Percentage and Profit & Loss

PrepBank · পাতা ১৩ / ১৭ · ১,২০১–১,৩০০ / ১,৬৯৬

১,২০১.

A shopkeeper sells a pen-drive by 5% discount. In 8% discount, he earns Tk.15. What is the marked price of the pen-drive?

ক
ক) Tk. 500
খ
খ) Tk. 750
গ
গ) Tk. 780
ঘ
ঘ) Tk. 820

ব্যাখ্যা

Suppose, marked price of the pen-drive is Tk. x
At 5% discount, selling price of pen-drive = (100 - 5)x = Tk. 95x
At 8% discount, selling price of pen-drive = (100 - 8)x = Tk. 92x
Therefore,
95% of x - 92% of x = 15
⇒ 95x/100 - 92x/100 = 15
⇒ 3x = 1500
⇒ x = 500

১,২০২.

If the price of an article is increased by 20% and then decreased by 20%, the net change in the price is -

ক
5% decrease
খ
8% decrease
গ
4% decrease
ঘ
6% decrease

ব্যাখ্যা

Question: If the price of an article is increased by 20% and then decreased by 20%, the net change in the price is -

Solution:
Let,
The price of an article is 100 Tk.

If the price increased by 20%,
So, the new price will be after increase = 100 + {100 × (20/100)} Tk.
= 100 + 20 Tk.
= 120 Tk.

Then the new price decreased by 20%,
So, the new price will be after decrease = 120 - {120 × (20/100)} Tk.
= 120 - 24 Tk.
= 96 Tk.

∴ The net change in the price of the article is = (100 - 96)
= 4 Taka

So, there is a 4% decrease in the price

১,২০৩.

By selling a laptop for Tk. 4,500, a shopkeeper gains 20%. If the profit is reduced to 10%, then the selling price will be?

ক
4125
খ
4250
গ
4200
ঘ
4050

ব্যাখ্যা

Question: By selling a laptop for Tk. 4,500, a shopkeeper gains 20%. If the profit is reduced to 10%, then the selling price will be?

Solution:
Let the cost price be x

According to the question,
x + 20% of x = 4500
⇒ x + 20x/100= 4500
⇒ x + 0.20x = 4500
⇒ 1.20x = 4500
⇒ x = 4500/1.20
∴ x = 3750

So, cost price = Tk. 3750

Now, Selling price when profit is 10%,
SP = 3750 + 10% of 3750
= 3750 + 375
= 4125
∴ The new selling price will be Tk. 4,125.

১,২০৪.

If the height of a right square pyramid is increased by 12% by what percent must the side of the base be increased, so that the volume of the pyramid is increased by 28%?

ক
ক) 3%
খ
খ) 7%
গ
গ) 10%
ঘ
ঘ) 36%

ব্যাখ্যা

আমরা জানি,
পিরামিডের ভূমি (base) বর্গাকৃতি
∴ (1/3×base₂×h₂) / (1/3×base₁×h₁) = 128/100
⇒ base₂×1.12h₁/base1×h1 = 128/100 [As, the height is increased by 12%, so h₂ = 1.12h₁]
⇒ base₂/base₁ = 128/(100×1.12)
⇒ x₂²/x₁² = 128/112 [ x₁, x₂ হলো বর্গাকৃতি ভূমি (base) ]
⇒ x₂/x₁ = √(128/112) = 1.07

∴ % = 100×1.07 = 107

সুতরাং, ভূমি (base) বৃদ্ধি করতে হবে = ( 107 - 100 )% = 7%

১,২০৫.

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-

ক
280
খ
240
গ
270
ঘ
290

ব্যাখ্যা

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

১,২০৬.

Any sold her bicycle for Taka. 5000 while making a profit of Taka. 70. Then what is the price at which she bought that cycle?

ক
4930 Taka
খ
4530 Taka
গ
4030 Taka
ঘ
493 Taka

ব্যাখ্যা

Question: Any sold her bicycle for Taka. 5000 while making a profit of Taka. 70. Then what is the price at which she bought that cycle?

Solution:
Given,
Selling Price (SP) = Taka. 5000
Profit = 70 Taka

Thus,
Cost Price = Selling Price - Profit
⇒ Cost Price = 5000 - 70
⇒ Cost Price = 4930 Taka

Thus, cost price of the bicycle is Taka 4930

১,২০৭.

After a 20% price decrease, a computer monitor is on sale for Tk. 7200. What is its original price?

ক
ক) Tk. 9000
খ
খ) Tk. 10,000
গ
গ) Tk. 11,000
ঘ
ঘ) Tk. 12,000

ব্যাখ্যা

At 20% decrease,
The price is = 80% = 7200
So, 100% = (7200×100) / 80
= 9000

১,২০৮.

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?

ক
Tk. 3920
খ
Tk. 4920
গ
Tk. 5000
ঘ
Tk. 4900

ব্যাখ্যা

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

১,২০৯.

A trader sells an article and losses (25/2)% . The ratio of cost price to the selling price is-

ক
ক) 7 : 5
খ
খ) 8 : 7
গ
গ) 7 : 6
ঘ
ঘ) 9 : 7

ব্যাখ্যা

Let
cost price is x
Loss = (25/2)%

S. P = {100 - (25/2)}% of x
= (175/2) × (1/100) × x
= 7x/8

Required ratio = x : 7x/8
= 1 : 7/8
= 8 : 7

১,২১০.

Meena and Rupa entered into a business with a capital of Tk. 15,000 and Tk. 12,000 and they made a total profit of Tk. 9,000. Find the amount of Rupa's share -

ক
Tk. 4500
খ
Tk. 5000
গ
Tk. 4000
ঘ
Tk. 5500

ব্যাখ্যা

Meena and Rupa invested Tk. 15,000 and Tk. 12,000 respectively
The ratio of their investment is = 15,000 : 12,000
= 5 : 4
Total profit is Tk. 9000
Rupa's share = Tk. [4/9 x 9000]
= Tk. 4000
Hence the answer is Tk. 4000

১,২১১.

A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:

ক
ক) 450
খ
খ) 588
গ
গ) 600
ঘ
ঘ) 672
ঙ
ঙ) 700

ব্যাখ্যা

He has = 100 - 40 = 60% apples
60% apples is equal to 420
1%. apples is equal to (420/60%)
100% apples is equal to (420/60%) × 100
= 700

১,২১২.

A student scores 70% marks in 10 papers of 100 marks each. He scores 14% of the total obtained marks in Math. How much does he score in Math?

ক
99
খ
98
গ
88
ঘ
70

ব্যাখ্যা

Question: A student scores 70% marks in 10 papers of 100 marks each. He scores 14% of the total marks in Math. How much does he score in Math?

Solution:
Here,
Total marks in 10 subjects = 10 × 100
= 1000

∴ He scores = 70% of 1000
= (70/100) of 1000
= 700

∴ He scores in Math = 14% of 700
= (14/100) of 700
= 98

১,২১৩.

The length of a rectangle is twice than that of its breadth. If the length of the rectangle is increased by 10%, while its breadth is decreased by 10% what is the percentage change in the perimeter?

ক
ক) 3(1/3) %
খ
খ) 3(2/3) %
গ
গ) 4%
ঘ
ঘ) No change

ব্যাখ্যা

Let, breadth = x unit & length = 2x unit
∴ Perimeter = 2(2x + x) unit = 6x unit
10% হ্রাসে, breadth = (x - 10x/100) = 9x/10 unit
10% বৃদ্ধিতে length (2x + 20x/100) = 11x/5 unit
∴ Perimeter = 2(9x/10 + 11x/5) unit = 2 × 31x/10 = 31x/5 unit
∴ Perimeter এর পরিবর্তনের হার = {(31x/5 - 6x) / 6x} × 100 %
= [{(31x - 30x)/5}/6x × 100] %
= 10/3 %
= 3(1/3)%; increase

১,২১৪.

The ratio 5 : 4 expressed as a percent equals

ক
ক) 125%
খ
খ) 40%
গ
গ) 80%
ঘ
ঘ) 12.5%

ব্যাখ্যা

Question: The ratio 5 : 4 expressed as a percent equals

Solution:
5 : 4 = 5/4
= (5/4) × (100/100)
= (5 × 100)/4 × (1/100)
= 125 × (1/100)
= 125%

১,২১৫.

The price of a loaf of bread was increased by 20%. How many leaves can be purchased now by the amount of money used to buy 300 loaves at the earlier price?

ক
240
খ
250
গ
280
ঘ
320

ব্যাখ্যা

Question: The price of a loaf of bread was increased by 20%. How many leaves can be purchased now by the amount of money used to buy 300 loaves at the earlier price?

Solution:
ধরি,
প্রতি পিস পাউরুটির পূর্বমূল্য ছিল 100 টাকা
300 পিস পাউরুটির পূর্বমূল্য ছিল = (100 × 300) টাকা
= 30000 টাকা

20% বৃদ্ধিতে ,
প্রতি পিস পাউরুটির বর্তমানমূল্য ছিল = 100 + 20 টাকা
= 120 টাকা

∴ বর্তমান মূল্যে 30000 টাকা দিয়ে পাউরুটি কেনা যাবে = 30000/120 টাকা
= 250 টাকা

১,২১৬.

40% of 650 + 80% 720 - 600 = ?

ক
236
খ
264
গ
196
ঘ
476

ব্যাখ্যা

Question: 40% of 650 + 80% 720 - 600 = ?

Solution:
40% of 650 + 80% 720 - 600
= (40/100) × 650 + (80/100) × 720 - 600
= (26000/100) + (57600/100) - 600
= 260 + 576 - 600
= 236

১,২১৭.

A number reduced by 25% becomes 225. What percent should it be increased so that it becomes 390?

ক
15%
খ
20%
গ
25%
ঘ
30%

ব্যাখ্যা

Question: A number reduced by 25% becomes 225. What percent should it be increased so that it becomes 390?

Solution:
Let
the number be x

Now
x - 25% of x = 225
⇒ x - 25x/100 = 225
⇒ (100x - 25x)/100 = 225
⇒ 75x/100 = 225
⇒ 75x = (225 × 100)
⇒ x = (225 × 100)/75
∴ x = 300

∴ Required increase
= (390 - 300)
= 90

∴ Increase percentage :
= (90/300) × 100%
= 30%

১,২১৮.

If the length of a rectangle is increased by 30% and the width is decreased by 30%, then the area will be-

ক
Decreased by 9%
খ
Increased by 9%
গ
Decreased by 16%
ঘ
Increased by 16%

ব্যাখ্যা

Question: If the length of a rectangle is increased by 30% and the width is decreased by 30%, then the area will be-

Solution:
Let,
The length and breadth be 10 unit each.
∴ Area of rectangle = 10 × 10 = 100 unit²

New length = 10 + 30% of 10 = 10 + 3 unit
= 13 unit

New breadth = 10 - 30% of 10 = 10 - 3 unit
= 7 unit

∴ New area of rectangle = 13 × 7 = 91 unit²
Percentage decrease in area = 100 - 91 = 9 unit²

∴ The decrease percent is 9%.

১,২১৯.

What percentage of numbers from 1 to 90 have 3 or 7 in the unit's digit?

ক
20%
খ
18%
গ
10%
ঘ
25%

ব্যাখ্যা

Question: What percentage of numbers from 1 to 90 have 3 or 7 in the unit's digit?

Solution:
Numbers from 1 to 90 with units digit 3 is-
3, 13, 23, 33, 43, 53, 63, 73, 83 = 9 numbers
And
Numbers from 1 to 90 with units digit 7is-
7, 17, 27, 37, 47, 57, 67, 77, 87 = 9 numbers

∴ Total numbers with units digit 3 or 7 = 9 + 9 = 18
And total numbers = 90

∴ Percentage = (18/90) × 100 = 20%

১,২২০.

Robin spends 70% of his salary and deposits 15% of his salary in the bank. If he is left with Tk. 1500, what is his monthly salary?

ক
Tk. 9000
খ
Tk. 9500
গ
Tk. 10000
ঘ
Tk. 10500

ব্যাখ্যা

Question: Robin spends 70% of his salary and deposits 15% of his salary in the bank. If he is left with Tk. 1500, what is his monthly salary?

Solution:
Let salary of Robin is Rs. x

As per question;
x - (70 % of x + 15 % of x) = 1500
⇒ x - 85% of x = 1500
⇒ 15% of x = 1500
⇒ (15x)/100= 1500
⇒ x = (1500 × 100)/15
∴ x = 10000

১,২২১.

A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Tk 392, what was his profit?

ক
ক) 62
খ
খ) 70
গ
গ) 72
ঘ
ঘ) 76

ব্যাখ্যা

C.P. = (100/122.5)x 392
= (1000/1225)x 392
= 320
Profit = (392 - 320) = 72.

১,২২২.

A student erroneously multiplied a number by 2/5 instead of 5/2.What is the percentage error in the calculation?

ক
24%
খ
54%
গ
74%
ঘ
84%

ব্যাখ্যা

Question: A student erroneously multiplied a number by 2/5 instead of 5/2.What is the percentage error in the calculation?

Solution:
Let the number be 100.
2/5 of 100 is 40 while 5/2 of 100 is 250.
Now the difference is 210 on a base of 250.
Therefore, percentage difference is (210/250) × 100 = 84%.

১,২২৩.

A grocer purchased a quantity of bananas at 3 pounds for $0.50 and sold the entire quantity at 4 pounds for $1.00. How many pounds did the grocer purchase if the profit from selling the bananas was $10.00?

ক
40
খ
60
গ
90
ঘ
120

ব্যাখ্যা

Question: A grocer purchased a quantity of bananas at 3 pounds for $0.50 and sold the entire quantity at 4 pounds for $1.00. How many pounds did the grocer purchase if the profit from selling the bananas was $10.00?

Solution:
Cost price of 3 pounds = $0.5
Selling price of 4 pounds = $1.00
Selling price of 3 pounds = (1/4) × 3 = $0.75
∴ Profit for every 3 pounds = 0.75 - 0.5 = $0.25
Total profit = $10

$0.25 profit in 3 pounds
∴ $1 profit in 3/0.25 pounds
∴ $10 profit in (3 × 10)/0.25 pounds
= 120 pounds

১,২২৪.

Scoring 86 runs, a batsman smashed 8 fours and 3 sixes. How much of his score was contributed by running?

ক
41.86%
খ
31.86%
গ
26.72%
ঘ
32.78%

ব্যাখ্যা

Question: Scoring 86 runs, a batsman smashed 8 fours and 3 sixes. How much of his score was contributed by running?

Solution:
The total score of batsman = 86 runs
runs from boundaries = 4 × 8 = 32
runs from sixes = 6 × 3 = 18
∴ Total runs from boundaries and sixes = 32 + 18 = 50 runs
Scores by running between the wickets = 86 - 50 = 36 runs

percentage of his score made by running between wickets = (36/86) × 100% = 41.86%

১,২২৫.

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

ক
ক) 175
খ
খ) 200
গ
গ) 150
ঘ
ঘ) 125

ব্যাখ্যা

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

১,২২৬.

Mr. A multiplies a number by 3 instead of dividing by 3. Resultant number is what percentage of the correct value?

ক
900
খ
400
গ
300
ঘ
200

ব্যাখ্যা

Question: Mr. A multiplies a number by 3 instead of dividing by 3. Resultant number is what percentage of the correct value?

Solution:
মনে করি, সংখ্যাটি x
সঠিকভাবে সমাধান করলে সংখ্যাটিকে 3 দিয়ে ভাগ করতে হবে।
তাহলে, সঠিক মান হবে = x/3

ভুলবশত সংখ্যাটিকে 3 দিয়ে গুণ করা হলে প্রাপ্ত সংখ্যাটি = 3x

∴ ভুল মানটি সঠিক মানের শতকরা = 3x/(x/3) × 100%
= 3x × (3/x) × 100%
= 900%

১,২২৭.

By selling an article for Tk 100 Rakib gains Tk 20. Then, his gain% is-

ক
15%
খ
20%
গ
25%
ঘ
30%

ব্যাখ্যা

Question: By selling an article for Tk 100 Rakib gains Tk 20. Then, his gain% is-

Solution:
ক্রয়মূল্য = ১০০ - ২০ টাকা
= ৮০ টাকা

এখন,
৮০ টাকায় লাভ হয় = ২০ টাকা
১ টাকায় লাভ হয় = ২০/৮০ টাকা
∴ ১০০ টাকায় লাভ হয় = (২০ × ১০০)/৮০ টাকা
= ২৫ টাকা বা ২৫%

১,২২৮.

A woman saves 25% of her salary. If her monthly income is Tk. 12000, how much does she spend?

ক
Tk. 7200
খ
Tk. 8550
গ
Tk. 8000
ঘ
Tk. 9000

ব্যাখ্যা

Question: A woman saves 25% of her salary. If her monthly income is Tk. 12000, how much does she spend?

Solution:
Total income = Tk.12,000
Saving = 25% of income
So, Spending = (100 - 25)% = 75%

∴ Spending = (75/100) × 12000 = 75 × 120 = Tk. 9000

১,২২৯.

A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Tk 22500. What is the reduced price per kg of tea?

ক
81 tk
খ
90 Tk
গ
93 Tk
ঘ
97 Tk

ব্যাখ্যা

Question: A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Tk 22500. What is the reduced price per kg of tea?

Solution:
Let 10% of 22500 = 2250
Now,
25 kg = 2250
⇒ 1kg = 2250/25
∴ 1kg = 90

১,২৩০.

By error, a student used 7/10 in place of 7/5 to multiply a number. Determine the percent error in the computation.

ক
40%
খ
45%
গ
50%
ঘ
60%

ব্যাখ্যা

Question: By error, a student used 7/10 in place of 7/5 to multiply a number. Determine the percent error in the computation.

Solution:
Let
the number be 100.

ATQ,
Actual calculation be: (7/5) × 100 = 140
and error calculation be: (7/10) × 100 = 70

∴ Difference = 140 - 70 = 70

∴ Percentage error = (70/140) × 100 = 50%

১,২৩১.

The price of a pen is 25% more than the price of a book. The price of a pen holder is 50% more than the price of the book. How much is the price of the pen holder more than the price of the pen?

ক
20%
খ
35%
গ
25%
ঘ
30%

ব্যাখ্যা

Let price of book = 100tk
Price of pen = 100 + 100 × 25%
= 125 tk
Price of pen-holder = 100 + 100 × 50%
= 150 tk

Difference is = 150 -125 = 25 tk

∴ Percentage = (25 × 100)/125
= 20%

১,২৩২.

Mr. Karim sold his cow for Tk. 30,000 at a 20% gain. Find the cost price.

ক
ক) 20,000
খ
খ) 22,000
গ
গ) 25,000
ঘ
ঘ) 28,000

ব্যাখ্যা

Question: Mr. Karim sold his cow for Tk. 30,000 at a 20% gain. Find the cost price.

Solution:
20% লাভে,
বিক্রয়মূল্য 120 টাকা হলে ক্রয়মূল্য = 100 টাকা
∴ বিক্রয়মূল্য 30000 টাকা হলে ক্রয়মূল্য = (100 x 30000)/120 টাকা
= 25000 টাকা

১,২৩৩.

A retailer bought 100 Bluetooth speakers at a cost of BDT 1,800 each. He sold each at a 30% markup. After a month, 20 speakers remained unsold, and he returned them to the supplier for a 50% refund of the cost price. What is the retailer’s approximate profit margin as a percentage of the total acquisition cost?

ক
10%
খ
12%
গ
14%
ঘ
20%
ঙ
None

ব্যাখ্যা

Question: A retailer bought 100 Bluetooth speakers at a cost of BDT 1,800 each. He sold each at a 30% markup. After a month, 20 speakers remained unsold, and he returned them to the supplier for a 50% refund of the cost price. What is the retailer’s approximate profit margin as a percentage of the total acquisition cost?

Solution:
Given,
Purchased = 100 speakers
∴ Total Cost = 100 × 1,800 = BDT 180,000

Sold = (100 - 20) = 80 units
Selling price (30% markup) = 1,800 × 1.30 = BDT 2,340
∴ Revenue from sold units = 80 × 2,340 = BDT 187,200

Refund for returns (50%) = 1,800 × 0.5 = BDT 900 per speaker
∴ Refund from unsold units = 20 × 900 = BDT 18,000

Total Income = 187,200 + 18,000 = BDT 205,200

Profit = 205,200 − 180,000 = BDT 25,200

Profit Margin % = (25,200/180,000) × 100 = 14%

১,২৩৪.

A profit of 25% could have been made if an item was sold for Tk.750. It was sold for a loss of 5% instead. What is the actual selling price?

ক
ক) Tk. 720
খ
খ) Tk. 570
গ
গ) Tk. 450
ঘ
ঘ) Tk. 620

ব্যাখ্যা

Question: A profit of 25% could have been made if an item was sold for Tk.750. It was sold for a loss of 5% instead. What is the actual selling price?

Solution:

Let be assume cost price of the item is 100x
⇒ 125x = 750
⇒ x = 6

⇒ Now, the actual selling price of the item was 5% less the cost price of the items
⇒ The actual selling price of item = 100x - 5x = 95x
⇒ 95 × 6 = 570

∴ The required result will be 570.

১,২৩৫.

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

ক
ক) 11%
খ
খ) 19%
গ
গ) 17%
ঘ
ঘ) 21%

ব্যাখ্যা

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

১,২৩৬.

If 15% of a number is 4.5, then 55% of the same number is -

ক
ক) 15
খ
খ) 9.5
গ
গ) 17.5
ঘ
ঘ) 16.5

ব্যাখ্যা

Question: If 15% of a number is 4.5, then 55% of the same number is -

Solution:
মনে করি,
সংখ্যাটি x

প্রশ্নমতে,
x এর 15% = 4.5
বা, 15x/100 = 4.5
বা, 15x = 4.5 × 100
বা, x = 450/15
∴ x = 30

সংখ্যাটির 55% = 30 এর 55%
= (30 × 55)/100
= 16.5

∴ নির্ণেয় সংখ্যাটি 16.5

১,২৩৭.

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?

ক
24.73%
খ
34.62%
গ
44.25%
ঘ
28.53%

ব্যাখ্যা

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.

১,২৩৮.

3 litre of water is added to 11 litres of a solution containing 42% of alcohol in the water. The percentage of alcohol in the new mixture is -

ক
20%
খ
33%
গ
30%
ঘ
25%

ব্যাখ্যা

We have an 11-liter solution containing 42% of alcohol in the water.
=> quantity of alcohol in the solution = (11 × 42)/100
Now 3 liter of water is added to the solution.
=> Total quantity of the new solution = 11 + 3 = 14
Percentage of alcohol in the new solution = {(11 × 42)/100}/14 × 100
= (11 × 3)/100
= 33%

১,২৩৯.

The cost price of 60 articles is the same as the selling price of 'q' articles. If the profit is 20%, then the value of 'q' is -

ক
40
খ
45
গ
50
ঘ
56

ব্যাখ্যা

Question: The cost price of 60 articles is the same as the selling price of 'q' articles. If the profit is 20%, then the value of 'q' is -

Solution:
Let,
The cost price of each article be = Tk. 1
The cost price of 'q' articles = Tk. q
The selling price of 'q' articles = Tk. 60

∴ Profit = Tk. (60 - q)

According to the question,
(60 - q)/q = 20%
⇒ 100(60 - q)/q = 20
⇒ 6000 - 100q = 20q
⇒ 120q = 6000
⇒ q = 6000/120
∴ q = 50

১,২৪০.

Find the cost price of a product. It is marked up by 45% more than the cost price and then a discount of 20% of marked price is given. Selling price is Tk. 4060.

ক
Tk. 3500
খ
Tk. 3600
গ
Tk. 3200
ঘ
Tk. 3800

ব্যাখ্যা

Question: Find the cost price of a product. It is marked up by 45% more than the cost price and then a discount of 20% of marked price is given. Selling price is Tk. 4060.

Solution:
Let,
Cost price be Tk. 100

Marked price = Tk. 100 + Tk. 45
= Tk. 145

Discount = 20% of marked price
∴ Selling price = (100 - 20) % of marked price = 80% of of marked price
= 80% of Tk. 145
= Tk. 116

Selling price 116 when cost price 100
∴ Selling price 1 when cost price 100/116
∴ Selling price 4060 when cost price (100 × 4060)/116
= Tk. 3500

১,২৪১.

A and B started a business investing Tk. 18,000 and Tk. 27,000 respectively. Out of a total profit of Tk. 15,000, what is B’s share?

ক
Tk. 9,000
খ
Tk. 5,000
গ
Tk. 7,000
ঘ
Tk. 1,000

ব্যাখ্যা

Question: A and B started a business investing Tk. 18,000 and Tk. 27,000 respectively. Out of a total profit of Tk. 15,000, what is B’s share?

Solution:
Investment of A = Tk. 18,000
Investment of B = Tk. 27,000

Ratio of investments = 18,000 : 27,000
= 2 : 3

Total profit = Tk. 15,000

B’s share of profit
= 3/(2 + 3) × 15,000
= 3/5 × 15,000
= 9,000

Therefore, B’s share of the profit is Tk. 9,000.

১,২৪২.

In an examination, Pankaj scored certain marks and failed by 48 marks. In the same examination, Rajan scored 56% marks, thus scored 84 marks above passing marks. Find the percentage of marks obtained by Pankaj if Rajan scored 224 marks.

ক
22%
খ
23%
গ
24%
ঘ
25%

ব্যাখ্যা

Question: In an examination, Pankaj scored certain marks and failed by 48 marks. In the same examination, Rajan scored 56% marks, thus scored 84 marks above passing marks. Find the percentage of marks obtained by Pankaj if Rajan scored 224 marks.

Solution:
Rajan scored 224 marks.
∴ Pass marks 224 - 84 = 140

∴ Pankaj scored 140 - 48 = 92

56% of Total marks = 224
∴ Total marks = (224 × 100)/56 = 400

Percentage of marks obtained by Pankaj = (92/400) × 100 %
= 23%

১,২৪৩.

In a university, 80 percent of the students lived in hostel, and 60 percent of the hostel students are lucky to get a single room. If number of lucky students is 1200, then how many students were there in the university?

ক
ক) 1800
খ
খ) 2000
গ
গ) 2400
ঘ
ঘ) 2500

ব্যাখ্যা

Question: In a university, 80 percent of the students lived in hostel, and 60 percent of the hostel students are lucky to get a single room. If number of lucky students is 1200, then how many students were there in the university?

Solution:
ধরি, বিশ্ববিদ্যালয়ে ছাত্র সংখ্যা x
হোস্টেলে বাস করে = x এর ৮০%
= ০.৮x জন ছাত্র

হোস্টেলে বাস করা ছাত্রদের মধ্যে ৬০% ভাগ্যবান ছাত্র সিঙ্গেল রুম পায়।

০.৮x এর ৬০% = ১২০০
⇒ ০.৪৮x = ১২০০
⇒ x = ১২০০/০.৪৮
∴ x = ২৫০০

অতএব, বিশ্ববিদ্যালয়ে ২৫০০ জন ছাত্র আছে।

১,২৪৪.

A litre of water evaporates from 6L of sea water containing 4% salt. Find the percentage of salt in the remaining solution.

ক
ক) 5(1/2)%
খ
খ) 3(1/2)%
গ
গ) 3%
ঘ
ঘ) 4(4/5)%
ঙ
ঙ) 5%

ব্যাখ্যা

Quantity of salt in 6L of sea water,
= (6×4)/100 = 0.24
Percentage of salt in 5L of sea water,
= (0.24×100)/5
= 4(4/5)%

১,২৪৫.

Which of the numbers below is not equivalent to 20%?

ক
1/5
খ
20/100
গ
0.5
ঘ
0.2

ব্যাখ্যা

20% = 20/100 = 1/5 = 0.2

১,২৪৬.

The total population of a village increased from 18000 to 22500 in a decade. The average percentage increase of population per year of that village is-

ক
2.37%
খ
2.5%
গ
3.6%
ঘ
6.75%

ব্যাখ্যা

Question: The total population of a village increased from 18000 to 22500 in a decade. The average percentage increase of population per year of that village is-

Solution:
Population increase in 10 years = (22500 - 18000) = 4500.
Increase% of ten year = (4500/18000) × 100% = 25%
∴ Required average = (25/10)% = 2.5%

১,২৪৭.

A shopkeeper marks his goods 40% above the cost price and offers a discount of 20% on the marked price. What is his gain percent?

ক
12%
খ
17%
গ
9%
ঘ
15%

ব্যাখ্যা

Question: A shopkeeper marks his goods 40% above the cost price and offers a discount of 20% on the marked price. What is his gain percent?

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

Marked Price = 40% more than cost price
= 100 + 40
= 140 Tk.

Discount = 20% of 140
= (20/100) × 140
= 28 Tk.

Selling Price (SP)= 140 - 28 = 112 Tk.

∴ Profit = SP - CP = 112 - 100 = 12 Tk.

∴ Gain percent = 12%

১,২৪৮.

If selling 12 items brings in the same amount as buying 15 items, what's the profit or loss percentage?

ক
20% profit
খ
12% loss
গ
25% profit
ঘ
32% loss

ব্যাখ্যা

Question: If selling 12 items brings in the same amount as buying 15 items, what's the profit or loss percentage?

Solution:
মনে করি,
প্রতিটি পণ্যের ক্রয়মূল্য = 1 টাকা
15 টি পণ্যের ক্রয়মূল্য = 15 টাকা

প্রশ্নমতে,
12 টি পণ্যের বিক্রয়মূল্য = 15 টাকা
1 টি পণ্যের বিক্রয়মূল্য = 15/12 টাকা
= 5/4 টাকা

∴ লাভ/ক্ষতি = বিক্রয়মূল্য - ক্রয়মূল্য = ( 5/4 ) - 1 = (5 - 4) / 4= 1/4

এখন,
1 টাকায় লাভ হয় = 1/4 টাকা
∴ 100 টাকায় লাভ হয় = ( 1/4 ) × 100 = 25 টাকা

সুতরাং, লাভের শতকরা পরিমাণ = 25%

১,২৪৯.

ক
3.2
খ
2.8
গ
1.2
ঘ
None

ব্যাখ্যা

Question:

Solution:

১,২৫০.

Sunny and Rajib bought the same item. Sunny paid Tk 15,000. Rajib got discount and paid Tk. 3,000 less than Sunny. How much discount did Rajib get?

ক
10%
খ
15%
গ
20%
ঘ
25%

ব্যাখ্যা

Question: Sunny and Rajib bought the same item. Sunny paid Tk 15,000. Rajib got discount and paid Tk. 3,000 less than Sunny. How much discount did Rajib get?

Solution:
In Tk. 15000 Rajib get discount Tk. 3000
In Tk. 1 Rajib get discount Tk. (3000/15000)
In Tk. 100 Rajib get discount Tk. (3000 × 100)/15000
= Tk. 20

∴ Rajib get 20% discount.

১,২৫১.

Pavel bought a television set with a 20% discount on the labelled price. He made a profit of Tk. 800 by selling it for Tk. 16800. The labelled price of the set was -

ক
Tk.15,903
খ
Tk.12,650
গ
Tk.23,541
ঘ
Tk.25,761
ঙ
Tk.20,000

ব্যাখ্যা

Let the labeled price of TV = Tk. X
∴ SP of the TV = [X x (100 - 20)]/100
= Tk. 4X/5
But 16,800 - 800 = 4X/5
∴ x = (16,000 x 5)/4
= Tk. 20,000

১,২৫২.

A table fan is quoted for Tk. 1500. Shakil pays Tk. 1173 for it. If he gets a series of two discounts and the rate of the first discount is 15%, then the rate of the second discount is?

ক
7%
খ
8%
গ
9%
ঘ
10%

ব্যাখ্যা

Question: A table fan is quoted for Tk. 1500. Shakil pays Tk. 1173 for it. If he gets a series of two discounts and the rate of the first discount is 15%, then the rate of the second discount is?

Solution:
After first discount = 1500 - 1500 × 15%
= 1500 - 1500 × 15/100
= 1500 -225
= 1275 taka

let second discount is x%

1275 - 1275 × x/100 = 1173
⇒ 1275x/100 = 1275 - 1173 = 102
⇒ x = 102 × 100/1275
= 8

১,২৫৩.

A pen was brought for Tk 75 and sold it again for 8%. What was its selling price in Tk?

ক
79 Tk
খ
81 Tk
গ
83 Tk
ঘ
85 Tk

ব্যাখ্যা

Question: A pen was brought for Tk 75 and sold it again for 8%. What was its selling price in Tk?

Solution:
দেওয়া আছে,
ক্রয়মূল্য = ৭৫ টাকা
৮% লাভে, বিক্রয়মূল্য = ১০০ + ৮ = ১০৮ টাকা

ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য = ১০৮ টাকা
ক্রয়মূল্য ১ টাকা হলে বিক্রয়মূল্য = ১০৮/১০০ টাকা
∴ ক্রয়মূল্য ৭৫ টাকা হলে বিক্রয়মূল্য = (১০৮ × ৭৫)/১০০ টাকা
= ৮১ টাকা

১,২৫৪.

If A's salary is 25% more than B's salary, then B's salary is how much lower than A's salary?

ক
25%
খ
30%
গ
20%
ঘ
15%

ব্যাখ্যা

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

Solution:
Let B's Salary is Tk. 100.
Then,
A's Salary = (100 + 25% of 100) = Tk. 125
Difference between A's Salary and B's Salary = 125 - 100 = Tk. 25

% Difference (lower) = (25/125) × 100 = 20%

১,২৫৫.

If the price of an item is increased by 20%, then decreased by 10%, and then increased by 5%, what is the equivalent single percentage change in the price?

ক
increase 5%
খ
Original Price
গ
increase 13.4%
ঘ
decrease 11.5%

ব্যাখ্যা

Question: If the price of an item is increased by 20%, then decreased by 10%, and then increased by 5%, what is the equivalent single percentage change in the price?

Solution:
ধরি,
প্রাথমিক দাম = 100 টাকা

20% বৃদ্ধি করলে = 100 + (100 এর 20%)
= 120 টাকা

10% হ্রাস করলে দাম = 120 - (120 এর 10%)
= 120 - 12 = 108 টাকা

5% বৃদ্ধি করলে = 108 + (108 এর 5%)
=108 + 5.4
= 113.4 টাকা

∴ বৃদ্ধি = (113.4 - 100) = 13.4 টাকা
∴ শতকরা হ্রাস = 13.4%

১,২৫৬.

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?

ক
20%
খ
30%
গ
35%
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%

১,২৫৭.

What is the original price of a T-shirt, if the sale price after 15% discount is 272?

ক
Tk. 320
খ
Tk. 300
গ
Tk. 420
ঘ
Tk. 231.20

ব্যাখ্যা

At 15% discount, selling price = 100 - 15 = Tk. 85
If the selling price is Tk. 85, then original price is Tk. 100
If the selling price is Tk. 272, then original price is Tk. (100 × 272/85) = Tk. 320

১,২৫৮.

If an article is sold for Tk. 540 at a loss of 10%, what should be its selling price in order to earn a profit of 15%?

ক
Tk. 648
খ
Tk. 666
গ
Tk. 690
ঘ
Tk. 700

ব্যাখ্যা

Question: If an article is sold for Tk. 540 at a loss of 10%, what should be its selling price in order to earn a profit of 15%?

Solution:
Selling Price of the article = Tk. 540
Loss % = 10%

∴ Cost Price = {100/(100 - 10)} × 540
= (540 × 100)/90 = 600

Now, Cost Price = Tk. 600 and Profit% = 15%
∴ New Selling Price = {(100 + 15)/100} × 600 = (115 × 600)/100
= 690 Tk.

Therefore, the article should be sold at Tk. 690

১,২৫৯.

If y exceeds x by 20%, then x is less than y by:

ক
ক) 16.00%
খ
খ) 16.33%
গ
গ) 16.67%
ঘ
ঘ) 16.60%

ব্যাখ্যা

আমরা জানি,
একটি সংখ্যা অপর সংখ্যার চেয়ে r% বেশি হলে
অপর সংখ্যাটি প্রথম সংখ্যার চেয়ে কম হবে = (100 × r)/(100 + r)

x, y এর চেয়ে কম হবে = (100 ×20)/(100 + 20)
= 16.67%

১,২৬০.

When a discount of 20% is given on a sweater, the profit is 20%. If the discount is 10%, then the profit is

ক
28.67%
খ
32%
গ
37.25%
ঘ
35%

ব্যাখ্যা

Question: When a discount of 20% is given on a sweater, the profit is 20%. If the discount is 10%, then the profit is

Solution:
Let the C.P. of sweater be Tk. 100 and its marked price be Tk. x.
ATQ,
x × (80/100) = 120
⇒ 4x/5 = 120
⇒ x = 150 Tk

When discount = 10%, then
S.P. of sweater = 150 × (100 - 10)%
= (150 × 90)/100
= 135 Tk

∴ Profit = 135 - 100 = 35

∴ Profit percentage = (35/100) × 100% = 35%

১,২৬১.

After getting two successive discounts, a shirt with a list price of 150 taka is available at 105 taka. If the second discount is 12.5% find the first discount?

ক
ক) 30%
খ
খ) 25%
গ
গ) 20%
ঘ
ঘ) 35%

ব্যাখ্যা

At second discount, 87.5% = 105 taka
So, 100% = 105/87.5 × 100 = 120 taka
The amount discounted in first place is 150 - 120 = 30 Taka
∴ First discount = 30/150 × 100 = 20%

১,২৬২.

What will be the difference between a single discount of 30% on Tk. 2000 and 2 successive discounts of 15% and 15%?

ক
ক) Tk. 0
খ
খ) Tk. 10
গ
গ) Tk. 45
ঘ
ঘ) Tk. 150

ব্যাখ্যা

30% discount = 30% of 2000 = Tk. 600
Now, if you offer two successive discounts of 15% each, it works out to
First discount of 15% = 15% of 2000
= Tk. 300
After discount value = Tk. 2000 - Tk.300
= Tk. 1700
Second discount of 15% = 15% of Tk. 1700
= {(15/100) × 1700}
= Tk. 255

Difference = 600 - (300+255)
= 600 - 555
= Tk. 45

১,২৬৩.

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

ক
ক) (bc/a)%
খ
খ) ac%
গ
গ) (b/a)%
ঘ
ঘ) (ac/b)%

ব্যাখ্যা

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.

১,২৬৪.

If a shopkeeper buys eggs at Tk. 25 per quad (hali) and sells at Tk. 56 per 2 quads, how much profit percentage will he make?

ক
20%
খ
12%
গ
15%
ঘ
6%

ব্যাখ্যা

Question: If a shopkeeper buys eggs at Tk. 25 per quad (hali) and sells at Tk. 56 per 2 quads, how much profit percentage will he make?

Solution: The cost price of 1 quad of eggs = Tk. 25
The cost price of 2 quads of eggs = Tk. 25 x 2 = Tk. 50

Again, the selling price of 2 quads of eggs = Tk. 56
Since the selling price is more than the cost price, there will be a profit.

Here, Profit = Tk. (56-50) = Tk. 6
In Tk. 50, profit is = Tk. 6
In Tk 1 profit is = 6/50 Tk
In Tk 100 profit is = (6 ×100)/ 50= 12 Tk
∴ profit is 12%.

১,২৬৫.

A trader mixes 26 kg of fertilizer at Tk. 20 per kg with 30 kg of fertilizer of other variety at Tk. 36 per kg and sells the mixture at Tk. 30 per kg. His profit percent is:

ক
4%
খ
5%
গ
6%
ঘ
8%

ব্যাখ্যা

Question: A trader mixes 26 kg of fertilizer at Tk. 20 per kg with 30 kg of fertilizer of other variety at Tk. 36 per kg and sells the mixture at Tk. 30 per kg. His profit percent is:

Solution:
Cost price of 56 kg fertilizer = Tk. (26 × 20) + (30 × 36)
= Tk. (520 + 1080)
= Tk. 1600

∴ Selling price of 56 kg rice = Tk. (56 × 30)
= Tk.1680

Profit = Tk. (1680 - 1600) = Tk. 80
∴ Gain = {(80/1600) × 100}
= 5%

১,২৬৬.

8 is 5% of what number?

ক
180
খ
140
গ
160
ঘ
148

ব্যাখ্যা

Question: 8 is 5% of what number?

Solution:
ধরি, ৮, x এর ৫%

x এর ৫% = ৮
⇒ x × ৫/১০০ = ৮
⇒ x/২০ = ৮
⇒ x = ২০ × ৮
= ১৬০

১,২৬৭.

A tradesman sold an article at a loss of 20%. If the selling price had been increased by 100 taka, there would have been a gain of 5%. What was the cost price of the article

ক
ক) 375 taka
খ
খ) 400 taka
গ
গ) 425 taka
ঘ
ঘ) 450 taka

ব্যাখ্যা

Question: A tradesman sold an article at a loss of 20%. If the selling price had been increased by 100 taka, there would have been a gain of 5%. What was the cost price of the article.

সমাধান:
ধরি,
দ্রব্যটির ক্রয়মূল্য ক টাকা

২০% ক্ষতিতে,
ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য ৮০ টাকা
∴ ক্রয়মূল্য ক টাকা হলে বিক্রয়মূল্য (৮ক)/১০ টাকা

বিক্রয়মূল্য ১০০ টাকা বেশি হলে মোট বিক্রয়মূল্য = (৮ক)/১০ + ১০০ টাকা
= (৮ক + ১০০০)/১০ টাকা

৫% লাভে,
বিক্রয়মূল্য ১০৫ টাকা হলে ক্রয়মূল্য ১০০ টাকা
∴ বিক্রয়মূল্য (৮ক + ১০০০)/১০ টাকা হলে ক্রয়মূল্য {১০০(৮ক + ১০০০)}/(১০৫ × ১০) টাকা
= (৮০ক + ১০০০০)/১০৫ টাকা

শর্তমতে,
(৮০ক + ১০০০০)/১০৫ = ক
বা, ৮০ক + ১০০০০ = ১০৫ক
বা, ১০০০০ = ২৫ক
বা, ক = ১০০০০/২৫
∴ ক = ৪০০

∴ দ্রব্যটির ক্রয়মূল্য ৪০০ টাকা

১,২৬৮.

In a survey, 30% of the people surveyed owned a personal computer and 75% owned a cellular telephone. If 25% owned both a cellular telephone and a personal computer, then the percentage of the people who does not have either of the instrument?

ক
ক) 40%
খ
খ) 30%
গ
গ) 25%
ঘ
ঘ) 20%

ব্যাখ্যা

Question: In a survey, 30% of the people surveyed owned a personal computer and 75% owned a cellular telephone. If 25% owned both a cellular telephone and a personal computer, then the percentage of the people who does not have either of the instrument?

Solution:
people owned a personal computer n(p) = 30%
people owned a cellular computer n(c) = 75%
people owned both personal and cellular computer, n(p ∩ c) = 25%
people owned any one or both of them = n (p ∪ c)

n (p ∪ c) = n(p) + n(c) - n(p ∩ c)
= 30% + 75% - 25%
= 80%

∴ the percentage of the people who does not have either of the instrument = 100% - 80%
= 20%

১,২৬৯.

A student scored 30% marks and failed by 15 marks. Another student scored 50% marks and secured 25 marks more than the pass marks. What is the pass percentage?

ক
33%
খ
37.5%
গ
40%
ঘ
45%

ব্যাখ্যা

Question: A student scored 30% marks and failed by 15 marks. Another student scored 50% marks and secured 25 marks more than the pass marks. What is the pass percentage?

Solution:
Let total marks = x

According to the question,
30% of x +15 = 50% of x - 25
⇒ 0.30x + 15 = 0.50x - 25
⇒ 0.50x - 0.30x = 25 + 15
⇒ 0.20x = 40
⇒ x = 40/0.20
∴ x = 200

∴ Pass marks = 30% of x + 15
= 0.30 × 200 + 15
= 60 + 15
=75

∴ Pass percentage = (75/200) × 100
= 37.5%

১,২৭০.

A single discount equivalent to discount series 20%, 20% and 10% is = ?

ক
ক) 50%
খ
খ) 48.4%
গ
গ) 42.4%
ঘ
ঘ) 40.4%

ব্যাখ্যা

Single equivalent discount for 20% and 20%
= 20+20−20 × 20/100
= 40−4 = 36%
Single equivalent discount for 36% and 10%
= 36+10−36 × 10/100
= 46−3.6 =42.4%

১,২৭১.

A company pays rent of Tk. 1500 per month for office space to its owner. But if the company pays the annual rate at the beginning of the year the owner gives a discount of 10% on the total annual rent. What is the annual amount the company pays to the owner after the discount?

ক
ক) Tk. 15500
খ
খ) Tk. 16200
গ
গ) Tk. 17300
ঘ
ঘ) Tk. 18000

ব্যাখ্যা

Question: A company pays rent of Tk. 1500 per month for office space to its owner. But if the company pays the annual rate at the beginning of the year the owner gives a discount of 10% on the total annual rent. What is the annual amount the company pays to the owner after the discount?

Solution:
Total annual rent = Tk. (1500 × 12) = Tk. 18000
Discount = 10% of Tk. 18000
= Tk. (10 × 18000)/100 = Tk. 1800
Annual rent paid after discount = Tk. (18000 - 1800) = Tk. 16200

১,২৭২.

A dishonest shopkeeper, at the time of selling and purchasing, weighs 10% less and 20% more per kilogram respectively. Find the percentage profit earned by treachery. (Assuming he sells at Cost Price)

ক
30%
খ
31%
গ
32%
ঘ
33%
ঙ
33.33%

ব্যাখ্যা

During purchase he got = 100 + 20 = 120
During sell he gave = 100 - 10 = 90
Profit % = (30/90) × 100
= 33.33%

১,২৭৩.

A shopkeeper suffers a loss of 20% upon selling a shirt for Tk. 4000. If he wants to make 15% profit after giving an 8% discount on the marked price, what is the marked of the shirt in Tk.?

ক
6000
খ
6250
গ
5000
ঘ
5750
ঙ
None

ব্যাখ্যা

Question: A shopkeeper suffers a loss of 20% upon selling a shirt for Tk. 4000. If he wants to make 15% profit after giving an 8% discount on the marked price, what is the marked of the shirt in Tk.?

Solution:
At 20% loss,
Selling price Tk. 80 when cost price Tk. 100
Selling price Tk. 1 when cost price Tk. 100/80
Selling price Tk. 4000 when cost price Tk. (100 × 4000)/80
= Tk. 5000

At 15% profit,
cost price Tk. 100 when selling price Tk. 115
cost price Tk. 1 when selling price Tk. 115/100
cost price Tk. 5000 when selling price Tk. (115 × 5000)/100
= Tk. 5750

At 8% discount,
Selling price Tk. 92 when marked price Tk. 100
Selling price Tk. 1 when marked price Tk. 100/92
Selling price Tk. 5750 when marked price Tk. (100 × 5750)/92
= Tk. 6250

১,২৭৪.

Idrak buys 80 kg sugar at taka 40 per kg. and 40 kg rice at taka 50 per kg. At what price approximately in taka per kg should he sell to make profit 10% of cost?

ক
ক) 42.3
খ
খ) 44.3
গ
গ) 47.7
ঘ
ঘ) 49.2

ব্যাখ্যা

80 কেজি চিনির ক্রয়মূল্য = 80 × 40 = 3200 টাকা
40 কেজি চালের ক্রয়মূল্য = 40 ×50 = 2000 টাকা

চিনি ও চালের মোট পরিমাণ = 80 + 40 = 120 কেজি

১০% লাভে
মোট বিক্রয়মূল্য = 5200 + 5200 এর 10%
= (5200 + 520)
= 5720 টাকা

প্রতিকেজির বিক্রয়মূল্য = 5720/120 = 47.7 টাকা

১,২৭৫.

P is 6 times greater than Q then by what percent is Q smaller than P?

ক
87%
খ
79.67%
গ
83.33%
ঘ
71%

ব্যাখ্যা

Question: P is 6 times greater than Q then by what percent is Q smaller than P?

Solution:
Let Q = 10.
Then, P = 60.
Q is 50 less than P.
Q, % less than P = (50/60) × 100
= 83.33%

১,২৭৬.

After getting two successive discounts, a shirt with a list price of 150 taka available at 105 taka. If the second discount is 12.5%, find the first discount.

ক
ক) 30%
খ
খ) 25%
গ
গ) 20%
ঘ
ঘ) 35%

ব্যাখ্যা

Question: After getting two successive discounts, a shirt with a list price of 150 taka available at 105 taka. If the second discount is 12.5%, find the first discount.

সমাধান:
Let,
The first discount be x%

Then, 87.5% of (100 - x)% of 150 = 105
⇒ 87.5/100 × (100 - x)/100 × 150 =105
⇒ 100 - x = (105 × 100 × 100)/(87.5 × 150)
⇒ 100 - x = 80
⇒ x = 20

∴ The first discount be 20%

১,২৭৭.

A shopkeeper lost 7% by selling an article. If he had bought it at 10% less and sold it for Tk. 45 more, he would have gained 20%. Find the cost price of the article.

ক
ক) 200 Tk.
খ
খ) 260 Tk.
গ
গ) 300 Tk.
ঘ
ঘ) 320 Tk.

ব্যাখ্যা

৭% ক্ষতিতে,
ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য = (১০০ - ৭) টাকা
= ৯৩ টাকা

১০% কমে,
দ্রব্যটির ক্রয়মূল্য = (১০০ - ১০) টাকা = ৯০ টাকা
২০% লাভে,
ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য = (৯০ + ৯০ এর ২০%) টাকা
= (৯০ + ৯০ এর ২০/১০০) টাকা
= ১০৮ টাকা

বিক্রয়মূল্য বেশি = (১০৮ - ৯৩) টাকা = ১৫ টাকা

১৫ টাকা বিক্রয়মূল্য বেশি যখন ক্রয়মূল্য ১০০ টাকা
১ টাকা বিক্রয়মূল্য বেশি যখন ক্রয়মূল্য ১০০/১৫ টাকা
৪৫ টাকা বিক্রয়মূল্য বেশি যখন ক্রয়মূল্য (১০০ × ৪৫)/১৫ টাকা
= ৩০০ টাকা

১,২৭৮.

405 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child receive?

ক
ক) 9
খ
খ) 10
গ
গ) 11
ঘ
ঘ) 12
ঙ
ঙ) Data Insufficient

ব্যাখ্যা

Let Children = X
A/Q,
405/X = 20% of X
Or, X² = 2025
Or, x = 45
So each children receive = 405/45
= 9

১,২৭৯.

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 eight books?

ক
600
খ
1200
গ
1800
ঘ
None of these

ব্যাখ্যা

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 eight books?

Solution:
Least Cost Price = Tk. (200 × 8) = Tk. 1600.

Greatest Selling Price = Tk. (425 × 8) = Tk. 3400.

Required profit = Tk. (3400 - 1600) = Tk. 1800.

১,২৮০.

If selling price is doubled, the profit sextuples. Find the profit percent?

ক
25%
খ
50%
গ
75%
ঘ
None of these

ব্যাখ্যা

Question: If selling price is doubled, the profit sextuples. Find the profit percent?

Solution:
Let,
The cost price be Tk.100 and sell price be Tk. x,
Then,
The profit is (x - 100)

Now, The sell price is doubled, then the new sell price is 2x
New profit is (2x - 100)

ATQ,
6(x - 100) = 2x - 100
⇒ 6x - 600 = 2x - 100
⇒ 6x - 2x = 600 - 100
⇒ 4x = 500
∴ x = 125

Then the Profit = (125 - 100) = 25
Hence the profit percentage is = (25/100) × 100 %
= 25%

১,২৮১.

A merchant has 1200 kg of rice, part of which he sells at 10% profit and the rest at 20% profit. If his overall gain is 16%, find the quantity of rice he sold at 20% profit.

ক
620 kg
খ
720 kg
গ
840 kg
ঘ
960kg

ব্যাখ্যা

Question: A merchant has 1200 kg of rice, part of which he sells at 10% profit and the rest at 20% profit. If his overall gain is 16%, find the quantity of rice he sold at 20% profit.

Solution:
Let the cost price per kg = Tk. x
∴ Total cost price = 1200x
Again,
Let the rice sold at 10% profit = y kg
Then the rice sold at 20% profit = (1200 - y) kg

Now,
Selling price of y kg at 10% profit,
SP₁ = (y × x) × (110/100)
= 110xy/100

Selling price of (1200 - y) kg at 20% profit,
SP₂ = (1200 - y) × (x) × (120/100)
= 120x(1200 - y)/100

Total Selling Price, SP = SP₁ + SP₂
= (110xy/100) + 120x(1200 - y)/100
= {110xy + 120x(1200 - y)}/100

Now,
Overall profit is 16%,
So, total SP =1200x × (116/100)
= 139200x/100

Now equating both total selling prices:
{110xy + 120x(1200 - y)}/100 = 139200x/100
⇒ 110xy + 120x(1200 - y) = 139200x
⇒ 110xy + 144000x - 120xy = 139200x
⇒ - 10xy = - 4800x
⇒ y = 4800x/10x
∴ y = 480

So, rice sold at 20% profit = 1200 - y
= 1200 - 480 = 720 kg

১,২৮২.

A man is in need of money for 90 days he asked Bank. The Bank charged taka 156 at 8%. What was the amount asked for?

ক
7500
খ
7200
গ
7127
ঘ
7231
ঙ
7800

ব্যাখ্যা

Here I = 156,
n=90 days=3/12=1/4
r=8%=8/100 = 2/25
Principal P=?

We know, I = Pnr
or, P = I/nr = 156/(1/4 × 2/25) = 156 × 50 = 7800

১,২৮৩.

A, B and C are partners of a company. During a particular year A received one-third of the profit, B received one-fourth of the profit and C received the remaining Tk. 5000. How much did B receive?

ক
ক) Tk. 5000
খ
খ) Tk. 4000
গ
গ) Tk. 2000
ঘ
ঘ) Tk. 3000

ব্যাখ্যা

Question: A, B and C are partners of a company. During a particular year A received one-third of the profit, B received one-fourth of the profit and C received the remaining Tk. 5000. How much did B receive?

Solution:
ধরি,
মোট লাভ = x টাকা

প্রশ্নমতে,
x - (x/3 + x/4) = 5000
⇒ x - (4x + 3x)/12 = 5000
⇒ x - 7x/12 = 5000
⇒ (12x - 7x)/12 = 5000
⇒ 5x/12 = 5000
⇒ 5x = 5000 × 12
⇒ x = (5000 × 12)/5
∴ x = 12000

∴ B পায় = (12000 × 1/4) টাকা = 3000 টাকা

১,২৮৪.

If the selling price of an article is 8/5 times its cost price, the profit percent on it is =?

ক
30%
খ
40%
গ
45%
ঘ
50%
ঙ
None

ব্যাখ্যা

Question: If the selling price of an article is 8/5 times its cost price, the profit percent on it is =?

Solution:
According to the question,
Selling price = (8/5) × Cost price
⇒ Selling price/Cost price = 8/5

So, gain = 8 - 5 = 3

∴ The profit percent = (3/5) × 100
= 60%

১,২৮৫.

The output of a glass factory was increased by 12% to keep up with the rising demand. Later, this new output was increased by another 25%, By approximately what percentage would the output now have to be decresed in order to restore to the original output?

ক
ক) 28.6%
খ
খ) 24.7%
গ
গ) 32.8%
ঘ
ঘ) 40%
ঙ
ঙ) None

ব্যাখ্যা

Question: The output of a glass factory was increased by 12% to keep up with the rising demand. Later, this new output was increased by another 25%, By approximately what percentage would the output now have to be decresed in order to restore to the original output?

Solution:
ধরি
পূর্বে Output ছিল = 100
12% বৃদ্ধিতে
বর্তমান output = 100 + 100 এর 12%
= 112
25% বৃদ্ধিতে
বর্তমান output = 112 + 112 এর 25%
= 140

Output কমাতে হবে = 140 - 100 = 40
Output শতকরা কমাতে হবে = (40/140) × 100% = 28.57% ≈ 28.6%

১,২৮৬.

A house worth Tk. 150000 is sold by X at a 5% profit to Y, Y sells the house back to X at a 2% loss. Then find profit and loss in the entire transaction = ?

ক
ক) X gains Tk. 3250
খ
খ) X loses Tk. 3250
গ
গ) X gains Tk. 3150
ঘ
ঘ) X loses Tk. 3150

ব্যাখ্যা

Money spent by X = Tk. 150000
Money received by X = 105% of Tk. 150000 = Tk. 157500
C.P. to X = 98% of Tk. 157500 = Tk. 154350
∴ X gains Tk. (157500 - 154350) = Tk. 3150

১,২৮৭.

A dealer paid a car manufacturer tk 1,35,000 for a car. What should be the selling price of the car, if after allowing a buyer 10% discount on the selling price, he made a profit of 8 % on his outlay?

ক
1,54,000 tk
খ
1,58,000 tk
গ
1,60,000 tk
ঘ
1,62,000 tk
ঙ
None of the above

ব্যাখ্যা

Question: A dealer paid a car manufacturer tk 1,35,000 for a car. What should be the selling price of the car, if after allowing a buyer 10% discount on the selling price, he made a profit of 8 % on his outlay?

Solution:
Let, the selling price be x
Discounted selling price = 0.9x

Profit = Discounted selling price - Cost price
⇒ 0.08 × 1,35,000 = 0.9x - 1,35,000
⇒10,800 = 0.9x - 1,35,000
⇒ 0.9x = 10,800 + 1,35,000
⇒ 0.9x = 1,45,800
⇒ x = 1,45,800/0.9
∴ x = 1,62,000

১,২৮৮.

A milkman purchases the milk at Tk. x per litre and sells it at Tk. 2x per litre still he mixes 2 litres water with every 6 litres of pure milk. What is the profit percentage?

ক
116%
খ
100%
গ
60%
ঘ
166.66%
ঙ
None of these

ব্যাখ্যা

Question: A milkman purchases the milk at Tk. x per litre and sells it at Tk. 2x per litre still he mixes 2 litres water with every 6 litres of pure milk. What is the profit percentage?

Solution:
the buying price of 6 litres of milk is = 6x Tk.

after mixing 2 litres of water the total amount of mixture is = 8 litres

selling 2x per litres the total selling price is = 16x
∴ profit = 16x - 6x = 10x

profit in percentage = (10x/6x)100%
= 166.66%

১,২৮৯.

There is a ratio of 5 : 4 between two numbers. If 40% of the first number is 12, then what would be 50% of the second number is ?

ক
24
খ
12
গ
18
ঘ
6

ব্যাখ্যা

Question: There is a ratio of 5 : 4 between two numbers. If 40% of the first number is 12, then what would be 50% of the second number is ?

Solution:
Let the numbers be 5x and 4x respectively

According to the question,
⇒ 5x × (40/100) = 12
⇒ 2x = 12
∴ x = 6

Now,
50% of the second number is,
= 4x of 50%
= 4 × 6 × (50/100)
= 12

So 50% of the second number is 12.

১,২৯০.

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?

ক
ক) 180
খ
খ) 190
গ
গ) 200
ঘ
ঘ) 220

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

১,২৯১.

Of a group of people surveyed in a political poll, 60 percent said that they would vote for candidate R. Of those who said they would vote for R, 90 percent actually voted for R, and of those who did not say that they would vote for R, 5 percent actually voted for R. What percent of the group voted for R?

ক
56%
খ
59%
গ
62%
ঘ
65%

ব্যাখ্যা

Question: Of a group of people surveyed in a political poll, 60 percent said that they would vote for candidate R. Of those who said they would vote for R, 90 percent actually voted for R, and of those who did not say that they would vote for R, 5 percent actually voted for R. What percent of the group voted for R?

Solution:
Let,
Group = 100 people
60% said they would vote R = 60 people

Of the 60 people only 90% actually voted R = 54

40% said they would NOT vote R = 40 people
Of the 40 people who would vote NOT R, 5% voted R instead = 2

So 54 + 2 = 56

১,২৯২.

A man sold two chairs at Tk. 1500 each. On one he gained 20% and on the other he lost 20%. His gain or loss in the whole transaction is -

ক
ক) 3% loss
খ
খ) 4% loss
গ
গ) 4.5% gain
ঘ
ঘ) 5% gain

ব্যাখ্যা

question: A man sold two chairs at Tk. 1500 each. On one he gained 20% and on the other he lost 20%. His gain or loss in the whole transaction is -

Solution:
in 20% profit,
selling price is 120 when buying price = 100
selling price is 1500 when buying price = (1500 × 100)/120
= 1250 Tk.

in 20% loss
selling price 80 if buying price = 100
selling price 1500 if buying price = (1500 × 100)/80
= 1875 Tk.

total selling price is = 1500 + 1500 = 3000 Tk.
total buying price is = (1250 + 1875) = 3125 Tk.

loss = 3125 - 3000 = 125

percentage of loss is = (125/3125) 100%
= (1/25) × 100%
= 4%

১,২৯৩.

If the numerator of a fraction is increased by 150% and the denominator of the fraction is increased by 350%, the resultant fraction is 25/51. What is the original fraction?

ক
11/17
খ
11/15
গ
15/17
ঘ
13/15

ব্যাখ্যা

Let,
The original fraction be x/y
Let us assume that,
The value of x is 100 and the value of y is 100
Then the numerator of the resultant fraction is 250% of x,
That is {100 + (150/100) × 100}
Similarly the denominator of the resultant fraction is 450%
Given that,
(250% of x)/(450% of y)=25/51
⇒ (x/y) × (250/450) = 25/51
⇒ (x/y) = (25/51)/(250/450)
⇒ (x/y) = (25/51) × (450/250)
⇒ x/y = 15/17.

১,২৯৪.

In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was-

ক
2500
খ
2700
গ
2900
ঘ
3100
ঙ
None of these

ব্যাখ্যা

Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was-

Solution:
Total number of votes = 7500
Given that 20% of Percentage votes were invalid
∴ Valid votes = 80%

Total valid votes = 7500 × (80/100)
1st candidate got 55% of the total valid votes.

Hence the 2nd candidate should have got 45% of the total valid votes
Valid votes that 2nd candidate got = total valid votes × (45/100) = 7500 × (80/100) × (45/100) = 2700

১,২৯৫.

In a city, 40% of the people are illiterate and 60% are poor. Among the rich, 10% are illiterate. What percent of the poor population are illiterate?

ক
ক) 36
খ
খ) 40
গ
গ) 50
ঘ
ঘ) 60

ব্যাখ্যা

Question: In a city, 40% of the people are illiterate and 60% are poor. Among the rich, 10% are illiterate. What percent of the poor population are illiterate?

Solution:
মনেকরি
মোট জনসংখ্যা = ১০০ জন
অশিক্ষিত লোকের সংখ্যা = ১০০ এর ৪০%৳
= ১০০ এর ৪০/১০০
= ৪০ জন

গরীব লোকের সংখ্যা = ১০০ এর ৬০%
= ১০০ এর ৬০/১০০
= ৬০ জন

ধনী লোকের সংখ্যা = ১০০ এর ৪০%
= ১০০ এর ৪০/১০০
= ৪০ জন

ধনীদের মধ্যে অশিক্ষিত লোকের সংখ্যা = ৪০ এর ১০%
= ৪০ এর ১০/১০০
= ৪ জন

গরীবদের মধ্যে অশিক্ষিত লোকের সংখ্যা = (৪০ - ৪) জন
= ৩৬ জন

৬০ জনের মধ্যে অশিক্ষিত ৩৬ জন
১ জনের মধ্যে অশিক্ষিত ৩৬/৬০ জন
১০০ জনের মধ্যে অশিক্ষিত (৩৬ × ১০০)/৬০ জন
= ৬০ জন

১,২৯৬.

If 60% of A's income is equal to 75% of B's income, then B's income is equal to x% of A's income. The value of x is :

ক
60
খ
70
গ
75
ঘ
80

ব্যাখ্যা

Question: If 60% of A's income is equal to 75% of B's income, then B's income is equal to x% of A's income. The value of x is :

Solution:
According to the question,
60 × (A/100) = 75 × (B/100)
60A = 75B
4A = 5B
B = 4A/5

Again
B = A × (x/100)
4A/5 = A × (x/100)
4/5 = x/100
5x = 400
x = 400/5
x = 80

১,২৯৭.

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.

ক
98%
খ
91%
গ
93%
ঘ
95%

ব্যাখ্যা

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, present volume = 11 × 12 × 15 = 1980 cubic unit.
Increase in volume = 1980 - 1000 = 980 cubic unit.
% increase in volume = (980/1000) × 100 = 98%

১,২৯৮.

How much would I have to pay for a book which cost Tk. 80 to produce, if the printing company sold it to a book seller at 25% profit and the book seller sold it to me at a profit of 20%?

ক
Tk. 105
খ
Tk. 110
গ
Tk. 112
ঘ
Tk. 120

ব্যাখ্যা

Question: How much would I have to pay for a book which cost Tk. 80 to produce, if the printing company sold it to a book seller at 25% profit and the book seller sold it to me at a profit of 20%?

Solution:
উৎপাদন খরচ = 80 টাকা

25% লাভে
উৎপাদন খরচ 100 টাকা হলে বিক্রয়মূল্য = 100 + 25 বা 125 টাকা
উৎপাদন খরচ 1 টাকা হলে বিক্রয়মূল্য = 125/100 টাকা
উৎপাদন খরচ 80 টাকা হলে বিক্রয়মূল্য = (125 × 80)/100 টাকা
= 100 টাকা

কোম্পানির বিক্রয়মূল্য = খুচরা বিক্রেতার ক্রয়মূল্য

খুচরা বিক্রেতার 20% লাভে
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য = 100 + 20 বা 120 টাকা

∴ বইয়ের জন্য আমাকে 120 টাকা দিতে হবে।

১,২৯৯.

The cost price of 6 oranges equals selling price of five. The profit or loss percent in the transaction is?

ক
20%
খ
25%
গ
30%
ঘ
50%

ব্যাখ্যা

Question: The cost price of 6 oranges equals selling price of five. The profit or loss percent in the transaction is?

Solution:
দেওয়া আছে,
6টি কমলার ক্রয়মূল্য = 5টি কমলার বিক্রয়মূল্য
ধরি, 1টি কমলার ক্রয়মূল্য = x টাকা
তাহলে,
6 টি কমলার ক্রয়মূল্য = 6x টাকা
5 টি কমলার বিক্রয়মূল্য = 6x টাকা

∴ 1টি কমলার বিক্রয়মূল্য = 6x/5 টাকা

∴ লাভ = বিক্রয়মূল্য - ক্রয়মূল্য
= (6x/5) - x
= (6x - 5x)/5
= x/5

∴ x টাকায় লাভ হয় x/5 টাকা
1 টাকায় লাভ হয় = (x/5)/x টাকা
100 টাকায় লাভ হয় = (1 × 100)/5 = 20 টাকা

∴ লাভ হয় 20%

১,৩০০.

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?

ক
20%
খ
25%
গ
40%
ঘ
66.67%

ব্যাখ্যা

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%