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Percentage and Profit & Loss

মোট প্রশ্ন১,৬৯৬এই পাতা১০০প্রতি পাতা১০০
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উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Percentage and Profit & Loss

PrepBank · পাতা ৯ / ১৭ · ৮০১–৯০০ / ১,৬৯৬

৮০১.
A started a business with tk 21000 and is joined afterwards by B with tk 36000. After how many months did B join if the profits at the end of the year are divided equally?
  1. ক
    ক) 3
  2. খ
    খ) 4
  3. গ
    গ) 5
  4. ঘ
    ঘ) 6
ব্যাখ্যা

Suppose B joined after x months
then,
21000 × 12 = 36000 × (12 - x)
⇒ 36x = 180
⇒ x = 5

৮০২.
The cost of a watch is Tk. 900. To make the deal attractive to its customers, the shop sells it at a discount of 12% and still makes a profit of 10%. What is the advertised price?
  1. ক
    ক) Tk.. 812.5
  2. খ
    খ) Tk. 1050
  3. গ
    গ) Tk. 1125
  4. ঘ
    ঘ) Tk. 1225
ব্যাখ্যা

Since profit of 10% is there,
∴ S.P. = (100+10)% of C.P. = (110/100) × 900
= Tk. 990
Discount = 12%
So,
SP = (100-12)% of List Price
∴ 990 = (88/100) × L.P.
∴ L.P. = Tk. 1125 [List price = Advertised Price = Marked Price]

৮০৩.
Every 2 minutes, 5 litres of water are poured into a 1,500 litre tank. After 3 hours, what percent of the tank will be full?
  1. ক
    20% 
  2. খ
    30% 
  3. গ
    35% 
  4. ঘ
    40% 
ব্যাখ্যা

Question: Every 2 minutes, 5 litres of water are poured into a 1,500 litre tank. After 3 hours, what percent of the tank will be full?

Solution:
In 2 minutes, 5 liters is poured
In 180 minutes = (180 × 5)/2 = 450 liters

So, percentage filled = (450 × 100)/1500
= 30%

৮০৪.
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?
  1. ক
    Tk. 62
  2. খ
    Tk. 82
  3. গ
    Tk. 72
  4. ঘ
    Tk. 75
ব্যাখ্যা
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
৮০৫.
The original funding to build a housing development was $0.5 billion. The funding was increased to $2 billion. By what percentage was the original funding increased?
  1. ক
    ক) 200%
  2. খ
    খ) 43%
  3. গ
    গ) 300%
  4. ঘ
    ঘ) None of the above
ব্যাখ্যা
Question: The original funding to build a housing development was $0.5 billion. The funding was increased to $2 billion. By what percentage was the original funding increased?

Solution: 
নির্মাণ ব্যয় বাড়ে = (2.0 - 0.5) = 1.5 বিলিয়ন ডলার 

নির্মাণ ব্যয় শতকরা বাড়ে = {(1.5/0.5) × 100}%
                                       = 300%
৮০৬.
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?
  1. ক
    Tk. 320.
  2. খ
    Tk. 290.
  3. গ
    Tk. 300.
  4. ঘ
    Tk. 390.
ব্যাখ্যা
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.
৮০৭.
If A’s income is 10% more than B’s, how much percentage is b’s income less than A’s?
  1. ক
    ক) 9%
  2. খ
    খ) 9(1/2)%
  3. গ
    গ) 9(1/11)
  4. ঘ
    ঘ) 10%
ব্যাখ্যা

B's income is less than A's by
[10/(100 + 10) × 100]%
= (100/11)%
= 9(1/11)%

৮০৮.
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?
  1. ক
    Tk. 750
  2. খ
    Tk. 800
  3. গ
    Tk. 850
  4. ঘ
    Tk. 900
ব্যাখ্যা
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.
৮০৯.
If two numbers are respectively 30% and 40% more than a third number, what percent is the first of the second?
  1. ক
    95.75%
  2. খ
    86.68%
  3. গ
    92.86%
  4. ঘ
    None of these
ব্যাখ্যা
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.
৮১০.
Notebooks used to cost Tk. 240 for a pack of 6. Now they cost Tk. 350 for a pack of 5. What is the percent increase in the price per notebook?
  1. ক
    50%
  2. খ
    65%
  3. গ
    70%
  4. ঘ
    75%
ব্যাখ্যা
Question: Notebooks used to cost Tk. 240 for a pack of 6. Now they cost Tk. 350 for a pack of 5. What is the percent increase in the price per notebook?

Solution:
Original cost = Tk. 240 for a pack of 6 notebooks.
Cost per notebook originally = 240/6 = Tk. 40 per notebook

New cost = Tk. 350 for a pack of 5 notebooks.
Cost per pen now = 350/5 = Tk. 70 per notebook.

Increase in cost = 70 - 40 = Tk. 30 per pen

Percent increase = (30​/40) × 100 = 75%
৮১১.
By selling a book for Tk. 675, a seller loses 2/9 of his outlay, by selling it for Tk. 810, his gain or loss percentage is -
  1. ক
    ক) 10% loss
  2. খ
    খ) 20% gain
  3. গ
    গ) 7% gain
  4. ঘ
    ঘ) No gain or loss
  5. ঙ
    ঙ) None
ব্যাখ্যা

Question: By selling a book for Tk. 675, a seller loses 2/9 of his outlay, by selling it for Tk. 810, his gain or loss percentage is -


Solution:
Let the cost price of the book be Tk. x
The loss of outlay is Tk. 2x/9

Given that,
Selling price of the book is Tk. 675
or, x - 2x/9 = 675
or, 7x/9 = 675
or, x = 675 × 9/7
or, x = 867.86

If the book is sold for Tk. 810
The loss = Tk. (867.86 - 810) = Tk. 57.86

Therefore loss percentage is
= (57.86/867.86) × 100 %
= 6.666 %
= 6.67%

৮১২.
A shopkeeper cheats to the extent of 10% while buying as well as selling by using false weights. His total gain is -
  1. ক
    ক) 10%
  2. খ
    খ) 11%
  3. গ
    গ) 20%
  4. ঘ
    ঘ) 21%
ব্যাখ্যা
Question: A shopkeeper cheats to the extent of 10% while buying as well as selling by using false weights. His total gain is -  

Solution:
মনে করি, 
দোকানদার প্রতারণা করে ১০০ টাকা দিয়ে পণ্যটি ক্রয় করে, এতে তার ১০% লাভ হয়।
তাহলে পণ্যটির প্রকৃতমূল্য = ১০০ + (১০০ × ১০%) = ১১০ টাকা

দোকানদার পণ্যটি বিক্রয় করার সময় আবার ১০% লাভ করে,
তাহলে বিক্রয়মূল্য = ১১০ + (১১০ × ১০%) = ১২১ টাকা

∴ তার মোট লাভ = ১২১ - ১০০ = ২১ টাকা
৮১৩.
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? 
  1. ক
    20 Tk/liter
  2. খ
    22 Tk/liter
  3. গ
    25 Tk/liter
  4. ঘ
    30 Tk/liter
ব্যাখ্যা

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.

৮১৪.
A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is -
  1. ক
    45 : 51
  2. খ
    5 : 13
  3. গ
    45 : 56
  4. ঘ
    2 : 3
ব্যাখ্যা
Question: A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is -

Solution: 
ধরি, ক্রয়মূল্য x টাকা 
মুদ্রিত মূল্য y টাকা 

১২% লাভে বিক্রয়মূল্য = x + x এর ১২% 
= x + 0.12x
= 1.12x

১০% ছাড়ে বিক্রয়মূল্য = (100 - 10)% y
= 90% y
= 0.9y 

1.12x = 0.9y
⇒ x/y = 0.9/1.12
= 90/112 [লব ও হরকে ১০০ দ্বারা গুণ করে]
= 45/56

∴ x : y = 45 : 56
৮১৫.
A bicycle is bought for Taka 200 and sold at a loss of 10%. Calculate the selling price and the amount of loss incurred.
  1. ক
    Taka 350
  2. খ
    Taka 80
  3. গ
    Taka 280
  4. ঘ
    Taka 180
ব্যাখ্যা
Question: A bicycle is bought for Taka 200 and sold at a loss of 10%. Calculate the selling price and the amount of loss incurred.

Solution:
Cost Price of the bicycle = Taka 200
Loss Percentage = 10%
Loss Amount = Loss Percentage × Cost Price = 10% × Taka 200 = Taka 20
Selling Price = Cost Price - Loss Amount = Taka 200 - Taka 20 = Taka 180
৮১৬.
If the salary of an employee is reduced by 10 percent for his late attendance and then increased by 10 percent can a pardon, how much does he lose?
  1. ক
    ক) 2%
  2. খ
    খ) 1%
  3. গ
    গ) 1/2%
  4. ঘ
    ঘ) 9%
ব্যাখ্যা

ধরি কর্মীর বেতন ছিল 100 টাকা
10% হ্রাসে তার বর্তমান বেতন হবে = (100 - 100 এর 10%) = [100 − {(100×10)/100}] =100 − 10 = 90 টাকা
আবার, 10% বৃদ্ধিতে তার বর্তমান বেতন হবে = (90 + 90 এর 10%) = [90 − {(90×10)/90}] = 90 + 9 = 99 টাকা
∴ তার মোটের উপর ক্ষতি হলো = 100 - 99 = 1 টাকা বা 1%

৮১৭.
Due to 25% fall in the rate of eggs one can buy 2 dozen eggs more than before by investing Tk. 162. The the original rate per dozen of the eggs is?
  1. ক
    ক) Tk. 17
  2. খ
    খ) Tk. 25
  3. গ
    গ) Tk. 27
  4. ঘ
    ঘ) Tk. 28
ব্যাখ্যা
Question: Due to 25% fall in the rate of eggs one can buy 2 dozen eggs more than before by investing Tk. 162. The the original rate per dozen of the eggs is?

Solution:
25% fall we get 2 dozen eggs extra.

∴ 25% = 2 dozen
100% = 8 dozen
So, old quantity = 8 - 2 = 6 dozen

∴ Rate = 162/6
= Tk. 27

Alternate:
Let the price of eggs one dozen be Tk. 4x
Price of eggs after fall in rate = 4x × 3/4 = 3x
According to question
⇒ 162 [1/3x - 1/4x] = 2
⇒ 162 [(4 - 3)/12x] = 2
⇒ 162 = 24x
⇒ x = 162/24

Price of eggs one dozen = 4 × 162/24 = Tk. 27
৮১৮.
If 45% of A = 15% of B, what percentage of A is B?
  1. ক
    30%
  2. খ
    150%
  3. গ
    300%
  4. ঘ
    60%
ব্যাখ্যা
Question: If 45% of A = 15% of B, what percentage of A is B?

Solution: 
45% of A = 15% of B
⇒ (45/100) × A = (15/100) × B
⇒ 9A/20 = 3B/20
⇒ 9A = 3B
⇒ B = 9A/3
∴ B = 3A

Required percentage = (B/A) × 100%
= (3A/A) × 100%
= 3 × 100%
= 300%
৮১৯.
The cost price of an article is Tk 7840. What should be the selling price of the article so that there is a profit of 7%?
  1. ক
    ক) Tk 8388.80
  2. খ
    খ) Tk 8300
  3. গ
    গ) Tk 8000
  4. ঘ
    ঘ) Tk 8500.50
ব্যাখ্যা
Question: The cost price of an article is Tk 7840. What should be the selling price of the article so that there is a profit of 7%?

Solution:
৭% লাভে বিক্রয়মূল্য = ১০০ + ৭ =১০৭ টাকা

ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য ১০৭ টাকা
∴ ক্রয়মূল্য ১ টাকা হলে বিক্রয়মূল্য ১০৭/১০০ টাকা
∴ ক্রয়মূল্য ৭৮৪০ টাকা হলে বিক্রয়মূল্য (১০৭ × ৭৮৪০)/১০০ টাকা
= ৮৩৮৮.৮০ টাকা
৮২০.
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 =?
  1. ক
    33.33%
  2. খ
    29.67%
  3. গ
    35.67%
  4. ঘ
    30.33%
ব্যাখ্যা
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
৮২১.
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?
  1. ক
    ক) Tk. 200
  2. খ
    খ) Tk. 150
  3. গ
    গ) Tk. 250
  4. ঘ
    ঘ) Tk. 300
ব্যাখ্যা
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
৮২২.
A machine is sold at a profit of 10%. Had it been sold for Tk. 40 less, there would have been a loss of 10%. What was the cost price?
  1. ক
    Tk.175
  2. খ
    Tk. 200
  3. গ
    Tk. 225
  4. ঘ
    Tk. 250
ব্যাখ্যা

Question: A machine is sold at a profit of 10%. Had it been sold for Tk. 40 less, there would have been a loss of 10%. What was the cost price?

Solution: 
Let, cost price of the machine is x taka 

Selling price = 1.1x taka 

ATQ, 
1.1x - 40 = 0.9x 
⇒ 1.1x - 0.9x = 40 
⇒ 0.2x = 40
⇒ x = 40/.2
= Tk. 200 

৮২৩.
A person make a profit of 10% on 25% of the quantity and a loss of 20% on the rest of the quantity. What is the gain or loss in percentage on the whole?
  1. ক
    10%
  2. খ
    - 12%
  3. গ
    12.5%
  4. ঘ
    20%
ব্যাখ্যা

Question: A person make a profit of 10% on 25% of the quantity and a loss of 20% on the rest of the quantity. What is the gain or loss in percentage on the whole?

Solution: 
Let Cost Price = 100
Profit = 25 x 10%
= 25/10
= 2.5

Loss = 75 x 20%
= 75/5
= 15

Net loss = 15 - 2.5 
= 12.5

∴ Net Loss as % = 12.5/100 x 100%
= 12.5%

৮২৪.
120% of 45 + 45% of 120 = ?
  1. ক
    90
  2. খ
    108
  3. গ
    98
  4. ঘ
    100
ব্যাখ্যা

Question: 120% of 45 + 45% of 120 = ?

Solution:
 120% of 45 + 45% of 120
= {(120/100) × 45} + {(45/100) × 120}
= 54 + 54
= 108

৮২৫.
40 litre of mixture of milk and water contains 25% of water. When 10 liters of water is added, what will be the percentage of milk in the final mixture?
  1. ক
    40%
  2. খ
    45%
  3. গ
    55%
  4. ঘ
    60%
ব্যাখ্যা
Question: 40 litre of mixture of milk and water contains 25% of water. When 10 liters of water is added, what will be the percentage of milk in the final mixture?

Solution:
25% of 40 litre = 10 litre. 
10 liter water is present in the mixture. 
When 10 liters more water is added in the mixture then the final mixture contains 20 liters water and 30 liters milk. 
% of milk in final mixture= (30/50) × 100 = 60%
৮২৬.
Rakibul has saved 1250 Taka by purchasing a laptop with a 5% discount on it. what is the quoted price of the laptop in Taka?
  1. ক
    20000 Tk.
  2. খ
    25000 Tk.
  3. গ
    30000 Tk.
  4. ঘ
    35000 Tk.
ব্যাখ্যা
প্রশ্ন: Rakibul has saved 1250 Taka by purchasing a laptop with a 5% discount on it. what is the quoted price of the laptop in Taka?

সমাধান :
5% ছাড়ে 
5 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য 100 টাকা 
1 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য 100/5 টাকা 
∴ 1250 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য (100 × 1250)/5 টাকা 
= 25,000 টাকা
৮২৭.
The population of a city grows from 175,000 to 262,500. What is the percentage growth in the city's population?
  1. ক
    40%
  2. খ
    43.5%
  3. গ
    50%
  4. ঘ
    60%
ব্যাখ্যা

Question: The population of a city grows from 175,000 to 262,500. What is the percentage growth in the city's population?

Solution:
জনসংখ্যা বৃদ্ধি পেয়েছে 
 = (262500 - 175000) = 87500

175000 জনে বৃদ্ধি পায় = 87500 জন
∴ 1 জনে বৃদ্ধি পায় = 87500/175000 জন
∴ 100 জনে বৃদ্ধি পায় = (87500 × 100)/175000 = 50 জন

∴ জনসংখ্যা বৃদ্ধির শতকরা হার = 50%

৮২৮.
By selling a shirt for Tk 450 the shopkeeper incurs a loss of 10%, then what will be the selling price of the shirt when he gets a profit of 10%?
  1. ক
    480 tk
  2. খ
    500 tk
  3. গ
    520 tk
  4. ঘ
    550 tk
ব্যাখ্যা
Question: By selling a shirt for Tk 450 the shopkeeper incurs a loss of 10%, then what will be the selling price of the shirt when he gets a profit of 10%?

Solution:
ধরি,
শার্টটির ক্রয়মূল্য = ১০০ক টাকা
১০% ক্ষতিতে,
বিক্রয়মূল্য = ১০০ক - ১০০ক এর ১০%
= ১০০ক - {১০০ক × (১০/১০০)}
= ৯০ক

প্রশ্নমতে,
৯০ক = ৪৫০
⇒ ক = ৪৫০/৯০
∴ ক = ৫
∴ ক্রয়মূল্য = ১০০ × ৫ =৫০০ টাকা

এখন,
১০% লাভে,
বিক্রয়মূল্য = ৫০০ + ৫০০ এর ১০%
= ৫০০ + {৫০০ × (১০/১০০)}
= ৫৫০ টাকা
৮২৯.
If 30% of x = y, then y% of 50 is equal to what percentage of x?
  1. ক
    15% of x
  2. খ
    10% of x
  3. গ
    25% of x
  4. ঘ
    None of these
ব্যাখ্যা
Question: If 30% of x = y, then y% of 50 is equal to what percentage of x?

Solution:
Here,
30% of x = y       
⇒ 30x/100 = y
∴ y = 3x/10

Now,
y% of 50 = 50y/100
= 50 × (3x/10) × 1/100
= 15x/100
= 15% of x
৮৩০.
A Stationery seller had some Pens, Sharpeners, Erasers & Pencils. He sells 65% of the total units and still has 175 units. Originally, he had-
  1. ক
    588 units
  2. খ
    400 units
  3. গ
    272 units
  4. ঘ
    500 units
ব্যাখ্যা
Question: A Stationery seller had some Pens, Sharpeners, Erasers & Pencils. He sells 65% of the total units and still has 175 units. Originally, he had-

Solution:
Suppose originally he had x units.
Then,
(100 - 65)% of x = 175.
⇒ (35/100) × x = 175
⇒ x = (175 × 100)/35
∴ x = 500
৮৩১.
A shopkeeper fixes the marked price of an item 35% above its cost price. The percentage of discount allowed to gain 8% is = ?
  1. ক
    ক) 20%
  2. খ
    খ) 27%
  3. গ
    গ) 31%
  4. ঘ
    ঘ) 43%
ব্যাখ্যা

Let C.P.=Tk. 100 
Then, 
 M.P. = Tk. 135,
S.P. =Tk.108
∴Discount %  =(27/135 ×100)% =20%

৮৩২.
A student bought a bag for Tk. 3500 and later sold it for Tk. 4000. Find the profit percentage he earned.
  1. ক
    10%
  2. খ
    14.29%
  3. গ
    18%
  4. ঘ
    25.5%
ব্যাখ্যা
Question: A student bought a bag for Tk. 3500 and later sold it for Tk. 4000. Find the profit percentage he earned.

Solution:
Here,
CP = 3500, and SP = 4000
As SP > CP,

∴ Profit = SP - CP
= (4000 - 3500)
= 500

Profit% = (500/3500) ×100%
= 100/7 %
= 14.29%
৮৩৩.
The school has a total of 800 students. Yesterday, 12% of the boys and 18% of the girls were absent, and today 10% of the boys and 15% of the girls are absent. If today, 20 more students are present than yesterday, then find the total number of boys in the school.
  1. ক
    400
  2. খ
    380
  3. গ
    420
  4. ঘ
    540
  5. ঙ
    370
ব্যাখ্যা

Question: The school has a total of 800 students. Yesterday, 12% of the boys and 18% of the girls were absent, and today 10% of the boys and 15% of the girls are absent. If today, 20 more students are present than yesterday, then find the total number of boys in the school.

Solution:
Let the Boys = B and the Girls = G
Then B + G = 800 ....... (1)

ATQ,
If absent 10% of boys and 15% of girls
So, present = 90% of boys and 85% of girls
⇒ 90% B + 85% G ........ (2)

If absent = 12% of boys and 18% of girls
So, present = 88% of boys and 82% of girls
⇒ 88% B + 82% G ......... (3)

Subtract equation (3) from (2)
90% B + 85% G - (88% B + 82% G) = 20
⇒ 2% B + 3% G = 20
⇒ 2B + 3G = 2000
⇒ 2B + 3(800 - B) = 2000 [From equation 1]
⇒ 2B - 3B = 2000 - 2400
∴ B = 400

৮৩৪.
40 is subtracted from 60% of a number, the result is 50. Find the number?
  1. ক
    ক) 150
  2. খ
    খ) 140
  3. গ
    গ) 130
  4. ঘ
    ঘ) 110
ব্যাখ্যা

Let the number be x
The problem could be 40 is subtracted from 60% of a number, the result is 50.
60% of x = 60/100×x= 60x/100
60x/100 - 40 = 50
(60x - 4000) /100 = 50
Cross multiplication
60x - 4000 = 50 ×100
60x -4000 = 5000
60x = 5000 + 4000
60x = 9000
x = 9000/60
x = 150
Hence, the number is 150

৮৩৫.
A merchant marks his goods 40% above the cost price and sell them at a discount of 15%. Find his gain % = ?
  1. ক
    19%
  2. খ
    20%
  3. গ
    22%
  4. ঘ
    25%
ব্যাখ্যা
Let the cost price = Tk. 100
Marked price = Tk. 140
At a 15% discount, selling price = Tk. (140 × 85/1000) = Tk. 119
Therefore, profit = 119 - 100 = Tk. 19 
Profit % = 19/100 ×100 = 19%
৮৩৬.
After receiving a 25% discount, Sue paid $180 for a lawnmower. What is the original price of the lawnmower before the discount?
  1. ক
    ক) $215
  2. খ
    খ) $220
  3. গ
    গ) $225
  4. ঘ
    ঘ) $240
ব্যাখ্যা
Question: After receiving a 25% discount, Sue paid $180 for a lawnmower. What is the original price of the lawnmower before the discount?

Solution: 
ঘাস কাটা যন্ত্রটির দাম x ডলার
২৫% ছাড়ে , দাম = x - ০.২৫x ডলার 
= ০.৭৫x

 ০.৭৫x = ১৮০
∴ x = ১৮০/০.৭৫ 
= ২৪০ ডলার 
৮৩৭.
Find the number of shares that can be bought for tk. 8200 if the market value is tk. 20 each with brokerage being 2.5%.
  1. ক
    ক) 450
  2. খ
    খ) 500
  3. গ
    গ) 400
  4. ঘ
    ঘ) 300
ব্যাখ্যা

Cost of each share = (20 + 2.5% of 20) = tk.20.5
Therefore, number of shares = 8200/20.5 = 400

৮৩৮.
A trader marks his goods 40% above the cost price and allows a discount of 25%. The profit he makes is:
  1. ক
    5%
  2. খ
    7%
  3. গ
    4%
  4. ঘ
    8%
  5. ঙ
    10%
ব্যাখ্যা
Let original CP = Tk. 100
Then, the Marked Price = 40% of 100 + 100 = 140
SP = 140 - 25% of 140 = 105
%Profit = (5×100)/100 = 5%

Net Graphic Change Method:
100 == 40%
UP ⇒ 140 == 25% discount ⇒ 105
So, % Profit = 5%
৮৩৯.
From a container having pure milk, 20% is replaced by water and the process is repeated thrice. At the end of the third operation, the milk is :
  1. ক
    ক) 40% pure
  2. খ
    খ) 50% pure
  3. গ
    গ) 51.2% pure
  4. ঘ
    ঘ) 58.8% pure
ব্যাখ্যা

Let total quantity of original milk = 1000 gm
Milk after first operation = 80% of 1000 = 800 gm
Milk after second operation = 80% of 800 = 640 gm
Milk after third operation = 80% of 640 = 512 gm
∴ Strength of final mixture = 51.2%

৮৪০.
The marked price of an article is Tk. 500. It is sold on two successive discounts of 20% and 10%. The selling price of that article is -
  1. ক
    ক) Tk. 350
  2. খ
    খ) Tk. 375
  3. গ
    গ) Tk. 360
  4. ঘ
    ঘ) Tk. 400
ব্যাখ্যা
Given that, 
The marked price of an article is Tk. 500.
Two successive discounts of 20% and 10%
discounts of 20% The selling price of that article is = 500×80/100
                                                                                   = 400
again,
10% discounts of 400 and the selling price of that article is=400×90/100
                                                                                             = 360 Tk.
৮৪১.
Fedora Technologies acquired 60 hard-drives and tried selling them at BDT 2400 apiece at 20 percent markup on cost price. After 3 months, 6 remained unsold and were returned to manufacturer at 50 percent refund of cost. Find out Fedora's approximate profit margin as a percentage of initial acquisition cost of the 60 hard-drives.
  1. ক
    5%
  2. খ
    7.5%
  3. গ
    10%
  4. ঘ
    12.5%
  5. ঙ
    None
ব্যাখ্যা

Question: Fedora Technologies acquired 60 hard-drives and tried selling them at BDT 2400 apiece at 20 percent markup on cost price. After 3 months, 6 remained unsold and were returned to manufacturer at 50 percent refund of cost. Find out Fedora's approximate profit margin as a percentage of initial acquisition cost of the 60 hard-drives.

Solution:
ধরি,
প্রতি ইউনিটের ক্রয়মূল্য = x

Markup ২০%, অর্থাৎ,
বিক্রয়মূল্য = 1.2x = 2400
⇒ x = 2400/1.2​
= (2400 × 10)/12
= 2000 টাকা

অতএব,
প্রতি হার্ডড্রাইভের ক্রয়মূল্য = ২০০০ টাকা
∴ মোট ক্রয়মূল্য = 60 × 2000 = 120000 টাকা

আবার,
বিক্রিত হার্ডড্রাইভ = 60 - 6 = 54
প্রতি হার্ডড্রাইভ বিক্রয়মূল্য = 2400 টাকা
∴ মোট বিক্রয়মূল্য =54 × 2400 = 129600

অবিক্রিত 6টি ফেরত দিয়ে,
রিফান্ড = 6 × (50% × 2000)
= 6 × 1000
= 6000 টাকা

∴ মোট আয় = (বিক্রয় + রিফান্ড)
= 129600 + 6000
= 135600 টাকা

∴  লাভ = 135600 - 120000 = 15600 টাকা

∴  লাভের হার = (15600/120000) × 100 = 13%

৮৪২.
An article when sold at a gain of 5% yields Tk. 15 more than when sold at a loss of 5%. Its cost price would be
  1. ক
    ক) Tk 100
  2. খ
    খ) Tk 150
  3. গ
    গ) Tk 200
  4. ঘ
    ঘ) Tk 250
ব্যাখ্যা

At 5% profit, selling price = 100+5 = 105 tk
At 5% loss, selling price = 100-5 = 95 tk
Difference between selling price = 105-95 = 10 tk
When the difference 10, buying price is 100 tk
∴ When the difference is 15, buying price is (100×15)/10 tk = 150 tk

৮৪৩.
An error 4% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
  1. ক
    2.02%
  2. খ
    4.04%
  3. গ
    6.08%
  4. ঘ
    8.16%
  5. ঙ
    None of them
ব্যাখ্যা

Question: An error 4% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:

Solution: 

100 cm is read as 104 cm.
∴ A1 = (100 x 100) sq. cm and A2 (104 x 104) sq. cm

Now,
(A2 - A1) = [(104)2 - (100)2]
= (104 + 100) x (104 - 100)
= 816 sq. cm

Percentage error in area = [(A2 - A1)/A1] × 100
= [816/(100 x 100)] × 100%
= 8.16% 

৮৪৪.
A man's salary was reduced by 50%, again the reduce salary was increased by 50%. Find the loss of in terms of percentage.
  1. ক
    ক) 25%
  2. খ
    খ) 50%
  3. গ
    গ) 75%
  4. ঘ
    ঘ) No loss
ব্যাখ্যা
ধরি 
বেতন ছিল 100 টাকা 
 50% কমে বেতন হবে =100−50=50 টাকা 
50% বৃদ্ধিতে বেতন হবে = 50 + 50 এর 50%
                                     = 50 + 50 এর 50/100
                                     = 50 + 25 
                                    = 75 টাকা 

শতকরা ক্ষতি = (100 - 75) টাকা 
                      = 25 টাকা
৮৪৫.
In a class 75% passed in English, 60% passed in Mathematics & 25% failed in both subjects. What is the percentage who passed in both subjects?
  1. ক
    50%
  2. খ
    55%
  3. গ
    60%
  4. ঘ
    45%
ব্যাখ্যা
Question: In a class 75% passed in English, 60% passed in Mathematics & 25% failed in both subjects. What is the percentage who passed in both subjects?  

Solution: 
25% failed in both subjects
So, Rest 75% passed at least in one subject.

∴ The percentage who passed in both subjects is = 60% + 75% - 75% 
= 60%
৮৪৬.
A washing machine is marked at 3600 tk and sold for 3312 tk. What are the discount percentage?
  1. ক
    6%
  2. খ
    8%
  3. গ
    9%
  4. ঘ
    12%
ব্যাখ্যা
Question: A washing machine is marked at 3600 tk and sold for 3312 tk. What are the discount percentage?

Solution:
Given
Marked Price = 3600
Selling Price = 3312
∴ Discount = M. P - S. P = 3600 - 3312 = 288 tk

So, Discount Percent = (Discount/M .P) × 100
= (288/3600) × 100
= 8%
৮৪৭.
A shopkeeper sells 15 notebooks for Tk. 720 and incurs a loss equal to the cost price of 5 notebooks. What is the cost price of one notebook?
  1. ক
    Tk. 62
  2. খ
    Tk. 72
  3. গ
    Tk. 82
  4. ঘ
    Tk. 102
ব্যাখ্যা

Question: A shopkeeper sells 15 notebooks for Tk. 720 and incurs a loss equal to the cost price of 5 notebooks. What is the cost price of one notebook?

Solution:
Let,
Cost price of 1 notebook = Tk. x

∴ Cost price of 15 notebooks = Tk. 15x
∴ Cost price of 5 notebooks = Tk. 5x

We know,
Loss = Cost price − Selling price

According to the question,
5x = 15x − 720
⇒ 15x − 5x = 720
⇒ 10x = 720
⇒ x = 720/10
⇒ x = 72

∴ The cost price of 1 notebook is Tk. 72

৮৪৮.
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.
  1. ক
    Tk. 6876.1
  2. খ
    Tk. 6995.4
  3. গ
    Tk. 7000
  4. ঘ
    None of these
ব্যাখ্যা
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
৮৪৯.
একজন ব্যবসায়ী তার দোকানের ৮০% কাপড় ২০% লাভে বিক্রি করে এবং বাকি ২০% কাপড় ২০% ক্ষতিতে বিক্রি করলে মোটের উপর তার কত টাকা লাভ বা ক্ষতি হবে?
  1. ক
    ১২% লাভ
  2. খ
    ১২% ক্ষতি
  3. গ
    ১৬% লাভ
  4. ঘ
    ১৬ ক্ষতি
  5. ঙ
    কোনোটিই নয়
ব্যাখ্যা
প্রশ্ন: একজন ব্যবসায়ী তার দোকানের ৮০% কাপড় ২০% লাভে বিক্রি করে এবং বাকি ২০% কাপড় ২০% ক্ষতিতে বিক্রি করলে মোটের উপর তার কত টাকা লাভ বা ক্ষতি হবে?

সমাধান:
ধরি,
মোট কাপড় = ১০০
প্রতিটির ক্রয়মূল্য = ১০০
গড় বিক্রয়মূল্য = ক

২০% লাভে বিক্রয়মূল্য = ১২০ টাকা
২০% ক্ষতিতে বিক্রয়মূল্য = ৮০ টাকা

এখন,
(৮০ × ১২০) + (২০ × ৮০) = (১০০ × ক)
⇒ ৯৬০০ + ১৬০০ = ১০০ক
⇒ ১০০ক = ১১২০০
∴ ক = ১১২ টাকা

গড়ে লাভ = (১১২ - ১০০) = ১২ টাকা
∴ শতকরা লাভ = (১২ × ১০০)/১০০ = ১২%
৮৫০.
In an examination, it is required to get 40% of the aggregate marks to pass. A student gets 261 marks and is declared failed by 4% marks. What are the maximum aggregate marks a student can get?
  1. ক
    600
  2. খ
    725
  3. গ
    850
  4. ঘ
    900
ব্যাখ্যা
Question: In an examination, it is required to get 40% of the aggregate marks to pass. A student gets 261 marks and is declared failed by 4% marks. What are the maximum aggregate marks a student can get?

Solution: 
let, aggregate marks x 

ATQ,
0.4x - .04x = 261
⇒ 0.36x = 261 
⇒ x = 261/0.36 = 725 
৮৫১.
A sum of money amounts to tk 460 in 3 years and to tk 500 in five years. Find the rate percent per amount -
  1. ক
    8 Tk
  2. খ
    4 Tk
  3. গ
    7 Tk
  4. ঘ
    10 Tk
  5. ঙ
    5 Tk
ব্যাখ্যা
After 5 years the sum = 500 tk

After 3 years the sum = 460 tk

The interest of 2 years = 500-460= 40 tk

The interest of 3 years, I = 40x(3/2) = 60 tk

The principle, P = 460-60 = 400 tk

 so,The rate= I/Pn = 60/(400x3) = 5%
৮৫২.
There is 12% salt in 300 mm mixture. If 200 mm water is added to it, then what percentage of salt is there in the new mixture?
  1. ক
    ক) 5.2%
  2. খ
    খ) 7%
  3. গ
    গ) 7.2%
  4. ঘ
    ঘ) 7.5%
ব্যাখ্যা
In 300 mm mixture, amount of salt = 12% of 300 = 36 mm
If 200 mm water is added to it, total mixture = 200 + 300 = 500 mm
Therefore, amount of salt percentage = 36/500 × 100% = 7.2%
৮৫৩.
The cost price of a table and a chair together is Tk. 690. If the table costs 30% more than the chair, then find the cost price of the table and the chair respectively .
  1. ক
    ক) Tk. 300 and Tk. 390
  2. খ
    খ) Tk. 390 and Tk. 300
  3. গ
    গ) Tk. 480 and Tk. 210
  4. ঘ
    ঘ) Tk. 400 and Tk. 290
ব্যাখ্যা
ধরি,
একটি চেয়ারের মূল্য x টাকা
একটি টেবিলের মূল্য = x + x এর 30% = x +  x এর 30/100
                                 = x + 3x/10
                                 = (10x + 3x)/10
                                   = 13x/10 

প্রশ্নমতে,
x + 13x/10 = 690
23x/10 = 690 
23x = 690 × 10 
x =( 690 × 10 )/23
x = 300 টাকা 

একটি চেয়ারের মূল্য 300 টাকা
একটি টেবিলের মূল্য = (13 × 300)/10 = 390 টাকা
৮৫৪.
A tradesman by means of a false balance defrauds to the extent of 8% in buying goods and also defrauds to 8% in selling. His gain percent is:
  1. ক
    ক) 15.48%
  2. খ
    খ) 16%
  3. গ
    গ) 16.64%
  4. ঘ
    ঘ) 18%
  5. ঙ
    ঙ) 22%
ব্যাখ্যা

Since he make 8% profit so his purchase = 100 + 8 = 108
He make 8% more profit during sales so his sales = (108/100) × 108 = 116.64
so profit = 116.64 - 100
= 16.64
Short Cut (with increase decrease short cut)
X + Y + (xy/100)
= 8 + 8 + (8×8/100) ( since he his making profit so count is as a increase)
= 16.64

৮৫৫.
At a certain boutique, profit is calculated as 80% of the cost. When the cost increases by 20% and the selling price stays the same, how much does the profit percentage diminish?
  1. ক
    35%
  2. খ
    25%
  3. গ
    20%
  4. ঘ
    30%
ব্যাখ্যা
Question: At a certain boutique, profit is calculated as 80% of the cost. When the cost increases by 20% and the selling price stays the same, how much does the profit percentage diminish?

Solution:
Let us assume CP = Tk. 100.
Then Profit = Tk. 80 and selling price = Tk. 180

The cost increases by 20%
∴ New CP = Tk. 120,
SP = Tk. 180.

∴ Profit = 180 - 120 = Tk. 60
Profit % = (60/120) × 100% = 50%.

Therefore, Profit decreases by (80 - 50)% = 30%
৮৫৬.
The cost of a book was Tk. 75. The cost was first increased by 20% and later on it was reduced by 20%. The present cost of the book is:
  1. ক
    Tk. 65
  2. খ
    Tk. 72
  3. গ
    Tk. 75
  4. ঘ
    Tk. 80
ব্যাখ্যা
Question: The cost of a book was Tk. 75. The cost was first increased by 20% and later on it was reduced by 20%. The present cost of the book 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.
৮৫৭.
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:
  1. ক
    150
  2. খ
    160
  3. গ
    175
  4. ঘ
    200
ব্যাখ্যা
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.
৮৫৮.
A shopkeeper incurs a loss by selling an article for Tk 550. If he had sold it for Tk 850, he would have made a profit which is four times the initial loss. At what price should he sell the article to make 10% profit?
  1. ক
    Tk. 650
  2. খ
    Tk. 671
  3. গ
    Tk. 690
  4. ঘ
    Tk. 710
ব্যাখ্যা

Question: A shopkeeper incurs a loss by selling an article for Tk 550. If he had sold it for Tk 850, he would have made a profit which is four times the initial loss. At what price should he sell the article to make 10% profit?

Solution:
ধরি, পণ্যের ক্রয়মূল্য = x টাকা
550 টাকায় বিক্রি করলে ক্ষতি = x - 550 টাকা
850 টাকায় বিক্রি করলে লাভ = 850 - x টাকা

প্রশ্নমতে,
850 - x = 4(x - 550)
⇒ 850 - x = 4x - 2200
⇒ 850 + 2200 = 4x + x
⇒ 3050 = 5x
∴ x = 610 টাকা

এখন,
10% লাভে,
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য 110 টাকা
ক্রয়মূল্য 1 টাকা হলে বিক্রয়মূল্য (110/100) টাকা
∴ ক্রয়মূল্য 610 টাকা হলে বিক্রয়মূল্য (110 × 610)/100 টাকা
= 671 টাকা

৮৫৯.
Selling a dozen of bananas for a taka causes a loss of 25%. How many bananas do you have to sell for a taka to get 50% profit?
  1. ক
    8
  2. খ
    6
  3. গ
    10
  4. ঘ
    5
ব্যাখ্যা
Let x bananas be purchased  for a Taka, causing 25% loss.
x/12 = 75/100
x = (75/100) * 12
x = 9

Let y bananas be sold for a Taka to get 50% profit.
y/9 = 100/150
y = (100/150)*9
y = 6

বিকল্প:
ক্রয়মূল্য ১০০ টাকা হলে,
২৫% ক্ষতিতে বিক্রয়মূল্য = ১০০-২৫ = ৭৫ টাকা।
৫০% লাভে বিক্রয়মূল্য = ১০০+৫০ = ১৫০ টাকা।
পূর্বের বিক্রয়মূল্য ৭৫ টাকা হলে বিক্রয় করতে হবে ১৫০ টাকায়।
পূর্বের বিক্রয়মূল্য ১ টাকা হলে বিক্রয় করতে হবে ১৫০/৭৫ = ২ টাকায়।
২ টাকায় বিক্রি করতে হবে = ১২ টি কলা।
১ টাকায় বিক্রি করতে হবে = ১২/২ = ৬ টি কলা।
৮৬০.
25% of 25% is equal to-
  1. ক
    ক) 0.0625
  2. খ
    খ) 0.0210
  3. গ
    গ) 0.0525
  4. ঘ
    ঘ) 0.0725
  5. ঙ
    ঙ) 0.0825
ব্যাখ্যা

25% of 25%
= 0.25 × 0.25
= 0.0625

৮৬১.
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?
  1. ক
    Tk. 19125 
  2. খ
    Tk. 12875 
  3. গ
    Tk. 5875 
  4. ঘ
    None of these
ব্যাখ্যা
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 
৮৬২.
The cost price of the goods for a shopkeeper was X. He marked them at a 20% higher price than the Cost Price. Finally he sold the goods at a 30% discount. Did he earn a profit or incur a loss? How much?
  1. ক
    ক) 5%Profit
  2. খ
    খ) 5.5%Profit
  3. গ
    গ) 10%Loss
  4. ঘ
    ঘ) 16%Loss
ব্যাখ্যা

Let C.P. = Tk. 100.
Marked Price = 20% more than C.P.
∴ M.P. = Tk. 120
Discount = 30% on marked price
∴ S.P. = (100-30)% of M.P.
∴ S.P. = (70/100) × 120 = Tk. 84

Loss% = (100 - 84)/100 × 100
= 16%

৮৬৩.
A fruit seller buys lemons at a rate of 2 lemons for a Taka and sells them at a rate of 5 lemons for 3 Taka. What is her profit margin (based on cost price)?
  1. ক
    ক) 10%
  2. খ
    খ) 15%
  3. গ
    গ) 20%
  4. ঘ
    ঘ) 30%
ব্যাখ্যা
Question: A fruit seller buys lemons at a rate of 2 lemons for a Taka and sells them at a rate of 5 lemons for 3 Taka. What is her profit margin (based on cost price)?

Solution:
The cost price of 2 lemons = 1 Tk
The cost price of 1 lemon = 1/2 Tk

Then,
The selling price of 5 lemons = 3 Tk
The selling price of 1 lemon = 3/5 Tk

So, profit = 3/5 - 1/2 = 1/10 Tk

Hence, profit percentage = {(1/10)/(1/2)} × 100 = 20%
৮৬৪.
A year ago the price of a toothbrush and the price of a comb were both Tk. 50. The price of the toothbrush was increased by 20% while the price of the com was decreased by 10%. What is the difference in Taka between the current price of the toothbrush and the comb?
  1. ক
    5
  2. খ
    10
  3. গ
    15
  4. ঘ
    20
ব্যাখ্যা
Question: A year ago the price of a toothbrush and the price of a comb were both Tk. 50. The price of the toothbrush was increased by 20% while the price of the com was decreased by 10%. What is the difference in Taka between the current price of the toothbrush and the comb?

Solution:
Original price of the toothbrush: Tk. 50
Price increase: 20%
New price of toothbrush = 50 + {(20/100) ​× 50} = 50 + 10 = Tk. 60

Original price of the comb: Tk. 50
Price decrease: 10%
New price of comb = 50 - {(10/100) × 50} = 50 - 5 = Tk. 45

Difference = 60 - 45 = Tk. 15
The difference in Taka between the current price of the toothbrush and the comb is Tk. 15.
৮৬৫.
An article when sold at a gain of 5% yields Tk. 15 more than when sold at a loss of 5%. lts cost price would be:
  1. ক
    Tk. 150
  2. খ
    Tk. 200
  3. গ
    Tk. 250
  4. ঘ
    Tk. 300
ব্যাখ্যা
Question: An article when sold at a gain of 5% yields Tk. 15 more than when sold at a loss of 5%. lts cost price would be:

Solution:
5% ক্ষতিতে বিক্রয়মূল্যে = 100 - 5 = 95 টাকা
5% লাভে বিক্রয়মূল্যে = 100 + 5 = 105 টাকা

বিক্রয়মূল্যের পার্থক্য = 105 - 95 = 10 টাকা

বিক্রয়মূল্য 10 টাকা বেশি হয় যখন ক্রয়মূল্য 100 টাকা
বিক্রয়মূল্য 1 টাকা বেশি হয় যখন ক্রয়মূল্য 100/10 টাকা
বিক্রয়মূল্য 15 টাকা বেশি হয় যখন ক্রয়মূল্য (100/10) × 15 = 150 টাকা
৮৬৬.
A shopkeeper marks up his goods by 50% above the cost price. He then offers a discount of 20% on the marked price. What is the overall percentage profit? 
  1. ক
    10%
  2. খ
    15%
  3. গ
    20%
  4. ঘ
    25%
ব্যাখ্যা

Question: A shopkeeper marks up his goods by 50% above the cost price. He then offers a discount of 20% on the marked price. What is the overall percentage profit?

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

Marked Price = 50% more than cost price
= 100 + 50
= Tk. 150

Discount = 20% of 150
= (20/100) × 150
= Tk. 30

Selling Price (SP) = 150 - 30 = Tk. 120
∴ Profit = SP - CP = 120 - 100 = Tk. 20

∴ Overall percentage profit = (profit/cost price) × 100%
= (20/100) × 100%
= 20%

৮৬৭.
If 4 (A's capital) = 6 (B's capital) = 10 (C's capital), then out of a profit of TK. 4650, C will receive:
  1. ক
    ক) TK. 900
  2. খ
    খ) TK. 1550
  3. গ
    গ) TK. 2250
  4. ঘ
    ঘ) TK. 465
ব্যাখ্যা

Let's, 4A = 6B = 10C = x
Now, A = x/4; B = x/6; C = x/10
So, A : B : C = x/4 : x/6 : x/10 
                    = x/4 × 60 : x/6 × 60 : x/10 × 60
                    = 15 : 10 : 6
 ∴ Profit of C = 4650 × 6/(15+10+6) = 900Tk.

৮৬৮.
A fruit seller had some apples. He sells 40% apples and still has 450 apples. Originally, he had:
  1. ক
    ক) 700
  2. খ
    খ) 750
  3. গ
    গ) 800
  4. ঘ
    ঘ) 850
ব্যাখ্যা
Suppose originally he had x apples.
Then, (100 - 40)% of x = 450
60% of x = 450
60x/100 = 450 
3x/5 = 450 
x = (450 × 5)/3
x = 750
৮৬৯.
What percentage of numbers from 1 to 50 has 2 or 9 in the unit digits? 
  1. ক
    23%
  2. খ
    32%
  3. গ
    20%
  4. ঘ
    25%
ব্যাখ্যা

Question: What percentage of numbers from 1 to 50 has 2 or 9 in the unit digits?

Solution:
Numbers from 1 to 50 has 2 or 9 in the unit digits
= 2, 9, 12, 19, 22, 29, 32, 39, 42, 49
= 10 Numbers

∴ Amount in percentage
= 10/50 × 100%
= 20%

৮৭০.
A shopkeeper takes 10% profit on his goods. He lost 20% of his goods during a theft. What is his loss percent?
  1. ক
    ক) 12%
  2. খ
    খ) 10%
  3. গ
    গ) 11%
  4. ঘ
    ঘ) 19%
ব্যাখ্যা
প্রশ্ন: A shopkeeper takes 10% profit on his goods. He lost 20% of his goods during a theft. What is his loss percent?

সমাধান: 
ধরি,
দোকানদারের পণ্যের পরিমাণ ক সংখ্যক
প্রতিটি পণ্যের ক্রয় মূল্য খ টাকা
∴ ক সংখ্যক পণ্যের ক্রয় মূল্য = কখ টাকা

২০% চুরি হওয়ার পর পণ্য বাকি থাকে = ক - (২০ক/১০০) সংখ্যক
= ৪ক/৫ সংখ্যক

১০% লাভে,
ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য = ১১০ টাকা
∴ ক্রয়মূল্য ১ টাকা হলে বিক্রয়মূল্য = ১১০/১০০ টাকা
∴ ক্রয়মূল্য কখ টাকা হলে বিক্রয়মূল্য =  ১.১কখ টাকা

ক সংখ্যক পণ্যের বিক্রয় মূল্য = ১.১কখ টাকা
∴ ১টি পণ্যের বিক্রয় মূল্য = ১.১কখ/ক = ১.১খ টাকা 
∴ ৪ক/৫ সংখ্যক পণ্যের বিক্রয় মূল্য = ৪.৪কখ/৫ টাকা 

সুতরাং,
ক্ষতি = কখ - ৪.৪কখ/৫
= ০.৬কখ/৫ টাকা

কখ টাকায় ক্ষতি হয় = ০.৬কখ/৫ টাকা
∴ ১ টাকায় ক্ষতি হয় = ০.৬/৫ টাকা 
∴ ১০০ টাকায় ক্ষতি হয় = (০.৬/৫) × ১০০ টাকা 
= ১২ টাকা 
৮৭১.
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:
  1. ক
    38
  2. খ
    16
  3. গ
    50
  4. ঘ
    80
ব্যাখ্যা

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:
 
Answer:
Let,
The cost price of each article is Taka 1
∴ Cost Price of x articles = x Taka

Selling Price of x articles = 20 Taka
∴ Profit = (20 - x) Taka

x টাকায় লাভ হয় 20 - x টাকা
∴ 1 টাকায় লাভ হয় (20 - x)/ x টাকা
∴ 100 টাকায় লাভ হয় = [(20 - x) × 100]/x টাকা
    
প্রশ্নমতে,
[(20 - x) × 100]/x = 25
⇒ 100(20-x) = 25x
⇒ 125x = 2000
∴ x = 2000/125
= 16

আরেকভাবে,
মনে করি, প্রতিটি আর্টিকেলের ক্রয়মূল্য (cost price) = ১০০ টাকা।
তাহলে ২০টি আর্টিকেলের ক্রয়মূল্য = ২০ × ১০০ = ২০০০ টাকা।

প্রশ্ন অনুসারে, এই ২০০০ টাকা x টি আর্টিকেলের বিক্রয়মূল্য (selling price) এর সমান।

লাভ ২৫% হলে,
ক্রয়মূল্য (cost price) = ১০০ টাকা। হলে,
অর্থাৎ, প্রতি আর্টিকেলের বিক্রয়মূল্য (SP) = ১২৫ টাকা।

তাহলে x টি আর্টিকেলের SP = x × ১২৫
ATQ,
 x × ১২৫  = ২০০০
⇒ x = ২০০০/১২৫
∴ x = ১৬ টাকা

৮৭২.
What is 55% of 12/66 of 270? 
  1. ক
    14
  2. খ
    12
  3. গ
    11
  4. ঘ
    10
  5. ঙ
    None of these
ব্যাখ্যা
Question: What is 55% of 12/66 of 270? 

Solution:
55% of 12/66 of 270
= (55/100) × (12/66) × 270
= 27
৮৭৩.
Two friends, Akash & Beenu had some candies each. One of them had 15 candies more than the other. The candies with Akash was 60% of the total candies with them. How many candies did each have?
  1. ক
    40, 25
  2. খ
    47, 32
  3. গ
    45, 30
  4. ঘ
    49, 34
ব্যাখ্যা
Question: Two friends, Akash & Beenu had some candies each. One of them had 15 candies more than the other. The candies with Akash was 60% of the total candies with them. How many candies did each have?

Solution:
Let the candies with be (x + 15) and x.
Therefore, x + 15 = (60/100) × (x + 15 + x)
⇒ (x + 15) = (3/5)(2x + 15)
⇒ 5x + 75 = 6x + 45
∴ x = 30

So, the candies of two friends are 45 and 30.
৮৭৪.
A $140 book is marked down by 25% and then by another 10%. What is final sale cost?
  1. ক
    $92.50
  2. খ
    $94.50
  3. গ
    $96.25
  4. ঘ
    $98.25
ব্যাখ্যা
Question: A $140 book is marked down by 25% and then by another 10%. What is final sale cost?

Solution:
১০০ টাকায় ছাড় ২৫ টাকা
১ টাকায় ছাড় ২৫/১০০ = ১/৪ টাকা
১৪০ টাকায় ছাড় ১৪০/৪ = ৩৫ টাকা

∴ প্রথম ছাড়ের পর মূল্য = ১৪০ - ৩৫ = ১০৫

আবার,
১০০ টাকায় ছাড় ১০ টাকা
১ টাকায় ছাড় ১০/১০০ = ১/১০ টাকা
১০৫ টাকায় ছাড় ১০৫/১০ = ১০.৫ টাকা

∴ চূড়ান্ত বিক্রয় মূল্য = ১০৫ - ১০.৫০ = ৯৪.৫০​
৮৭৫.
A man bought some eggs of which 10% are rotten. He gives 80% of the remainder to his neighbor. Now he is left out with 36 eggs. How many eggs he bought?
  1. ক
    40
  2. খ
    72
  3. গ
    100
  4. ঘ
    200
ব্যাখ্যা
Question: A man bought some eggs of which 10% are rotten. He gives 80% of the remainder to his neighbor. Now he is left out with 36 eggs. How many eggs he bought?
 
Solution: 
Let he bought 100 eggs.
Eggs after removing rotten one = 90.
Eggs given to neighbour = 80% of 90 = 72 eggs.
Now he left with eggs = 90 - 72 = 18 eggs.
 
Remain 18 eggs when total eggs 100
∴ Remain 1 egg when total eggs 100/18
∴ Remain 36 eggs when total eggs (100 × 36)/18 = 200

So, he bought 200 eggs.
৮৭৬.
25% of 30% Is equal to-
  1. ক
    0.0625
  2. খ
    0.075
  3. গ
    0.03145
  4. ঘ
    0.3210
ব্যাখ্যা
Question: 25% of 30% Is equal to-

Solution:
25% of 30%
= (25/100) × (30/100)
= (1/4) × (3/10)
= 3/40
= 0.075
৮৭৭.
By selling a book at 600 taka, Salim makes a profit of 25%. What was the cost of the book in taka?
  1. ক
    ক) 480
  2. খ
    খ) 500
  3. গ
    গ) 520
  4. ঘ
    ঘ) 540
  5. ঙ
    ঙ) None of these
ব্যাখ্যা
Question: By selling a book at 600 taka, Salim makes a profit of 25%. What was the cost of the book in taka?

Solution: 
25% লাভে 
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য 100 + 25 টাকা   = 125 টাকা 

বিক্রয়মূল্য 125 টাকা হলে ক্রয়মূল্য 100 টাকা 
বিক্রয়মূল্য 1 টাকা হলে ক্রয়মূল্য 100/125 টাকা 
বিক্রয়মূল্য l টাকা হলে ক্রয়মূল্য (100 × 600)/125 টাকা 
= 480 টাকা 
৮৭৮.
A man buys Tk. 25 shares paying 8% dividend. The man wants to have an interest of 10% on his money. The market value of each share is-
  1. ক
    Tk. 10
  2. খ
    Tk. 20
  3. গ
    Tk. 15
  4. ঘ
    Tk. 18
  5. ঙ
    Tk. 13
ব্যাখ্যা
Problem: A man buys Tk. 25 shares paying 8% dividend. The man wants to have an interest of 10% on his money. The market value of each share is-

Solution:
Dividend on Tk. 25 = Tk. (8/100) × 25
= Tk. 2

Tk. 10 is an income on = Tk. 100.
∴ Tk. 2 is an income on = Tk. 100/(10 × 2)
= Tk. 20
৮৭৯.
A man spends 75% of his income. His income has increased by 20% and he has increased his expenses by 10%. His saving are increased by
  1. ক
    ক) 50%
  2. খ
    খ) 37.50%
  3. গ
    গ) 25%
  4. ঘ
    ঘ) 10%
ব্যাখ্যা

Let his initial income is 100 taka
He spends = 75 taka
So, his savings is = 100 - 75 = 25 taka
Income increases by 20%
So new income is 120 taka
At 10% increase, the expense is = 75 + 10% of 75 = 83.5
So, now the savings is = 120 - 83.5 = 37.5
His savings increases = 37.5 - 25 = 12.5 taka
In percent = (12.5×100) / 25 = 50%

৮৮০.
A shopkeeper sells a badminton racket, whose marked price is Tk.200, at a discount of 15% and gives a shuttle cock costing Tk.20 free with each racket. Even then he makes a profit of 25%. His cost price per racket is-
  1. ক
    ক) 150 Tk.
  2. খ
    খ) 140 Tk.
  3. গ
    গ) 130 Tk.
  4. ঘ
    ঘ) 120 Tk.
ব্যাখ্যা
Question: A shopkeeper sells a badminton racket, whose marked price is Tk.200, at a discount of 15% and gives a shuttle cock costing Tk.20 free with each racket. Even then he makes a profit of 25%. His cost price per racket is-

Solution:
Marked price = 200 tk
After 15% discount selling price = (100 - 15)% of 200
= 85% of 200
= (85/100) × 200
= 170
cost of shuttle cock 20 Tk
so, actual selling price = 170 - 20 tk
= 150 tk

let, cost price per racket is x tk
at 25% profit, selling price = 1.25x tk

So, 1.25x = 150
⇒ x = 150/1.25
= 120 Tk

His cost price per racket is 120 Tk
৮৮১.
The marked price of a bag is Tk. 500, and a 15% discount is offered on it. Find the selling price.
  1. ক
    Tk. 415
  2. খ
    Tk. 420
  3. গ
    Tk. 425
  4. ঘ
    Tk. 430
ব্যাখ্যা
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.
৮৮২.
The price of a car depreciates in the first year by 25% in the second year by 20% in third year by 15% and so on. The final price of the car after 3 years, if the present cost of the car is Tk. 10,00,000-
  1. ক
    7,80,000
  2. খ
    1,70,000
  3. গ
    6,90,000
  4. ঘ
    5,10,000
ব্যাখ্যা
Question: The price of a car depreciates in the first year by 25% in the second year by 20% in third year by 15% and so on. The final price of the car after 3 years, if the present cost of the car is Tk. 10,00,000-

Solution:
The final price of the car after 3 years = 1000000 × 0.75 × 0.80 × 0.85
= Tk. 5,10,000
৮৮৩.
In a country 55% population is female. 80% of the male population is literate. How much of females are literate if total literacy is 58%?
  1. ক
    38%
  2. খ
    36%
  3. গ
    40%
  4. ঘ
    43%
  5. ঙ
    46%
ব্যাখ্যা
Question: In a country 55% population is female. 80% of the male population is literate. How much of females are literate if total literacy is 58%?

Solution:
Let x = female literacy rate
Male contribution = (Male population % × Male literacy rate)
= 45% × 80%
= 36%

Total literacy = Female contribution + Male contribution
58% = (55% × x) + 36%
⇒ 58% = 55x + 36%
⇒ 58% - 36% = 55x
⇒ 22% = 55x
⇒ x = 22%/55%
⇒ x = 40%

Therefore, the female literacy rate is 40%.
৮৮৪.
In a city 90% of the population own a car, 15% own a motorcycle, and everybody owns one or the other or both. What is the percentage of motorcycle owners who own cars?
  1. ক
    ক) 5%
  2. খ
    খ) 15%
  3. গ
    গ) 33.33%
  4. ঘ
    ঘ) 50%
  5. ঙ
    ঙ) 90%
ব্যাখ্যা
Question: In a city 90% of the population own a car, 15% own a motorcycle, and everybody owns one or the other or both. What is the percentage of motorcycle owners who own cars?

Solution:
Let,
Total number of people = 100
Car owner = 90
Motorcycles owner = 15
Number of people who have No Car, No Motorcycle = 0


Then
Number who do not own a car= 100 - 90 = 10

Number of motorcycle owners who do not own a car = 10 [because 0 own neither Motorcycle and No Car]

Number of car and motorcycle owners = 15 - 10 = 5 

The percentage of motorcycle owners who own cars = (5/15) × 100%
=33.33%
৮৮৫.
If the ratio of principal and yearly amount be in the ratio 25 : 28, then the yearly rate of interest is -
  1. ক
    ক) 10%
  2. খ
    খ) 12%
  3. গ
    গ) 20%
  4. ঘ
    ঘ) 36%
ব্যাখ্যা
Given, principal : yearly amount = 25 : 28
So, interest = 28 - 25 = 3

So, rate of interest
= 3/25 × 100 %
= 12%
৮৮৬.
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 =?
  1. ক
    20% gain
  2. খ
    15% loss
  3. গ
    25% loss
  4. ঘ
    10% gain
ব্যাখ্যা
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 
৮৮৭.
A merchant has 1000 kg of sugar, part of which he sells at 8% and the remaining at 18% profit. He gains 14% on the whole. Find the quantity of sugar that he sold at 18% profit.
  1. ক
    ক) 400kg
  2. খ
    খ) 560kg
  3. গ
    গ) 600kg
  4. ঘ
    ঘ) 640kg
ব্যাখ্যা
Question: A merchant has 1000 kg of sugar, part of which he sells at 8% and the remaining at 18% profit. He gains 14% on the whole. Find the quantity of sugar that he sold at 18% profit.

Solution:
Let the cost price of 1kg of sugar be Tk.100.

The selling price of 1kg sugar sold at 8% profit
⇒ 100 × 108/100 = Tk.108

The selling price of 1kg sugar sold at 18% profit
⇒ 100 × 118/100 = Tk.118

The average selling price of 1kg of sugar
⇒ 100 × 114/100 = Tk.114

Using the rule of the allegation,

The ratio of sugar sold at 8% and 18% profit
⇒ (118 - 114) : (114 - 108)
⇒ 4 : 6 = 2 : 3

∴ Quantity sold at 18% profit = 3/5 × 1000 = 600 kg
৮৮৮.
Of 24 kg of salt water 8% is salt; of another 4% is salt, how many kgs of the second mixture should be added to the first mixture in order to get a mixture that is 5% salt?
  1. ক
    48
  2. খ
    56
  3. গ
    64
  4. ঘ
    72
  5. ঙ
    None of these
ব্যাখ্যা

(C1 × Q1 + C2 × Q2)/(Q1 + Q2) = P
or, (8 × 124 + 4 × Q2)/(24 + Q2) = 5
or, 192 + 4 × Q2 = 120 + 5 × Q2
or, Q2 = 72

৮৮৯.
A village has a population of 8,000. It increases by 10% in the first year and then by 20% in the second year.What will be the population of the village after 2 years?
  1. ক
    10560
  2. খ
    8976
  3. গ
    10500
  4. ঘ
    10650
ব্যাখ্যা
Question: A village has a population of 8,000. It increases by 10% in the first year and then by 20% in the second year.What will be the population of the village after 2 years?

Solution: 
৮৯০.
If a man were to sell his chair for Tk. 720, he would lose 25%. To gain 25% he should sell it for:
  1. ক
    Tk. 1100
  2. খ
    Tk. 1200
  3. গ
    Tk. 1300
  4. ঘ
    Tk. 1400
ব্যাখ্যা
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
৮৯১.
A man bought some eggs of which 10% are rotten. He gives 80% of the remainder to his neighbors. Now he is left out with 36 eggs. Then he ate two eggs. How many eggs did he buy?
  1. ক
    200
  2. খ
    190
  3. গ
    180
  4. ঘ
    210
ব্যাখ্যা
Question: A man bought some eggs of which 10% are rotten. He gives 80% of the remainder to his neighbors. Now he is left out with 36 eggs. Then he ate two eggs. How many eggs did he buy?

Solution:
let, the man bought  x eggs
10% are rotten

so eggs remained = x - x × 10%
= x - x/10
= 9x/10

80% of 9x/10
= (9x/10) × (80/100)
= 18x/25

he is left with = (9x/10) - (18x/25)
= (45x - 36x)/50
= 9x/50

So, (9x/50) = 36
⇒ 9x = 36 × 50
⇒ x = (36 × 50)/9
= 200

∴ He bought 200 eggs
৮৯২.
A buys a product for Tk. 500 and sells it to B at a profit of 25%. B then sells it to C at a profit of 20%. How much does C pay to B?
  1. ক
    Tk. 600
  2. খ
    Tk. 650
  3. গ
    Tk. 720
  4. ঘ
    Tk. 750
ব্যাখ্যা

Question: A buys a product for Tk. 500 and sells it to B at a profit of 25%. B then sells it to C at a profit of 20%. How much does C pay to B?

সমাধান:
A এর 25% লাভে বিক্রয়মূল্য = 500 + 500 এর 25%
= 500 + (500 × 25 / 100)
= 500 + 125
= 625

A এর বিক্রয়মূল্য = B এর ক্রয়মূল্য

B এর 20% লাভে বিক্রয়মূল্য = 625 + 625 এর 20%
= 625 + (625 × 20 / 100)
= 625 + 125
= 750

সুতরাং, B এর বিক্রয়মূল্য = C এর ক্রয়মূল্য = Tk. 750

৮৯৩.
On selling 20 books for 800 Tk, a man incurs a loss equal to the cost price of 4 books. What is the cost price of one book?
  1. ক
    Tk. 45
  2. খ
    Tk. 50
  3. গ
    Tk. 60
  4. ঘ
    Tk. 48
ব্যাখ্যা
Question: On selling 20 books for 800 Tk, a man incurs a loss equal to the cost price of 4 books. What is the cost price of one book?

Solution:
Let,
cost price of 1 book is = Tk. x
cost price of 20 book is = Tk. 20x
We know,
Loss = Cost price - Selling price
⇒ 4x = 20x - 800
⇒ 20x - 4x = 800
⇒ 16x = 800
⇒ x = 800/16
∴ x = 50

So the cost price of one book is Tk. 50
৮৯৪.
On Dhaka- Sylhet highway 7% of the drivers are fined for exceeding the speed limit. However, 80% of the drivers who exceed the speed limit are not fined. What percentage of drivers on this highway exceed the speed limit?
  1. ক
    28
  2. খ
    31
  3. গ
    33
  4. ঘ
    35
ব্যাখ্যা
Question: On Dhaka- Sylhet highway 7% of the drivers are fined for exceeding the speed limit. However, 80% of the drivers who exceed the speed limit are not fined. What percentage of drivers on this highway exceed the speed limit?

Solution:
ধরি,
হাইওয়েতে 100 জন চালক ছিল।

এখন,
গতিসীমা অতিক্রম করার জন্য 7% চালককে জরিমানা করা হয়।
∴ 100 জন চালকের 7% বা 7 জন চালককে জরিমানা করা হয়।

আবার,
চালকদের মধ্যে যারা গতিসীমা অতিক্রম করেছিল তাদের মধ্যে 80% চালককে জরিমানা করা হয়নি।
∴ চালকদের মধ্যে যারা গতিসীমা অতিক্রম করেছিল তাদের মধ্যে 20% চালককে জরিমানা করা হয়।

প্রশ্নমতে,
20% = 7
∴ 1% = 7/20
∴ 100% = (7 × 100)/20
= 35
৮৯৫.
By selling 90 mangoes for Tk.160 a person loses 20%. What is the cost price of nine mangoes?
  1. ক
    ক) Tk. 20
  2. খ
    খ) Tk.15
  3. গ
    গ) Tk. 21
  4. ঘ
    ঘ) Tk.18
ব্যাখ্যা
প্রশ্ন: By selling 90 mangoes for Tk.160 a person loses 20%. What is the cost price of nine mangoes?

সমাধান: 
২০% ক্ষতিতে,
বিক্রয়মূল্য ৮০ টাকা হলে ক্রয়মূল্য ১০০ টাকা 
∴ বিক্রয়মূল্য ১৬০ টাকা হলে ক্রয়মূল্য (১০০ × ১৬০)/৮০ টাকা 
= ২০০ টাকা 

৯০টি আমের ক্রয়মূল্য ২০০ টাকা 
∴ ৯টি আমের ক্রয়মূল্য (২০০ × ৯)/৯০ টাকা 
= ২০ টাকা
৮৯৬.
If 30% of 1520 + 40% of 800 = x % of 5000, find the value of x.
  1. ক
    14.42%
  2. খ
    15.52%
  3. গ
    12.22%
  4. ঘ
    18.82%
ব্যাখ্যা
Question: If 30% of 1520 + 40% of 800 = x % of 5000, find the value of x.

Solution:
30% of 1520 + 40% of 800 = x% of 5000
⇒ (30/100) × 1520 + (40/100) × 800 = (x/100) × 5000
⇒ 456 + 320 = 50x
⇒ 50x = 776
⇒ x = 776/50
∴ x = 15.52
৮৯৭.
30% of a number when subtracted from 91, gives the number itself. Find the number.
  1. ক
    50
  2. খ
    55
  3. গ
    60
  4. ঘ
    65
  5. ঙ
    None
ব্যাখ্যা
Question: 30% of a number when subtracted from 91, gives the number itself. Find the number.

Solution:
Let the number be p

According to the question,
91 - 30p/100 = p
⇒ 9100 - 30p = 100p
⇒ 9100 = 130p
∴ p = 70

Hence, the number = 70
৮৯৮.
If a is 150 percent of B, then B is what percent of (A + B)?
  1. ক
    ক) 40%
  2. খ
    খ) 33(1/3)%
  3. গ
    গ) 66(2/3)%
  4. ঘ
    ঘ) 75%
ব্যাখ্যা

A = 150% of B
⇒ A = 150/100 B
⇒ A/B = 3/2
⇒ A/B + 1 = 3/2 + 1
⇒ (A + B)/B = 5/2
⇒ B/(A + B) = 2/5

∴ Required percentage:
= {B / (A + B)} × 100 %
= (2/5 × 100) %
= 40%

৮৯৯.
If 20 percent of 80 percent of a number is 12.8, then what is the number?
  1. ক
    ক) 80
  2. খ
    খ) 50
  3. গ
    গ) 40
  4. ঘ
    ঘ) 9
ব্যাখ্যা
Question: If 20 percent of 80 percent of a number is 12.8, then what is the number?

Solution: 
ধরি,
সংখ্যাটি = ক
ক এর ৮০% এর ২০% = ১২.৮
ক এর (৮০/১০০ × ২০/১০০) = ১২.৮
ক = ৮০
৯০০.
The ratio of the number of boys and girls in a college is 7 ∶ 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
  1. ক
    11 ∶ 12
  2. খ
    21 ∶ 22
  3. গ
    13 ∶ 15
  4. ঘ
    27 ∶ 29
ব্যাখ্যা

Question: The ratio of the number of boys and girls in a college is 7 ∶ 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

Solution: 
ধরি,
কলেজে ছেলে এবং মেয়ের সংখ্যা যথাক্রমে 7x এবং 8x

∴ ছেলেদের বর্ধিত সংখ্যা = 120% × 7x 
= (120/100) × 7x 
= (6/5) × 7x 
= (42x)/5

এবং, মেয়েদের বর্ধিত সংখ্যা = 110% × 8x
= (110/100) × 8x
= (11/5) × 4x
= (44x)/5

 ∴ বর্ধিত সংখ্যার অনুপাত (New ratio) = (42x)/5 ∶ (44x)/5
= 21 ∶ 22