ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: 88% of 370 + 24% of 210  - ? = 118

Solution: 
 88% of 370 + 24% of 210  - x = 118
⇒ 88 × 370/100 + 24 × 210/100 - x = 118 
⇒ 325.6 + 50.4 - x = 118 
⇒ x = 325.6 + 50.4 - 118 = 258  

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: 
SP per Lemons = 40/45 = Tk. 0.88.
Let, CP was Tk. X per Lemons.
SP = CP - 20% of CP
⇒ 0.88 = 0.8X
⇒ X = Tk. 1.11

To get 20% profit,
SP = 1.11 + 20% of 1.11 = Tk.1.33

Thus, he can sell = 24/1.33
= 18 Lemons in Tk. 24.

Question: It costs Tk. 1 to photocopy a sheet of paper. However, 2% discount is allowed on all photocopies done after the first 1000 sheets. How much will it cost to copy 5000 sheets of paper?

Solution: 
For the first 1000 sheets, cost = 1000 × 1 = Tk. 1000 

Cost for rest (5000 - 1000) or 4000 sheets = 4000 × (1 - 0.02)
= 4000 × 0.98
= Tk. 3920 

Total cost = 3920 + 1000 
= Tk. 4920 

Question: A cloth merchant sold half of his cloth at 40% profit, half of remaining at 40% loss and the rest was sold at the cost price. In the total transaction his gain or loss will be =?

Solution: 
Let, total price 100 taka

Half at 40% = 50 + 50 × 0.4
= 70 taka 

half of remaining at 40% loss = 25 - 25 × 0.4
= 15 taka 

rest = 25 taka 

Total = 70 + 25 + 15 
=110 taka

In the total transaction his gain = 110 - 100 
= 10 

Question: Altaf saved Tk. 2.50 in buying an item on sale. If he spent Tk. 25 for the item, approximately how much percent he save in the transaction?

Solution: 
cost price = 25 + 2.5 = 27.5 taka

Approximate save = (2.5/27.5) × 100%
= (100/11)%

Question: A cloth merchant on selling 33 meters of cloth obtains a profit equal to the selling price of 11 meters of cloth the profit is = ?

Solution:
Profit = selling price of 11 m of cloth = 1/3 selling price of 33 m of cloth

Let selling price of 33 meters of cloth = 3x
∴ profit = 1/3 (3x) = x

So, cost price = selling price - profit = 3x - x = 2x

 % Profit = (x/2x) × 100% = 50%

Question: Alal sold an article at 6% loss. Had he sold it for Tk. 64 more, he would have made a profit of 10%. Then the cost of the article is =?

Solution: 
Let, the cost of the article is x taka

Selling price = 0.94x 

ATQ, 
0.94x + 64 = 1.1x
⇒ 1.1x - 0.94x = 64 
⇒ 0.16x = 64 
⇒ x = 64/0.16 = 400 taka 

Question: Rana buys goods worth Tk. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @10%. Find the amount he will have to pay for the goods.

Solution: 
After  a rebate of 6%, 
Rana has to pay  = 6650 - 6650 × 6/100 
= 6650 - 399
= 6251


After getting the rebate, he pays sales tax @10%

He will have to pay = 6251 + 6251 × 10% 
= 6251 + 625.1 
= Tk. 6876.1

Question: What percentage of the whole week does Rakibul spend in office, if his office hours are 9 am to 5 pm from Sunday to Thursday?

Solution: 
Percentage = {(5 × 8)/(7 × 24)} × 100%
= (5/21) × 100%
= 23.81%

Question: A clock was sold for Tk. 144. If the percentage of profit was numerically equal to the cost price, the cost of the clock was -

Solution: 
Let, the percentage of profit be x% 
cost of the clock was x taka.

x + x × x/100 = 144 
⇒ x + (x²/100) = 144
⇒ (x² + 100x) = 14400
⇒ x² + 100x - 14400 = 0
⇒ x² + 180x - 80x - 14400 = 0
⇒ x(x + 180) - 80 (x + 180) = 0
⇒ (x + 180) (x - 80) = 0
⇒ x = 80

Question: When 15% is lost in grinding wheat, a country can export 30 lakh tons of wheat. On the other hand, if 10% is lost in grinding, it can export 40 lakh tons of wheat. The production of wheat in the country is:

Solution: 
Let, The production of wheat in the country is x lakh tons. 

(0.9 - 0.85)x = 40 - 30 
⇒ 0.05x = 10 
⇒ x = 10/0.05 
= 200 

Question: If 75% of the students in a school are boys and the number of girls is 420, the number of boys is:

Solution: 
75% of the students in a school are boys
girls = 25%

25% of total students = 420
⇒ total students = 420/0.25
= 1680

∴  the number of boys is = 1680 - 420 
= 1260

Question: Two persons contested an election of Parliament. The winning candidate secured 57% of the total votes polled and won by a majority of 42000 votes. The number of total votes polled is :

Solution: 
Winning candidates secured 0.57x votes and other gets 0.43x votes.

ATQ,
0.57x - 0.43x = 42000 
⇒ 0.14x = 42000 
⇒ x = 42000/0.14 
= 300000

Question: In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State? 

Solution: 
Let, the number of candidates appeared from each State was x

0.07x - 0.06x = 80 
⇒ 0.01x = 80 
⇒ x = 80/0.01
= 8000 

Question: A person subscribes to LiveMCQ for a year pack Tk. 1200. If the monthly subscription is Tk. 200, how much discount does a yearly subscriber get?

Solution:
The monthly subscription is Tk. 125, so for a year pack should be = (12 × 200) taka
= Tk.2400

Discount = 2400 - 1200 
= 1200 taka

%discount = (1200/2400) × 100%
= 50%

Question: The price of a cycle is Tk. 25,000. It was insured to 85% of its price. The cycle was damaged completely in an accident and the insurance company paid 90% of the insurance. What was the difference between the price of the cycle and the amount received?

Solution: 
Insured price = 25000 × 0.85 
= 21250 taka 

the insurance company paid = 21250 × 0.9
=  19125 taka 

∴ Difference = 25000 - 19125 
= Tk. 5875 

Question: Payel bought an item at 20% discount on its original price. he sold it with 40% increase on the price he bought it. The new sale price is by what percent more than the original price?

Solution: 
Let, the original price be 100 
After 20% discount, the price is = 100 - 20 
= 80 taka 

Selling price = 80 + 80 × 0.4
= 80 + 32 
= 112 taka 

%increase = (112 - 100)%
= 12%

Question: Kalam buys an article at a discount of 25%. At what percentage above the cost price should he sell it to make a profit of 25% over the original list price?

Solution: 
Let, the original price is 100 taka
Buying price = 100 - 25
= 75 taka 

To make 25% over original price = 100 + 25
= 125 taka 

percentage above the cost price = {(125 - 75)/75} × 100%
= (50/75) × 100%
= (2/3) × 100%
= 66.67%

Question: Which number is 60% less than 80? 

Solution: 
let, the number is x 

x = 80 - 80 × . 6
= 80 - 48
= 32 

Question: The price of an article is raised by 30% and then two successive discounts of 10% each are allowed. Ultimately, the price of the article is:

Solution: 
let, the price be 100 taka 

after 30% raise = 100 + 30 = 130 taka

after first 10% discount = 130 - 13 = 117 taka

after second 10% discount = 117 - 117 × 0.1 
= 117 - 11.7
= 105.3

Question: In a test, the minimum passing percentage for girls and boys is 45% and 60% respectively. A boy scored 767 marks and failed by 313 marks. What are the minimum passing marks for girls?

Solution: 
pass mark = 767 + 313 
= 1080 

0.6 × total marks = 1080 
⇒ total marks = 1080/0.6 
= 1800 

the minimum passing marks for girls is = 1800 × 0.45
= 810 

Question: 25 percent of 30 is 75 percent of what number?

Solution: 
let, 25 percent of 30 is 75 percent of x

25% of 30 = 75% of x
⇒ (25/100) × 30 = (75/100) × x
⇒ 15/2 = 3x/4
⇒ 6x = 60
∴ x = 10

Question: The price of a certain book is discounted by 10% and the reduced price is then discounted by 10%. The series of successive discounts is equivalent to a single discount of

Solution:
10% ছাড়ে মূল্য = (100 - 10) = 90 টাকা
পুনরায়, 10% ছাড়ে মূল্য = {90 - 90 × (10/100)} টাকা
= (90 - 9) টাকা
= 81 টাকা

এককালীন ছাড় = (100 - 81) টাকা
= 19 টাকা

Question: In an office, 40% of the staff is female. 70% of the female staff and 50% of the male staff are married. The percentage of the unmarried staff in the office is 

Solution: 
Let, total staff 100 

female = 40 
male = 100 - 40 
= 60 

married staff = 40 × 0.7 + 60 × 0.5
= 28 + 30 
= 58 

∴ unmarried staff = 100 - 58 
= 42

Question: Arjun purchased 30 kg of wheat at the rate of Tk. 11.50 per kg and 20 kg of wheat at the rate of Tk 14.25 per kg. he mixed the two and sold the mixture. Approximately what price per kg should he sell the mixture to make 30% profit?

Solution: 
Total cost = 30 × 11.5 + 20 × 14.25 
= 345 + 285
= 630

Selling price = 630 + 630 × 30% 
= 630 + 189 
= 819

Then, price per kg = 819/50 
= 16.38 taka

Question: A number is increased by 15% and then decreased by 25% and the number becomes 22 less than the original number. The original number is :

Solution: 
Let the number is = 100x

Now after 15% of increase = 100x + 15% of 100x = 115x
Now 25% decrease = 115x - 25% of 115x = 115x - 28.75x = 86.25x

Actual decreased = 100x - 86.25x = 13.75x

According to the question,
13.75x = 22
⇒ x = 22/13.75
⇒ 100x = (22/13.75) × 100
⇒ 100x = 160.

∴ Original number = 160.

Question: Akash multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation? 

Solution:
Let the number be x

Error = (5x/3) - (3x/5)
= (25x - 9x)/15
= 16x/15

 % Error ={(16x/15) × (3/5x) × 100}% = 64%

Question: Rafi went to the stationers and bought things worth Tk. 25 out of which 30 paisa went on sales tax on taxable purchases. if the tax rate was 6%, then what was the cost of the tax-free items?  

Solution: 
Let, cost of taxable purchases is x taka 

ATQ, 
0.06x = 30/100 
⇒ x = 30/(100 × 0.06) 
= 5 taka 

∴ The cost of the tax-free items was = 25 - 5 - 0.3
= Tk. 19.7