 1250.

Question: If two numbers are respectively 30% and 40% more than a third number, what percent is the first of the second?

Solution:
Let the third number be 100
Then,
1st number = 100 + 30 = 130
2nd number = 100 + 40 = 140

To find what percent the first number is of the second number is,
=(130 × 100)/140
= 650/7
=92.86%

∴ The first number is 92.86% of the second number.