ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: If a watch is sold for Tk. 560, there is a loss 20%. What is the cost price of the watch?

Solution:
দেওয়া আছে,
বিক্রয়মূল্য ৫৬০ টাকা
২০% ক্ষতিতে বিক্রয়মূল্য = (১০০ - ২০) = ৮০ টাকা

বিক্রয়মূল্য ৮০ টাকা হলে ক্রয়মূল্য ১০০ টাকা
বিক্রয়মূল্য ৫৬০ টাকা হলে ক্রয়মূল্য (১০০ × ৫৬০)/৮০ টাকা
= ৭০০ টাকা

Question: If a man were to sell his chair for Tk. 720, he would lose 25%. To gain 25% he should sell it for:

Solution:
Let the Cost price of the Chair is x.
Selling price = x - 25% of x
⇒ 720 = x - (25x/100)
⇒ 720 = 75x/100
⇒ 75x = 72000
∴ x = 960

To gain 25% = 960 + 25% of 960
= Tk. 1200

Question: The sale price of an article including the Sales Tax is Tk. 616. The rate of Sales Tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is-

Solution:
Let,
Cost price be x.
Selling price = x + 12% of x
= x + (12x/100)
= 28x/25

ATQ,
(28x/25) + 10% of (28x/25) = 616
⇒ (28x/25) + (280x/2500) = 616
⇒ (28x/25) + (14x/125) = 616
⇒ (140x + 14x)/125 = 616
⇒ 154x = 77000
∴ x = 500

∴ Cost price tk. 500.

Question: A book in sold for Tk. 65. This price gives the seller a profit 30% on his cost. What will be the new selling price, if he cuts his profit to 10% of the cost?

Solution:
৩০% লাভে বিক্রয়মূল্য = (১০০ + ৩০) টাকা = ১৩০ টাকা

বিক্রয়মূল্য ১৩০ টাকা হলে ক্রয়মূল্য ১০০ টাকা
বিক্রয়মূল্য ১ টাকা হলে ক্রয়মূল্য ১০০/১৩০ টাকা
বিক্রয়মূল্য ৬৫ টাকা হলে ক্রয়মূল্য (১০০ × ৬৫)/১৩০ টাকা
= ৫০ টাকা

১০% লাভে বিক্রয়মূল্য = (৫০ + ৫০ এর ১০%) টাকা
= (৫০ + ৫) টাকা
= ৫৫ টাকা

Question: The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is -

Solution:
Let,
Cost price of each article be Tk. 1
Cost price of x articles = Tk. x
Selling price of x articles = Tk. 20

∴ Profit = Tk. (20 - x)

ATQ,
(20 - x)/x = 25%
Or, 100(20 - x)/x = 25
Or, 2000 - 100x = 25x
Or, 125x = 2000
∴ x = 16

Question: If 5% more is gained by selling an article for Tk. 250 then by selling it for Tk. 240. The cost of the article is?

Solution: 
Selling price more = (250 - 240) = Tk. 10

If tk. 5 more gained then cost price 100
If tk. 1 more gained then cost price 100/5
If tk.10 more gained then cost price (100 × 10)/5
= Tk. 200

Question: A dealer buys an article marked at Tk. 25000 with 20% and 5% off. He spends Tk. 1000 for its repairs and sells it for Tk. 25000. What is his proft or loss percent?

Solution:
Given,
Marked Price = 25000.

After first discount it become,
= 25000 - 20% of 25000
= Tk. 20000.

After second discount, it becomes
= 20000 - 5% of 20000
= Tk. 19000.

So, Selling price = Tk. 19000.

Cost price for the man who bought it, as he spends tk. 1000 on repair.

∴ Cost price = (19000 + 1000) = Tk. 20000

∴ Profit = 25000 - 20000 = Tk. 5000.
% Profit = (5000 × 100)/20000
= 25%

Question: Due to a decrease of 10% in the price of rice, 3 more quintals of rice can be bought for Tk. 1500. What is the present price of 12 quintals of rice?

Solution:
৩ কুইণ্টাল চালের দাম = ১৫০০ এর ১০%
= ১৫০ টাকা
∴ ১ কুইণ্টাল চালের দাম = ১৫০/৩ টাকা
∴ ১২ কুইণ্টাল চালের দাম = (১৫০ × ১২)/৩ টাকা
= ৬০০ টাকা

Question: One-fifth of half of a number is 20. Then 20% of that number is:

Solution:
Let the number is = x

ATQ,
1/5 of 1/2 of x = 20
⇒ 1/5 × 1/2 × x = 20
⇒ x/10 = 20
∴ x = 200

∴ 20% of 200 = (20/100) × 200
= 40

Question: A total profit of Tk. 5400 is to be distributed amongst A, B and C such that A : B = 5 : 4 and B : C = 8 : 9. The share of B in the profit is:
 
Solution:
A Total Profit = Tk. 5400

Profit ratio,
A : B = 5 : 4
B : C = 8 : 9
As B is common in both ratio, we make B equal in both ratio by multiplying One B in another.
A : B = (5 × 8) : (4 × 8) = 40 : 32
B : C = (8 × 4) : (9 × 4) = 32 : 36

So, ratio of A : B : C = 40 : 32 : 36 = 10 : 8 : 9

Now,
B shares in profit = (5400 × 8)/27
= Tk. 1600

Question: 60% of a number added to 60 gives the result as the number itself, then the number is:

Solution:
Let x be the number which is added to 60.
Now,
60% of x = 0.6x

ATQ,
⇒ 60 + 0.6x = x
⇒ x - 0.6x = 60
⇒ 0.4x = 60
⇒ x = 60/0.4
∴ x = 150

Question: 220% of a number m is 44. What is 44% of m.

Solution:
Given,
220% of m = 44
⇒ (220 × m)/100 = 44
⇒ m = 20

44% of 20
= 44 × (20/100)
= 8.8

Question: A bookseller procures 40 books for Tk. 3200 and sells them at a profit equal to the selling price of 8 books. What is the selling price of one dozen books, if the price of each book is same?

Solution:
Cost price of each book = 3200/40
= Tk. 80.

ATQ,
Selling Price of 40 books = Cost price of 40 books + Selling Price of 8 books.
Or, Selling Price of 40 books - SP of 8 books = CP of 40 books.
Or, Selling Price of 32 books = Tk. 3200
Or, Selling Price of 1 book = 3200/32
= Tk. 100.

∴ Selling price of one dozen or 12 book = 12 × 100 = Tk. 1200.

Question: How many litres of a 30% alcohol solution should be added to 40 litres of a 60% alcohol solution to prepare a 50% solution?

Solution:
Let,
x litres of 30% alcohol solution be added.

ATQ,
30% of x + 60% of 40 = 50% of (x + 40)
⇒ (30x/100) + (60 × 40)/100 = 50 × (x + 40)/100
⇒ (30x + 2400)/100 = (50x + 2000)/100
⇒ 30x + 2400 = 50x + 2000
⇒ 50x - 30x = 2400 - 2000
⇒ 20x = 400
∴ x = 20

Question: A trader sells his goods at a discount of 20%. He still makes a profit of 25%. If he sells the goods at the marked price only, his profit will be:

Solution: 
ধরি,
দ্রব্যটির বাজার মূল্য = 100 টাকা
∴ 20% ছাড়ে বিক্রয়মূল্য = (100 - 20) = 80 টাকা।

আবার, ধরি,
দ্রব্যটির উৎপাদন খরচ = x টাকা।

প্রশ্নমতে,
∴ x + x এর 25/100 = 80
বা, x + (x/4) = 80
বা, 5x/4 = 80
∴ x = 64

∴ বাজার মূল্যে পন্যটি বিক্রি করলে,
লাভ =(100 - 64) = 36 টাকা।

∴ 64 টাকায় লাভ হয় = 36 টাকা
∴ 100 টাকায় লাভ হয় = (36 × 100)/64
= 56.25%

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: The length, breadth and height of a room in the shape of a cuboid are increased by 10%, 20% and 50% respectively. Find the percentage change in the volume of the cuboid.

Solution:
Let each side of the cuboid be 10 unit initially.
Initial Volume of the cuboid,
= Length × Breadth × Height
= (10 × 10 × 10)
= 1000 cubic unit.

After increment dimensions become,
Length = (10 + 10% of 10) = 11 unit.
Breadth = (10 + 20% of 10) = 12 unit.
Height = (10 + 50% of 10) = 15 unit.

Now, New volume = (11 × 12 × 15) = 1980 cubic unit.

∴ Increase in volume = 1980 - 1000 = 980 cubic unit.
Increase in volume percent = (980/1000) × 100
= 98%

Question: A person sold a book at a gain of 15%. Had he bought it for 25% less and sold it for Tk. 600 less, he would have made a profit of 32%. The cost price of the book was:

Solution:
Let the original cost price = Tk. x

Selling price = x + 15% of x
= 115x/100
= 23x/20

Cost price = x - 25% of x
= x - (25x/100)
= 75x/100
= 3x/4

Selling price = (3x/4) + 32% of (3x/4)
= (3x/4) + (32/100) × (3x/4)
= 99x/100

ATQ,
(23x/20) - (99x/100) = 600
⇒ (115x - 99x)/100 = 600
⇒ 16x = 600 × 100
⇒ x = (600 × 100)/16
∴ x = 3750

Question: If a% of x is equal to b% of y, then of c% of y is what % of x?

Solution:
ax/100 = by/100
⇒ ax = by
⇒ y = ax/b

Again,
c% of y = cy/100
= cy/100
= cax/100b
Thus, c% of y= (ac/b)% of x.

Question: A makes an article for Tk.120 and sells it to B at a profit of 25% . B sells it to C who sells it for Tk.198 making a profit of 10%. What profit percent did B make?  

Solution:
২৫% লাভে A এর বিক্রয়মূল্য = (১০০ + ২৫) = ১২৫ টাকা
ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য ১২৫ টাকা
ক্রয়মূল্য ১২০ টাকা হলে বিক্রয়মূল্য (১২৫ × ১২০)/১০০ টাকা
= ১৫০ টাকা।

B এর ক্রয়মূল্য ১৫০ টাকা
১০% লাভে বিক্রয়মূল্য = (১০০ + ১০) = ১১০ টাকা

C এর বিক্রয়মূল্য ১১০ টাকা হলে ক্রয়মূল্য ১০০ টাকা
C এর বিক্রয়মূল্য ১৯৮ টাকা হলে ক্রয়মূল্য (১০০ × ১৯৮)/১১০ টাকা
= ১৮০ টাকা

B এর বিক্রয়মূল্য ১৮০ টাকা।
∴ লাভ = (১৮০ - ১৫০) টাকা = ৩০ টাকা

১৫০ টাকায় লাভ হয় ৩০ টাকা
১০০ টাকায় লাভ হয় (৩০ × ১০০)/১৫০ টাকা
= ২০%

Question: The profit earned after selling an article for Tk. 1754 is the same as loss incurred after selling the article for Tk. 1492. What is the cost price of the article?

Solution:
Let,
The cost price of the article be Tk. x.

ATQ,
x - 1492 = 1754 - x
⇒ 2x = 1754 + 1492
⇒ 2x = 3246
⇒ x = 3246/2
∴ x ​= 1623

∴ The cost price of the article is Tk. 1623.

Question: The population of a village is 25000. One-fifth are females and the rest are males, 5% of males and 40% of females are uneducated. What percentage on the whole are educated?

Solution:
Number of females = 25000 × 1/5
= 5000
Number of males = (25000 - 5000)
= 20000

Number of educated females = 5000 × 60/100
= 3000
Number of educated males = 20000 × 95/100
= 19000

Total educated population = 22000
Percentage of educated population = (22000/25000) × 100
= 88%

Question: A tradesman marks his goods 30% above the cost price. If he allows a discount of 10% Then his gain precent is?

Solution:
At 30% above,
Market price of goods = 100 + 30 = Tk. 130

At 10% discount,
Selling price = 130 - 10% of 130
= 130 - 13
= Tk. 117

∴ Gain = 117 - 100 = Tk. 17
Gain % = (17/100) × 100
= 17%

Question: A person bought an article for Tk. 1200 and sold it at a profit of 15%. The buyer sold it to a third person at a loss of 5%. Calculate the last selling price?

Solution:
১৫% লাভে,
১০০ টাকার দ্রব্যের বিক্রয়মূল্য = ১১৫ টাকা
১ টাকার দ্রব্যের বিক্রয়মূল্য = ১১৫/১০০ টাকা
∴ ১২০০ টাকার দ্রব্যের বিক্রয়মূল্য = (১১৫ × ১২০০)/১০০ টাকা
= ১৩৮০ টাকা

৫% ক্ষতিতে,
১০০ টাকার দ্রব্যের বিক্রয়মূল্য = ৯৫ টাকা
১ টাকার দ্রব্যের বিক্রয়মূল্য = ৯৫/১০০ টাকা
∴ ১৩৮০ টাকার দ্রব্যের বিক্রয়মূল্য = (৯৫ × ১৩৮০)/১০০ টাকা
= ১৩১১ টাকা

Question: The marked price of a radio is 20% more than its cost price. If a discount of 10% is given on the marked price, the profit percent is:

Solution:
Let,
Cost price = Tk.100

Market price = 100 + 20% of 100
= 100 + (100 × 20/100)
= Tk. 120

Now,
Selling price  = 120 - 10% of 120
= 120 - (120 × 10)/100
= Tk. 108

Profit = 108 - 100 = Tk. 8
∴ Profit % = (8 × 100)/100
= 8%

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 + 15
= Tk. 90
Now, Cost is decreased by 20%, So cost will become,
(90 - 20% of 90)
= 90 - 18 
=Tk. 72
So, present cost is Tk. 72.