Percentage and Profit & Loss

PrepBank · পাতা ৮ / ১৭ · ৭০১–৮০০ / ১,৬৯৬

৭০১.

Which number is 25% less than 120?

ক
80
খ
86
গ
90
ঘ
100

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: Which number is 25% less than 120?

Solution:
Let the number be x.
x = 120 - 120 × 0.25
⇒ x = 120 - 30
∴ x = 90

So, the number is 90.

৭০২.

When the length of a rectangle grows by 25%, what percentage reduction in the width is required to maintain the same area?

ক
15%
খ
20%
গ
22%
ঘ
30%

সঠিক উত্তর: খ

20%

উত্তর

সঠিক উত্তর: খ

20%

খ

ব্যাখ্যা

Question: When the length of a rectangle grows by 25%, what percentage reduction in the width is required to maintain the same area?

Solution:
We can let the original length = 4, and the original width = 10.
So the original area is 40.

When the length increases by 25% we have 4 × 1.25 = 5
Thus, for the area to remain 40, the width must be 8.

Since {(8 - 10)/10} × 100 = - 20,

we see that 8 is 20 percent less than 10. In other words, the width has to decrease by 20%.

৭০৩.

At the beginning of each year, the price of item X is 10 percent higher than its price at the beginning of the previous year. During three consecutive years, if the price of item X is Tk. 80 at the beginning of the first year, what is its price at the beginning of the third year?

ক
Tk. 88
খ
Tk. 96
গ
Tk. 96.8
ঘ
Tk. 100
ঙ
Tk. 160

সঠিক উত্তর: গ

Tk. 96.8

উত্তর

সঠিক উত্তর: গ

Tk. 96.8

গ

ব্যাখ্যা

Question: At the beginning of each year, the price of item X is 10 percent higher than its price at the beginning of the previous year. During three consecutive years, if the price of item X is Tk. 80 at the beginning of the first year, what is its price at the beginning of the third year?

Solution:
The price of item X is increasing 10% each year then the previous year.

At the beginning of the first year, the price of item X = Tk. 80

At the beginning of the second year, the price of item X = 80 × (1 + 10/100) = Tk. (80 × 1.1) = Tk. 88

At the beginning of the third year, the price of item X = 88 × (1 + 10/100) = Tk. (88 × 1.1) = Tk. 96.8

৭০৪.

The price of salt has risen by 25%. If a family wants to keep their expenses on salt the same as earlier, the family will have to decrease its consumption of salt by

ক
25%
খ
30%
গ
15%
ঘ
10%
ঙ
None

সঠিক উত্তর: ঙ

None

উত্তর

সঠিক উত্তর: ঙ

None

ঙ

ব্যাখ্যা

Question: The price of salt has risen by 25%. If a family wants to keep their expenses on salt the same as earlier, the family will have to decrease its consumption of salt by

Solution:

Let the initial expenses on salt was Tk. 100.

Now, the price of salt has risen 25%.

So, to buy the same amount of salt, they need to spend,

= (100 + 25% of 100) = Tk. 125.

But, They want to keep expenses on salt, so they have to cut Tk. 25 in the expenses to keep it to Tk. 100.

Now, % decrease in Consumption,
(25/125) × 100 = 20%

৭০৫.

A shirt is sold for Tk. 1500 at a profit of 20%. What would have been the actual profit or loss if it had been sold for Tk. 1200?

ক
profit 5%
খ
loss of 8%
গ
profit 4.5%
ঘ
None of these

সঠিক উত্তর: ঘ

None of these

উত্তর

সঠিক উত্তর: ঘ

None of these

ঘ

ব্যাখ্যা

Question: A shirt is sold for Tk. 1500 at a profit of 20%. What would have been the actual profit or loss if it had been sold for Tk. 1200?

Solution:
Firstly let us find the cost price of the same. C.P. = 1500 × (100/120) = 1250.
New selling price = 1200
Loss = 1250 - 1200 = 50

∴ Loss percentage = 100 × (50/1250)
= 4%.

If sold at Tk. 1200, there would be a loss of 4%.

৭০৬.

A manufacturer sells a pair of shoes to a wholesale dealer at a profit of 20%. Wholesalers sell them to retailers at a profit of 25 %. The shoes are again sold to the customer for Tk. 50.50, thereby earning a profit of 30 %. Find the cost price of the manufacturer.

ক
Tk. 20.36
খ
Tk. 22.90
গ
Tk. 25.89
ঘ
Tk. 30.50

সঠিক উত্তর: গ

Tk. 25.89

উত্তর

সঠিক উত্তর: গ

Tk. 25.89

গ

ব্যাখ্যা

Profit earned by manufacturer = 20%
Profit earned by wholesaler = 25%
Profit earned by retailer = 30%
S.P. of shoes = Tk. 50

Therefore, 130% of 125% of 120% of x = 50.50
⇒ 120/100 × 125/100 × 130/100 × x = 5050/100
⇒ (195/100) x = 5050/100
⇒ x = (5050 × 100)/(195 × 100)
⇒ x = 25.89
Cost price of shoes = Tk. 25.89

৭০৭.

A man buys a chair and table for Tk. 6000. He sells the chair at a loss of 10% and the table at gain of 10%. He still gains Tk. 100 on the whole. Cost price of chair is:

ক
2500
খ
2850
গ
3050
ঘ
2100

সঠিক উত্তর: ক

2500

উত্তর

সঠিক উত্তর: ক

2500

ক

ব্যাখ্যা

Question: A man buys a chair and table for Tk. 6000. He sells the chair at a loss of 10% and the table at gain of 10%. He still gains Tk. 100 on the whole. Cost price of chair is:

Solution:
Given,
Total cost price (CP) of chair and table = Tk. 6000
Total profit = Tk. 100

Let, the Cost Price (CP) of the chair be x Tk.
So, the Cost Price of the table is = (6000 - x) Tk.

At 10% loss,
Selling Price of chair = x - 10% of x
= x - (10x/100)
= 90x/100

At 10% gain,
Selling Price of table = (6000 - x) + 10% of (6000 - x)
= (6000 - x) + {(10/100) × (6000 - x)}
= 110(6000 - x)/100

So, Total Selling Price of chair and table,
= 90x/100 + {110(6000 - x)/100}
= {90x + 110(6000 - x)}/100

Now,
Total SP = Total CP + Profit
⇒ {90x + 110(6000 - x)}/100 = 6000 + 100
⇒ 90x + 110(6000 - x) = 100 × 6100
⇒ 90x + 660000 - 110x = 610000
⇒ - 20x = - 50000
⇒ x = 2500
∴ Cost price of the chair = Tk. 2500

৭০৮.

If 0.05 is a% of 0.5, then the value of a is-

ক
ক) 100
খ
খ) 1
গ
গ) 10
ঘ
ঘ) 1/10

সঠিক উত্তর: গ

গ) 10

উত্তর

সঠিক উত্তর: গ

গ) 10

গ

ব্যাখ্যা

a% of 0.5 = 0.05
⇒ 0.5 × (a/100) = 0.05
⇒ a/100 =0.05/0.5
⇒ a/100 = 0.1
∴ a = 10

৭০৯.

By selling an article at 2/3 of the marked price, there is a loss of 10%. The profit when the article is sold at the marked price is -

ক
ক) 30%
খ
খ) 35%
গ
গ) 20%
ঘ
ঘ) 15%

সঠিক উত্তর: খ

খ) 35%

উত্তর

সঠিক উত্তর: খ

খ) 35%

খ

ব্যাখ্যা

Question: By selling an article at 2/3 of the marked price, there is a loss of 10%. The profit when the article is sold at the marked price is -

Solution:
Let the marked price be Tk x.
Then, S.P. = 2x/3
At 10% loss C.P. = (100/90) × (2x/3) = 20x/27

If an article is sold at M.P.
Then, Profit = x - (20x/27) = 7x/27

∴ Profit% = (7x/27) × (27/20x) × 100% = 35%

৭১০.

A printer was sold at the loss of 6% If it were sold at Tk. 2600 more, there would be a profit of 7%. What was the cost price of the printer?

ক
10,000 tk.
খ
15,000 tk.
গ
20,000 tk.
ঘ
25,000 tk.

সঠিক উত্তর: গ

20,000 tk.

উত্তর

সঠিক উত্তর: গ

20,000 tk.

গ

ব্যাখ্যা

Question: A printer was sold at the loss of 6% If it were sold at Tk. 2600 more, there would be a profit of 7%. What was the cost price of the printer?

Solution:
মনে করি,
ক্রয়মূল্য = 100 টাকা
∴ 6% ক্ষতিতে বিক্রয়মূল্য = 100 - 6 = 94 টাকা

এবং
7% লাভে বিক্রয়মূল্য = 100 + 7 = 107 টাকা
∴ বিক্রয়মূল্য (107 - 94) = 13 টাকা বেশি হলে, 7% লাভে হতো।

এখন,
বিক্রয়মূল্য 13 টাকা বেশি হলে ক্রয়মূল্য 100 টাকা
∴ বিক্রয়মূল্য 1 টাকা বেশি হলে ক্রয়মূল্য (100/13) টাকা
∴ বিক্রয়মূল্য 2600 টাকা বেশি ক্রয়মূল্য (100 × 2600/13) টাকা
= 20000 টাকা।

সুতরাং, ক্রয়মূল্য 20000 টাকা।

৭১১.

Jobayer spent 2700 taka, which is 20 percent of his monthly salary. What is his monthly salary?

ক
13500 taka
খ
22500 taka
গ
16500 taka
ঘ
8000 taka

সঠিক উত্তর: ক

13500 taka

উত্তর

সঠিক উত্তর: ক

13500 taka

ক

ব্যাখ্যা

Question: Jobayer spent 2700 taka, which is 20 percent of his monthly salary. What is his monthly salary?

Solution:
If 20% is equal to 2700 taka
Then 100% is equal to (2700 × 100)/20 taka
= 13500 taka

৭১২.

Karim's salary is 5000 takas. If his salary increases by 5%, 10%, and 20% consecutively over three years, what will his salary be at the end of three years?

ক
Tk. 7560
খ
Tk. 6930
গ
Tk. 6875
ঘ
Tk. 7930
ঙ
Tk. 10250

সঠিক উত্তর: খ

Tk. 6930

উত্তর

সঠিক উত্তর: খ

Tk. 6930

খ

ব্যাখ্যা

Question: Karim's salary is 5000 takas. If his salary increases by 5%, 10%, and 20% consecutively over three years, what will his salary be at the end of three years?

Solution:
১ম বছর ৫% বৃদ্ধিতে,
নতুন বেতন = ৫০০০ +{৫০০০ × (৫/১০০)}
=৫০০০ + ২৫০ = ৫২৫০ টাকা

২য় বছর ১০% বৃদ্ধিতে,
নতুন বেতন = ৫২৫০ +{৫২৫০ × (১০/১০০)}
=৫২৫০ + ৫২৫ = ৫৭৭৫ টাকা

৩য় বছর ৫% বৃদ্ধিতে,
নতুন বেতন = ৫৭৭৫ +{৫৭৭৫ × (২০/১০০)}
=৫৭৭৫ + ১১৫৫ = ৬৯৩০ টাকা

∴ তিন বছর শেষে করিম সাহেবের বেতন হবে ৬৯৩০ টাকা

৭১৩.

After selling a saree for Tk. 3360 a shopkeeper suffers a loss of 16%. If he wants to earn 15% profit after giving the discount of 8%, what will be the marked price of the saree?

ক
Tk. 4800
খ
Tk. 5000
গ
Tk. 5500
ঘ
Tk. 4000

সঠিক উত্তর: খ

Tk. 5000

উত্তর

সঠিক উত্তর: খ

Tk. 5000

খ

ব্যাখ্যা

Question: After selling a saree for Tk. 3360 a shopkeeper suffers a loss of 16%. If he wants to earn 15% profit after giving the discount of 8%, what will be the marked price of the saree?

Solution:
After selling a saree for Tk. 3360 a shopkeeper suffers a loss of 16%.

Selling price Tk. 84 when Cost price = Tk. 100
∴ Selling price Tk. 3360 when Cost price = Tk. (100 × 3360)/84
= Tk. 4000

15% profit,
Cost price Tk. 100 then Selling price = Tk. 115
∴ Cost price Tk. 4000 then Selling price = Tk. (115 × 4000)/100
= Tk. 4600

discount 8%,
Selling price Tk. 92 When Marked price = Tk. 100
∴ Selling price Tk. 4600 When Marked price = Tk. (100 × 4600)/92
= Tk. 5000

৭১৪.

Rana earns 30% more than Mina. Tina earns 60% more than Mina. How much % is the wages earned by Tina more than that earned by Rana?

ক
17.03%
খ
27.42%
গ
23.08%
ঘ
26.17%
ঙ
15.09%

সঠিক উত্তর: গ

23.08%

উত্তর

সঠিক উত্তর: গ

23.08%

গ

ব্যাখ্যা

Question: Rana earns 30% more than Mina. Tina earns 60% more than Mina. How much % is the wages earned by Tina more than that earned by Rana?

Solution:
Let's assume Mina's wage is 100 tk.
Rana's wage = 100 + (30% of 100) =130 tk
Tina's wage = 100 + (60% of 100) = 160 tk

Percentage difference = (Difference in wages/Rana's wage) × 100
= {(Tina's wage - Rana's wage)/Rana's wage} × 100
= {(160 - 130)/130} × 100
= 23.08%
Therefore, the wages earned by Tina is 23.08% more than the wages earned by Rana.

৭১৫.

A car dealership has 40 cars on the lot, 30% of which are silver. If the dealership receives a new shipment of 80 cars, 40% of which are not silver, what percent of the total number of cars are silver?

ক
40%
খ
45%
গ
50%
ঘ
55%

সঠিক উত্তর: গ

50%

উত্তর

সঠিক উত্তর: গ

50%

গ

ব্যাখ্যা

Question: A car dealership has 40 cars on the lot, 30% of which are silver. If the dealership receives a new shipment of 80 cars, 40% of which are not silver, what percent of the total number of cars are silver?

Solution:
old silver car = 30% of 40 = 12
new silver car = (100 - 40)% of 80
= 60% of 80
= 48

% silver car = {(12 + 48)/ (40 + 80)} × 100%
=(60/120)× 100%
= 1/2 × 100%
= 50%

৭১৬.

A line of length 1.5 metres was measured as 1.55 metres by mistake. What will be the value of the error percent?

ক
7%
খ
5.33%
গ
4%
ঘ
3.33%
ঙ
None

সঠিক উত্তর: ঘ

3.33%

উত্তর

সঠিক উত্তর: ঘ

3.33%

ঘ

ব্যাখ্যা

Question: A line of length 1.5 metres was measured as 1.55 metres by mistake. What will be the value of the error percent?

Solution:
Percentage error = 1.55 - 1.50 = 0.05

∴ Percentage error % = (0.05/1.50) × 100
= (5/150) × 100
= 10/3
= 3.33%

৭১৭.

The ratio between Karim's age and Rahim's age is 10 : 11. What is the age of Rahim in percentage of Karim's age ?

ক
121%
খ
90%
গ
100%
ঘ
110%

সঠিক উত্তর: ঘ

110%

উত্তর

সঠিক উত্তর: ঘ

110%

ঘ

ব্যাখ্যা

Question: The ratio between Karim's age and Rahim's age is 10 : 11. What is the age of Rahim in percentage of Karim's age ?

Solution:
Given that,
The ratio of Karim's age to Rahim's age = 10 : 11

Let, Karim's age = 10x
and Rahim's age = 11x

Now, we find Rahim's age as a percentage of Karim's age,

∴ Percentage = (Rahim’s age/Karim’s age) × 100
= (11x/10x) × 100
= 110

So, Rahim's age is 110% of Karim's age.

৭১৮.

A batsman scored 100 runs which include 6 boundaries and 6 sixes. What percent of his total score did he make by running between the wickets?

ক
ক) (500/111)%
খ
খ) 40%
গ
গ) (20/7)%
ঘ
ঘ) 60%

সঠিক উত্তর: খ

খ) 40%

উত্তর

সঠিক উত্তর: খ

খ) 40%

খ

ব্যাখ্যা

Question: A batsman scored 100 runs which include 6 boundaries and 6 sixes. What percent of his total score did he make by running between the wickets?

Solution:
Total score of batsman = 100 runs
runs from boundaries = 6 × 4 = 24
runs from sixes =6 × 6 = 36

∴ Total runs from boundaries and sixes = 24 + 36
= 60 runs

Total runs by the batsman = 100 - 60 = 40 runs
percentage of his score made by running between wickets = (40/100) × 100 = 40%

৭১৯.

If the list price of a shirt is Tk. 800, and a Tk. 160 discount is offered on the shirt, then what is the discount percentage?

ক
15%
খ
16%
গ
20%
ঘ
22%

সঠিক উত্তর: গ

20%

উত্তর

সঠিক উত্তর: গ

20%

গ

ব্যাখ্যা

Question: If the list price of a shirt is Tk. 800, and a Tk. 160 discount is offered on the shirt, then what is the discount percentage?

Solution:
Discount % = (Discount/marked Price) × 100
Marked Price = Tk. 800
Discount = Tk. 160

Discount (%) = (160/800) ×100%
= 20%

∴ Therefore, the discount percentage is calculated as 20%.

৭২০.

What percent of 1/2 is 12/16?

ক
100%
খ
120%
গ
160%
ঘ
150%
ঙ
None of these

সঠিক উত্তর: ঘ

150%

উত্তর

সঠিক উত্তর: ঘ

150%

ঘ

ব্যাখ্যা

Question: What percent of 1/2 is 12/16?

Solution:
Percentage = (3/4)/(1/2) × 100
= (3/4) × (2/1) × 100
= (3/2) × 100
= 150%

Therefore, 12/16 is 150% of 1/2.

৭২১.

A ball and a bat costs 110 taka. The bat costs 100 taka more than the ball. How much does the ball cost?

ক
ক) 5
খ
খ) 10
গ
গ) 15
ঘ
ঘ) 100

সঠিক উত্তর: ক

ক) 5

উত্তর

সঠিক উত্তর: ক

ক) 5

ক

ব্যাখ্যা

প্রশ্ন: একটি ব্যাট ও বলের মূল্য একত্রে ১১০ টাকা। ব্যাটের দাম বলের থেকে ১০০ টাকা বেশি হলে, বলের দাম কত?

সমাধান:
ধরি,
বলের দাম = p টাকা
∴ ব্যাটের দাম = p + 100

প্রশ্নমতে,
p + p + 100 = 110
2p = 10
p = 5

∴ বলের দাম = 5 টাকা

৭২২.

A shopkeeper takes 10% profit on his goods. He lost 20% of his goods during a theft. What is his loss percent?

ক
10%
খ
15%
গ
14%
ঘ
12%

সঠিক উত্তর: ঘ

12%

উত্তর

সঠিক উত্তর: ঘ

12%

ঘ

ব্যাখ্যা

Question: A shopkeeper takes 10% profit on his goods. He lost 20% of his goods during a theft. What is his loss percent?

Solution:

Let the number of goods be 100, and

C.P. of each item be Tk. 1

∴ Total C.P. = Tk. 100

Profit% on each item = 10%

20% of goods are lost in a theft

Number of goods left = 80

Now,
S.P. of 1 item = [(100 + 10)/100] × 1 = Tk. 1.10

S.P. of 80 items = 80 × 1.10 = Tk. 88

Loss = 100 - 88 = 12

Loss% = (12/100) × 100% = 12%

Thus, the shopkeeper bears 12% loss.

৭২৩.

Which of these is NOT a correct way to find 75% of 35?

ক
ক) 75 × 35
খ
খ) (75 × 35 )/100
গ
গ) (75/100) × 35
ঘ
ঘ) 35 × (3/4)

সঠিক উত্তর: ক

ক) 75 × 35

উত্তর

সঠিক উত্তর: ক

ক) 75 × 35

ক

ব্যাখ্যা

75% of 35 = (75/100) × 35.
75% কে লেখা যায় = (75/100) = .75 = 3/4

৭২৪.

A mixture contains milk and water in the ratio 7 : 3 cost Tk. 500. Then 2 litters of water were added. What is the profit percentage?

ক
10%
খ
20%
গ
30%
ঘ
40%

সঠিক উত্তর: খ

20%

উত্তর

সঠিক উত্তর: খ

20%

খ

ব্যাখ্যা

Question: A mixture contains milk and water in the ratio 7 : 3 cost Tk. 500. Then 2 litters of water were added. What is the profit percentage?

Solution:
Let
Milk = 7 liters
Water = 3 liters
Original mixture quantity = 10 liters

Cost of original mixture = 500 Taka
Cost per liter = 500 / 10 = 50 Taka

Water added = 2 liters
New total water = 3 + 2 = 5 liters
Milk remains = 7 liters
Total mixture = 7 + 5 = 12 liters

Total Selling Price = 12 × 50 = 600 Taka

Profit = SP - CP = 600 - 500 = 100
Profit % = (100/500) × 100 = 20%

∴ Profit percent = 20%

৭২৫.

A man paid tax on 9000 Taka at 30%. He paid the tax in 12 equal payments. Each payment was

ক
2.25 Taka
খ
22.50 Taka
গ
225 Taka
ঘ
250 Taka

সঠিক উত্তর: গ

225 Taka

উত্তর

সঠিক উত্তর: গ

225 Taka

গ

ব্যাখ্যা

Question: A man paid tax on 9000 Taka at 30%. He paid the tax in 12 equal payments. Each payment was

Solution:
∴ ১০০ টাকায় কর দেয় = ৩০ টাকা
∴ ১ টাকায় কর দেয় = ৩০/১০০ = ৩/১০ টাকা
∴ ৯০০০ টাকায় কর দেয় = (৩ × ৯০০০)/১০ = ২৭০০ টাকা

∴ মোট কর = ২৭০০ টাকা

১২টি সমান কিস্তিতে পরিশোধ করে।

∴ প্রতি কিস্তিতে পরিশোধ = ২৭০০/১২ = ২২৫ টাকা

৭২৬.

Lubana purchases 20kg of pulses at a rate of Tk. 14.25 per kg and 30kg of pulses at a rate of Tk. 11.50 per kg. She decided to mix the two and sold the mixture. To make a profit of 30%, what price per kg should he sell the mixture?

ক
ক) 15.60
খ
খ) 14.80
গ
গ) 16.38
ঘ
ঘ) 18.20

সঠিক উত্তর: গ

গ) 16.38

উত্তর

সঠিক উত্তর: গ

গ) 16.38

গ

ব্যাখ্যা

Question: Lubana purchases 20kg of pulses at a rate of Tk. 14.25 per kg and 30kg of pulses at a rate of Tk. 11.50 per kg. She decided to mix the two and sold the mixture. To make a profit of 30%, what price per kg should he sell the mixture?

Solution:
20 কেজি ডালের মোট মূল্য = (14.25 × 20) টাকা
= 285 টাকা

30 কেজি ডালের মোট মূল্য = (11.50× 30) টাকা
= 345 টাকা

(20 + 30)কেজি বা 50 কেজি ডালের মোট মূল্য = (285 + 345) টাকা
= 630 টাকা

1 কেজি ডালের মূল্য =630/50 = 12.60 টাকা

30% লাভে
1 কেজি ডালের মূল্য = (12.6 + 12.6 এর 30/100) টাকা
= 12.6 + 3.78
= 16.38 টাকা

৭২৭.

605 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
55
খ
44
গ
33
ঘ
11

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: 605 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?

Solution:
Let Children = X
A/Q,
605/X = 20% of X
⇒ 605/X = X/5
⇒ X² =5 × 605
⇒ X² = 5² × 11²
X = 55

So each children receive = 605/55
= 11

৭২৮.

0.01 is what percent of 0.1?

ক
1/100
খ
1/10
গ
10
ঘ
100

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: 0.01 is what percent of 0.1?

Solution:
ধরি
0.1 এর x% = 0.01
বা, 0.1 এর x/100 = 0.01
বা, 0.1x/100 = 0.01
বা, 0.1x = 0.01 × 100
বা, x = (0.01 × 100)/0.1
x = 10

৭২৯.

Each side of a rectangular field diminished by 40%. By how much per cent is the area of the field diminished?

ক
32%
খ
64%
গ
25%
ঘ
16%
ঙ
None of these

সঠিক উত্তর: খ

64%

উত্তর

সঠিক উত্তর: খ

64%

খ

ব্যাখ্যা

Solution: Each side of a rectangular field diminished by 40%. By how much per cent is the area of the field diminished?

Solution:
Let,
The Original length of the rectangle be 20 unit and breadth be 10 unit.
Then Original Area = length × breadth = 20 × 10 = 200 Square unit.
40% decrease in each side, then
Length = (20 - 40% of 20) = 12 unit.
Breadth = (10 - 40% of 10) = 6 unit.
Now,
Area = 12 × 6 = 72 Square unit.
Decrease in area = 200 - 72 = 128 square unit.
% Decrease in Area = (128/200) × 100 = 64%

৭৩০.

An employee's annual salary was increased $15,000. If her new annual salary now equals $90,000, what was the percent increase?

ক
ক) 15%
খ
খ) 20%
গ
গ) 22%
ঘ
ঘ) 24%

সঠিক উত্তর: খ

খ) 20%

উত্তর

সঠিক উত্তর: খ

খ) 20%

খ

ব্যাখ্যা

Question: An employee's annual salary was increased $15,000. If her new annual salary now equals $90,000, what was the percent increase?

Solution:
আমরা জানি,
বেতন বৃদ্ধির হার = {(বর্ধিত বেতন/পূর্বের বেতন) × 100}%
= {15000/(90000 - 15000) × 100}%
= {(15000/75000) × 100}%
= 20%

৭৩১.

A merchant sells 30 metres of cloth and gains a selling price of 10 metres. Find the gain percent.

ক
ক) 15%
খ
খ) 25%
গ
গ) 50%
ঘ
ঘ) 75%

সঠিক উত্তর: গ

গ) 50%

উত্তর

সঠিক উত্তর: গ

গ) 50%

গ

ব্যাখ্যা

Here,
The selling price of 10 m cloth is obtained as profit.
Profit of 10 m cloth = (S.P. of 30 m cloth) – (C.P. of 30 m cloth)
The selling price of 20 m cloth = Selling Price of 30 m of cloth

Let the cost of each metre be Tk. 100.

Therefore,
the cost price of 20 m cloth = 20 × 100 = Tk. 2000 and
S.P. of 20 m cloth = Tk. 3000

Profit% = (10/20) × 100
= 50%

৭৩২.

A shopkeeper marks his goods 30% above the cost price, but allows a 20% discount for cash purchase. What percent profit does he make?

ক
12%
খ
8%
গ
4%
ঘ
2%

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: A shopkeeper marks his goods 30% above the cost price, but allows a 20% discount for cash purchase. What percent profit does he make?

Solution:
At 30% above,
The market price of goods = (100 + 30)
= Tk. 130

At 20% discount,
Selling price = 130 - 20% of 130
= 130 - 26
= Tk. 104

∴ Profit = (104 - 100) = Tk. 4
Profit % = (4/100) × 100
= 4%

৭৩৩.

Nafiza bought a ticket of a cricket match for Tk. 25 and later sold the ticket to Raida for tk. 75. What was the percent increase in the price of the ticket?

ক
ক) 200%
খ
খ) 150%
গ
গ) 300%
ঘ
ঘ) 100%

সঠিক উত্তর: ক

ক) 200%

উত্তর

সঠিক উত্তর: ক

ক) 200%

ক

ব্যাখ্যা

Question: Nafiza bought a ticket of a cricket match for Tk. 25 and later sold the ticket to Raida for tk. 75. What was the percent increase in the price of the ticket?

Solution:
ক্রয়মূল্য = 25 টাকা
বিক্রয়মূল্য = 75 টাকা
লাভ = 75 -25 = 50 টাকা

25 টাকায় লাভ হয় = 50 টাকা
1 টাকায় লাভ হয় = 50/25 টাকা
100 টাকায় লাভ হয় = (50 × 100)/25 টাকা
= 200 টাকা

৭৩৪.

What will be the fraction of 4%

ক
ক) 1/20
খ
খ) 1/50
গ
গ) 1/75
ঘ
ঘ) 1/25

সঠিক উত্তর: ঘ

ঘ) 1/25

উত্তর

সঠিক উত্তর: ঘ

ঘ) 1/25

ঘ

ব্যাখ্যা

4% = 4/100 = 1/25

৭৩৫.

In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school?

ক
72
খ
100
গ
124
ঘ
180

সঠিক উত্তর: খ

100

উত্তর

সঠিক উত্তর: খ

100

খ

ব্যাখ্যা

Question: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school?

Solution:
Given,
20% of students are below 8 years of age
Number of students of 8 years of age = 48
Number of students above 8 years = 2/3 of students of 8 years

∴ Students above 8 years = 2/3 × 48 = 32
∴ Students of 8 years or above = 48 + 32 = 80

Since 20% are below 8 years, then 80% are of 8 years or above.
So, 80% of total students = 80

Let, total number of students = x
80% of x = 80
⇒ (80/100) × x = 80
⇒ x = 80 × (100/80)
∴ x = 100

৭৩৬.

What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?

ক
ক) 10%
খ
খ) 20%
গ
গ) 15%
ঘ
ঘ) 7%

সঠিক উত্তর: খ

খ) 20%

উত্তর

সঠিক উত্তর: খ

খ) 20%

খ

ব্যাখ্যা

Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1.
Such numbers from 1 to 70 are
1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.

Number of such number =14

Required percentage = {(14/70) × 100}%
= 20%

৭৩৭.

The original retail price of an appliance was 60 percent more than its wholesale cost. If the appliance was actually sold for 20 percent less than the original retail price, then it was sold for what percent more than its wholesale cost?

ক
20%
খ
28%
গ
36%
ঘ
40%
ঙ
42%

সঠিক উত্তর: খ

28%

উত্তর

সঠিক উত্তর: খ

28%

খ

ব্যাখ্যা

Question: The original retail price of an appliance was 60 percent more than its wholesale cost. If the appliance was actually sold for 20 percent less than the original retail price, then it was sold for what percent more than its wholesale cost?

Solution:
Let Wholesale cost be = 100
Original retail price = 60% more than wholesale cost = 160% of 100 = (160/100) × 100 = 160

Selling price = 20% less than original retail price = 80% of 160 = (80/100) × 160 = 128

Difference between Wholesale Cost and Selling price = 128 - 100 = 28

∴ Percent change = (Difference in cost / initial cost) × 100 = (28/100) × 100 = 28%

৭৩৮.

A fruit seller had some apples. He sold 70% apples and still has 510 apples left. Originally he had:

ক
1700
খ
1500
গ
1440
ঘ
1260

সঠিক উত্তর: ক

1700

উত্তর

সঠিক উত্তর: ক

1700

ক

ব্যাখ্যা

He sold 70% apples
He has left = 100 - 70 = 30%
30% of apples = 510
100% of apples
= 510 × 100/30
= 1700

৭৩৯.

The ratio of the cost of two articles is 7 : 3 . The first one was sold at a loss of 20% and the second one was sold at a gain of 40% What is the overall percentage of gain/loss?

ক
ক) 2% loss
খ
খ) 2% gain
গ
গ) 4% loss
ঘ
ঘ) 4% gain

সঠিক উত্তর: ক

ক) 2% loss

উত্তর

সঠিক উত্তর: ক

ক) 2% loss

ক

ব্যাখ্যা

দেওয়া আছে,
১ম টির ক্রয়মূল্য : ২য় টির ক্রয়মূল্য = 7 : 3
মনেকরি, ১ম টির ক্রয়মূল্য = 70 টাকা
এবং ২য় টির ক্রয়মূল্য = 30 টাকা
∴ মোট ক্রয়মূল্য = 70 + 30 = 100 টাকা
এখন,
১ম টির বিক্রয়মূল্য = 80/100 × 70 = 56 টাকা
২য় টির বিক্রয়মূল্য = 140/100 × 30 = 42 টাকা
∴ মোট বিক্রয়মূল্য = 56 + 42 = 98 টাকা
∴ ক্ষতি = 100 - 98 = 2 টাকা

৭৪০.

A school only 3 classes having 20, 30 and 40 students respectively. The percentages of students passed are 30%, 50% and 60% respectively. Find the percentage of passed students of the entire school.

ক
ক) 40
খ
খ) 50
গ
গ) 60
ঘ
ঘ) 30

সঠিক উত্তর: খ

খ) 50

উত্তর

সঠিক উত্তর: খ

খ) 50

খ

ব্যাখ্যা

১ম শ্রেণিতে পাস = 20 এর 30%
= 20 এর 30/100
= 6 জন

২য় শ্রেণিতে পাস = 30 এর 50%
= 30 এর 50/100
= 15 জন

৩য় শ্রেণিতে পাস = 40 এর 60%
= 40 এর 60/100
= 24 জন

মোট পাস করে = (6 + 15 + 24)= 45 জন

এখন, মোট শিক্ষার্থী = (20 + 30 + 40) = 90 জন

:: শতকরা পাস করে = {(45/90) × 100}%
=50%

৭৪১.

A mobile and a monitor have the same price. If the price of the mobile goes up by 20% and that of the monitor goes down by 10%, how much more will it cost be buy 4 mobiles and 4 computers?

ক
4%
খ
5%
গ
6%
ঘ
10%

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: A mobile and a monitor have the same price. If the price of the mobile goes up by 20% and that of the monitor goes down by 10%, how much more will it cost be buy 4 mobiles and 4 computers?

Solution:
ধরি,
মোবাইল বা মনিটরের মূল্য = ক টাকা

২০% বৃদ্ধিতে,
মোবাইলের দাম = ক + ক এর ২০%
= ক + {ক × (২০/১০০)}
= (৫ক + ক)/৫
= ১.২ক

১০% ক্ষতিতে,
মনিটরের দাম = ক - ক এর ১০%
= ক - {ক × (১০/১০০)}
= (১০ক - ক)/১০
= ০.৯ক

পূর্বে ৪টি মোবাইল ও ৪টি মনিটরের দাম = ৮ক টাকা
বর্তমানে ৪টি মোবাইল ও ৪টি মনিটরের দাম = (৪ক × ১.২) + (৪ক × ০.৯) = ৮.৪ক টাকা

∴ শতকরা বৃদ্ধি = {(৮.৪ক - ৮ক)/৮} × ১০০
= (.৪/৮) × ১০০
= ৫ টাকা বা ৫%

৭৪২.

A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?

ক
ক) 74%
খ
খ) 64%
গ
গ) 84%
ঘ
ঘ) 54%

সঠিক উত্তর: খ

খ) 64%

উত্তর

সঠিক উত্তর: খ

খ) 64%

খ

ব্যাখ্যা

Let the number be x.
The number was asked to be multiplied by 5/3.
Hence Correct result would be = x×(5/3) = 5x/3.
By mistake the multiplication is = 3x/5
Then, error = (5x/3 - 3x/5) = 16x/15

∴ Error % = (error/True value) × 100%
= {(16x/15) / (5x/3)} × 100%
= 16/25 × 100%
= 64 %

৭৪৩.

The current birth rate per thousand is 30, whereas the corresponding death rate is 10 per thousand. Find the net growth rate in terms of population increase in percent.

ক
1.5%
খ
2%
গ
2.5%
ঘ
3%

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

We are given that,
1) Current birth rate per thousand is 30
2) Corresponding death rate is 10 per thousand

Hence, net growth on 1000 = Current birth rate - the death rate
= 30 – 10 =20

We are asked to find,
the net growth rate in terms of population increase in percent (which means net growth on 100)
Net worth on 100 = {(Net worth of 1000)/1000} × 100
Net worth on 100 = (20/1000) × 100
= 2%.

৭৪৪.

Chocolates are bought at 10 for Tk 20 and sold at 12 for Tk 30. The gain percent is-

ক
22%
খ
25%
গ
30%
ঘ
35%

সঠিক উত্তর: খ

25%

উত্তর

সঠিক উত্তর: খ

25%

খ

ব্যাখ্যা

Question: Chocolates are bought at 10 for Tk 20 and sold at 12 for Tk 30. The gain percent is-

Solution:
Cost per chocolate = 20/10 Tk.
= 2 Tk.

Sell per chocolate = 30/12 Tk.
= 2.5 Tk.

So, gain percentage = {(2.5 - 2)/2} × 100
= 25 Tk. or 25%

৭৪৫.

An employee’s monthly salary was Tk. 12,000 and his monthly expenditure was Tk. 8,000. The next year, his salary increased by 25% and his expenditure increased by 10%. Find the difference of his savings.

ক
Tk. 1200
খ
Tk. 1500
গ
Tk. 1800
ঘ
Tk. 2000
ঙ
Tk. 2200

সঠিক উত্তর: ঙ

Tk. 2200

উত্তর

সঠিক উত্তর: ঙ

Tk. 2200

ঙ

ব্যাখ্যা

Question: An employee’s monthly salary was Tk. 12,000 and his monthly expenditure was Tk. 8,000. The next year, his salary increased by 25% and his expenditure increased by 10%. Find the difference of his savings.

Solution:
Savings before increased income = Tk. (12000 - 8000)
= Tk. 4000

New salary = 125% of 12000 = Tk. (125/100) × 12000
= Tk. 15000

New expenditure = 110% of 8000 = Tk. (110/100) × 8000
= Tk. 8800

Saving after Increased income = Tk. (15000 - 8800)
= Tk. 6200

So the difference of his savings = Tk. (6200 - 4000)
= Tk. 2200

৭৪৬.

What is 10% of y/3, if 2y/3 is 10% of 400?

ক
ক) 3
খ
খ) 2
গ
গ) 1
ঘ
ঘ) 5

সঠিক উত্তর: খ

খ) 2

উত্তর

সঠিক উত্তর: খ

খ) 2

খ

ব্যাখ্যা

Question: What is 10% of y/3, if 2y/3 is 10% of 400?

Solution:
2y/3 = 10% of 400
⇒ 2y/3 = 400 ×10/100
⇒ 2y/3 = 40
⇒ y = 40 × 3/2
⇒ y = 60

10% of y/3 is = 10% of 60/3
= 10% of 20
= 20 × 10/100
= 2

৭৪৭.

Mamun buys 1,000 shares of stock for the current stock price of 20 tk. per share. If the stock price goes up to 25 tk. per share, by what percentage does Mamun increase his money?

ক
ক) 20%
খ
খ) 25%
গ
গ) 12.5%
ঘ
ঘ) None of these

সঠিক উত্তর: খ

খ) 25%

উত্তর

সঠিক উত্তর: খ

খ) 25%

খ

ব্যাখ্যা

Question: Mamun buys 1,000 shares of stock for the current stock price of 20 tk. per share. If the stock price goes up to 25 tk. per share, by what percentage does Mamun increase his money?

Solution:
প্রতি শেয়ার ২০ টাকা হলে, মোট শেয়ার = ১০০০ × ২০ টাকা
= ২০০০০ টাকা

২৫ টাকা হলে মোট শেয়ার = ১০০০ × ২৫ টাকা
= ২৫০০০ টাকা

টাকা বৃদ্ধি পাবে = ২৫০০০ - ২০০০০ টাকা
= ৫০০০ টাকা

শতকরা বৃদ্ধি = (৫০০০/২০০০০) × ১০০%
= ২৫%

৭৪৮.

Seventy-two percent of a number is 30 less than three-fourths of that number. What is the number?

ক
1120
খ
980
গ
1240
ঘ
1000

সঠিক উত্তর: ঘ

1000

উত্তর

সঠিক উত্তর: ঘ

1000

ঘ

ব্যাখ্যা

Question: Seventy-two percent of a number is 30 less than three-fourths of that number. What is the number?

Solution:
Let, the number = x.

ATQ,
72% of x = (3/4) of x - 30
⇒ 72x/100 = (3x/4) - 30
⇒ 18x/25 = (3x/4) - 30
⇒ (3x/4) - (18x/25) = 30
⇒ (75x - 72x)/100 = 30
⇒ 3x/100 = 30
⇒ 3x = 3000
⇒ x = 3000/3
∴ x = 1000

So, the number is 1000

৭৪৯.

A person buys certain number of marbles at 20 per taka and an equal number at 30 per taka. He mixes them and sells them at 25 per taka. His gain or loss in the transaction is-

ক
2% loss
খ
4% loss
গ
2% gain
ঘ
4% gain

সঠিক উত্তর: খ

4% loss

উত্তর

সঠিক উত্তর: খ

4% loss

খ

ব্যাখ্যা

Question: A person buys certain number of marbles at 20 per taka and an equal number at 30 per taka. He mixes them and sells them at 25 per taka. His gain or loss in the transaction is-

Solution:
Cost price of a each marble at 20 per Tk. = Tk. 1/20
Cost price of a each marble at 30 per Tk. = Tk. 1/30
∴ Average cost of marble = {(1/20) + (1/30)}/2
= (3 + 2)/(2 × 60)
= 5/120
= 1/24

Selling price of mixed marble = Tk. 1/25

∴ Loss = (1/24) - (1/25) = 1/600
Cost price 1/24 then loss Tk. 1/600
Cost price 1 then loss Tk. (1/600)/(1/24)
∴ Cost price 1 then loss Tk. {(1/600)/(1/24)} × 100
= 4%

∴ There is loss of 4%

৭৫০.

A bicycle originally cost Tk. 100 and was discounted 10%. After three months it was sold after being discounted another 15%. How much was the bicycle sold for?

ক
ক) Tk. 76.50
খ
খ) Tk. 75
গ
গ) Tk. 73.50
ঘ
ঘ) Tk. none of these

সঠিক উত্তর: ক

ক) Tk. 76.50

উত্তর

সঠিক উত্তর: ক

ক) Tk. 76.50

ক

ব্যাখ্যা

According to the question,
Original price = Tk. 100
10% discounted price = Tk. 90
The bicycle was sold after another 15% discount.
Meaning, the bicycle was sold at 85% of the discounted price.
Selling price= Tk. 90 × 85%
= Tk. 76.50

৭৫১.

The selling price of an article is tk 39. If its cost price is numerically equal to its profit percent, then its cost price is -

ক
29
খ
27
গ
33
ঘ
30
ঙ
32

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Let, cost price be x, sales price is 39. Then gain percentage = x%.

According to question,

Sales Price = (100 + profit%)/100 * cost price

Or, 39 = {(100 + x)/100} * x

Or, 3900 = x² + 100x

Or, x² + 100x - 3900 = 0

Or, x² + 130x -30x - 3900 = 0

Or, x( x + 130) - 30 ( x + 130) = 0

Or, ( x + 130) (x - 30) = 0

So, x = 30, x = -130 ( Cost price can not be negative)

৭৫২.

180 fazley mangoes were bought from a fruits shop. After two days 9 mangoes rotted. How many mangoes are quite good?

ক
80%
খ
85%
গ
90%
ঘ
95%

সঠিক উত্তর: ঘ

95%

উত্তর

সঠিক উত্তর: ঘ

95%

ঘ

ব্যাখ্যা

Question: 180 fazley mangoes were bought from a fruits shop. After two days 9 mangoes rotted. How many mangoes are quite good?

Solution:
The total number of mangoes which were bought = 180
The number of rotten mangoes = 9.

The number of good mangoes = 180 - 9 = 171.

The percentage of good mangoes is (171 × 100)/180
= 95%.

৭৫৩.

Jafar paid Tk. 100 tax. If X was his income then which of the following statements is true?

ক
ক) 6,000 < X < 8,000
খ
খ) 4,000 < X < 6,000
গ
গ) 0 < X < 4,000
ঘ
ঘ) All of the above

সঠিক উত্তর: ক

ক) 6,000 < X < 8,000

উত্তর

সঠিক উত্তর: ক

ক) 6,000 < X < 8,000

ক

ব্যাখ্যা

Question: Jafar paid Tk. 100 tax. If X was his income then which of the following statements is true?

Solution:
ধরি জাফরের ইনকাম = X টাকা

৬০০০ টাকায় টেক্স দিতে হয় = ৪০ + (৪০০০ টাকার বেশি ইনকামের ২%)
= ৪০ + (৬০০০ -৪০০০) এর ২%
= ৮০ টাকা

৮০০০ টাকায় টেক্স দিতে হয় = ৮০ + (৬০০০ এর বেশি ইনকামের ৩%)
= ৮০ + (৮০০০ - ৬০০০) এর ৩%
= ৮০ + ৬০
= ১৪০ টাকা

অর্থাৎ তার ইনকাম ৬০০০ থেকে ৮০০০ এর মধ্যে।

∴ 6000 < X < 8000

৭৫৪.

A number reduced by 25% becomes 225. What percent should it be increase so that it becomes 360 ?

ক
15%
খ
20%
গ
25%
ঘ
30%

সঠিক উত্তর: খ

20%

উত্তর

সঠিক উত্তর: খ

20%

খ

ব্যাখ্যা

Question: A number reduced by 25% becomes 225. What percent should it be increase so that it becomes 360 ?

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 :

= (360 - 300)

= 60

Increase % :
= (60/300) × 100%
= 20%

৭৫৫.

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

ক
ক) 4%
খ
খ) 6%
গ
গ) 8%
ঘ
ঘ) 12%

সঠিক উত্তর: গ

গ) 8%

উত্তর

সঠিক উত্তর: গ

গ) 8%

গ

ব্যাখ্যা

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

Solution:
Let,
Cost price = Tk.100

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

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

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

৭৫৬.

Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?

ক
ক) 57%
খ
খ) 60%
গ
গ) 65%
ঘ
ঘ) 90%

সঠিক উত্তর: ক

ক) 57%

উত্তর

সঠিক উত্তর: ক

ক) 57%

ক

ব্যাখ্যা

Total number of votes polled = (1136 + 7636 + 11628) = 20400.
Required percentage =(11628/20400)x 100%
= 57%.

৭৫৭.

Rakib purchased sugar worth of Tk. 800. He sold (3/4)^th at a loss of 10% and the remainder at a gain of 10%. On the whole, he gets-

ক
5.5% loss
খ
5% loss
গ
5% gain
ঘ
5.5% gain

সঠিক উত্তর: খ

5% loss

উত্তর

সঠিক উত্তর: খ

5% loss

খ

ব্যাখ্যা

Question: Rakib purchased sugar worth of Tk. 800. He sold (3/4)^th at a loss of 10% and the remainder at a gain of 10%. On the whole, he gets-

Solution:

৭৫৮.

The sum of two numbers is 456. If the bigger number is decreased by 20% and the smaller number is increased by 10%, then the numbers obtained are equal. The smaller number is-

ক
250
খ
188
গ
264
ঘ
192

সঠিক উত্তর: ঘ

192

উত্তর

সঠিক উত্তর: ঘ

192

ঘ

ব্যাখ্যা

Question: The sum of two numbers is 456. If the bigger number is decreased by 20% and the smaller number is increased by 10%, then the numbers obtained are equal. The smaller number is-

Solution:
Let,
Larger number = x and smaller number = 456 - x

According to the question
⇒ 80x/100 = {(456 - x)/100} × 110
⇒ 80x = (456 - x) × 110
⇒ 80x = 456 × 110 - 110x
⇒ 110x + 80x = 456 × 110
⇒ 190x = 456 × 110
⇒ x = (456 × 110)/190
⇒ x = 264

∴ Smaller number = 456 - 264 = 192

৭৫৯.

Out of 120 students, 70% students passed in math and 80% students passed in English. If only 12 students failed in both subjects. How many students passed only in English?

ক
ক) 10
খ
খ) 12
গ
গ) 24
ঘ
ঘ) 36
ঙ
ঙ) None

সঠিক উত্তর: গ

গ) 24

উত্তর

সঠিক উত্তর: গ

গ) 24

গ

ব্যাখ্যা

Number of students who passed = 120 - 12 = 108
Passed student in percent = 108/120 × 100 = 90%
Passed in both subject = (70 + 80)% - 90% = 60%
∴ Only passed in English = (80 - 60)% of 120
= 20/100 × 120
= 24

৭৬০.

In the onion trade, farmers receive a profit of 5%, while wholesalers must cover 10% of the wholesale price for transportation and other unforeseen expenses. The wholesalers make 20% profit, as do the retailers. What is the approximate percentage of the onion's production costs that we pay?

ক
67%
খ
55%
গ
170%
ঘ
166%

সঠিক উত্তর: ক

67%

উত্তর

সঠিক উত্তর: ক

67%

ক

ব্যাখ্যা

Question: In the onion trade, farmers receive a profit of 5%, while wholesalers must cover 10% of the wholesale price for transportation and other unforeseen expenses. The wholesalers make 20% profit, as do the retailers. What is the approximate percentage of the onion's production costs that we pay?

Solution :
Let,
Production cost of onion = Tk 100

After farmer's 5% profit, the wholesale price = Tk 100 + 100 × 5%
= Tk 105

wholesalers total cost = Tk. 105 × 110%
= Tk 115.5

As the wholesalers make 20% profit,
The cost of reatilers = Tk 115.5 × 120%
= Tk 138.6

As the retailers make 20% profit,
The cost of onion for public = Tk 138.6 × 120%
= Tk 166.32

∴ The percentage of the onion's production cost we pay = (166.32 - 100)%
= 66.32%
≈ 67%

৭৬১.

By selling a water heater for Rs. 3200, the shopkeeper incurs a loss of 20%. If he wants to earn a profit of 20%, at what price should he sell the water heater?

ক
Tk. 4000
খ
Tk. 4200
গ
Tk. 4800
ঘ
Tk. 5760

সঠিক উত্তর: গ

Tk. 4800

উত্তর

সঠিক উত্তর: গ

Tk. 4800

গ

ব্যাখ্যা

We know,
If loss is A%, then Selling Price = (100 - A)% of cost price.

Selling Price = 3200 = (100 - 20)% of CP = (80 × CP)/100
∴ CP = (3200 × 100)/80

For profit 20% = Selling Price = (100 + 20)% of CP = (120/100) × (3200 × 100)/80
∴ Selling Price = Tk. 4800

৭৬২.

A shopkeeper sells his goods at cost price but uses a weight of 970 grams for a kg. weight. What is his gain percent?

ক
ক) 5.08%
খ
খ) 4.23%
গ
গ) 3.26%
ঘ
ঘ) 3.09%

সঠিক উত্তর: ঘ

ঘ) 3.09%

উত্তর

সঠিক উত্তর: ঘ

ঘ) 3.09%

ঘ

ব্যাখ্যা

Gain% = [ Error/(True weight - Error)]%

Error = True weight - False weight
Error = 1000 - 970
= 30
Gain% = [{30/(1000 - 30)} × 100]%
Gain% = 3.09%

৭৬৩.

The price of an article is raised by 20% and then two successive discounts of 10% each are allowed. Ultimately, the price of the article is -

ক
ক) decreased by 1%
খ
খ) increased by 2.8%
গ
গ) decreased by 2.8%
ঘ
ঘ) remain unchanged

সঠিক উত্তর: গ

গ) decreased by 2.8%

উত্তর

সঠিক উত্তর: গ

গ) decreased by 2.8%

গ

ব্যাখ্যা

Question: The price of an article is raised by 20% and then two successive discounts of 10% each are allowed. Ultimately, the price of the article is -

Solution:
Let the original price be 100
Then, increased price = 100 × 120% = 120

After 10% discount = 120 × 90% = 108
Again 10% discount = 108 × 90% = 97.2

Decreased price in percentage = 100 - 97.2 = 2.8%

৭৬৪.

A tradesman makes his marks his goods 30% above the C.P If he allows a discount of (25/4)%, then his gain percent is-

ক
ক) 20.875%
খ
খ) 18.875%
গ
গ) 21.875%
ঘ
ঘ) 16.875%

সঠিক উত্তর: গ

গ) 21.875%

উত্তর

সঠিক উত্তর: গ

গ) 21.875%

গ

ব্যাখ্যা

Let C.P be 100
then the marked price Tk. 130

Sell price = {100 - (25/4)} % of 130
= {(400 - 25)/4}% of 130
= (375/400) × 130
= 121.875

Gain% = (121.875 - 100)%
= 21.875%

৭৬৫.

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
180
খ
195
গ
200
ঘ
206

সঠিক উত্তর: গ

200

উত্তর

সঠিক উত্তর: গ

200

গ

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

৭৬৬.

(33 - 56 ) : Read the following questions carefully and choose the right answer.
33. In an office, 44% of the workers prefer coffee and 72% prefer tea. If each of them prefers coffee or tea and 40 like both, the total number of workers in the office is

ক
ক) 200
খ
খ) 250
গ
গ) 240
ঘ
ঘ) 210

সঠিক উত্তর: খ

খ) 250

উত্তর

সঠিক উত্তর: খ

খ) 250

খ

ব্যাখ্যা

Question: In an office, 44% of the workers prefer coffee and 72% prefer tea. If each of them prefers coffee or tea and 40 like both, the total number of workers in the office is-

Solution:
Out of 100%, 44% drink coffee and 72% drink tea,

Using the formula,
n(A ∪ B) = n(A) + n(B) - n(A∩ B)
⇒ 100 = 72 + 44 - n(A∩ B)
⇒ 100 = 116 - n(A ∩ B)
⇒ n(A ∩ B) = 16

According to the question,
⇒ 16% = 40
⇒ 1%= 40/16
⇒ 100% = 100 × 40/16
= 25 × 10
= 250

৭৬৭.

যদি কোনও পণ্যের দাম ৫০% বৃদ্ধি পায়, তবে তার ব্যয় একই রাখতে এর ব্যবহারের পরিমাণ কত ভগ্নাংশ কমাতে হবে?

ক
১/২
খ
১/৩
গ
১/৪
ঘ
২/৩
ঙ
কোনটি নয়

সঠিক উত্তর: খ

১/৩

উত্তর

সঠিক উত্তর: খ

১/৩

খ

ব্যাখ্যা

প্রশ্ন: যদি কোনও পণ্যের দাম ৫০% বৃদ্ধি পায়, তবে তার ব্যয় একই রাখতে এর ব্যবহারের পরিমাণ কত ভগ্নাংশে কমাতে হবে?

সমাধান:
দেওয়া আছে,
'ক' কেজি পণ্যের মূল্য ১০০ টাকা।

৫০% বৃদ্ধি পেলে,
∴ ক কেজির মূল্য = ১০০ + ১০০ × ০.৫ = ১৫০ টাকা

১০০ টাকায় নতুন পরিমাণ পণ্য = (১০০ × ক)/১৫০ = ২ক/৩ কেজি

ভোগের পরিমাণ যে ভগ্নাংশ কমাতে হবে = {ক - (২ক/৩)}/ক
= (ক/৩)/ক
= ১/৩

৭৬৮.

A merchant buys an article for Tk. 27 and sells it at a profit of 10 percent of the selling price. The selling price of the article is -

ক
Tk. 30
খ
Tk. 35
গ
Tk. 40
ঘ
Tk. 32
ঙ
None

সঠিক উত্তর: ক

Tk. 30

উত্তর

সঠিক উত্তর: ক

Tk. 30

ক

ব্যাখ্যা

Question: A merchant buys an article for Tk. 27 and sells it at a profit of 10 percent of the selling price. The selling price of the article is -

Solution:
Let, the selling price of the article be Tk. p

Cost price = Tk. 27
Profit = 10% of p

Again,
Profit = Selling price - Cost price
⇒ 10% of p = p - 27
⇒ p - 10% of p = 27
⇒ 90% of p = 27
⇒ 9p/10 = 27
⇒ p = 27 × (10/9)
⇒ p = 30

Hence, The selling price of the article is Tk. 30

৭৬৯.

A man buy 10 articles for Tk. 8 and sells them at the rate of Tk. 1.25 per article. His gain percent is:

ক
ক) (215/4)%
খ
খ) (225/4)%
গ
গ) (225/2)%
ঘ
ঘ) (325/4)%

সঠিক উত্তর: খ

খ) (225/4)%

উত্তর

সঠিক উত্তর: খ

খ) (225/4)%

খ

ব্যাখ্যা

Cost price of 10 articles (C.P.) = Tk. 8
Selling price of 10 articles (S.P.) = 1.25×100
= Tk.12.50
Profit = S.P - C.P.
=12.50 - 8
=Tk. 4.50.

∴ Gain % ={(4.50×100)/8}%
= (450/8)%
= (225/4)%

৭৭০.

An agent sells goods worth Tk. 18,000. If his commission rate was 12.5%, what was the amount of his commission?

ক
1125
খ
1875
গ
2250
ঘ
2500

সঠিক উত্তর: গ

2250

উত্তর

সঠিক উত্তর: গ

2250

গ

ব্যাখ্যা

Question: An agent sells goods worth Tk. 18,000. If his commission rate was 12.5%, what was the amount of his commission?

Solution:

Commission = 12.5% of 18000
= (125/10) × (1/100) × 18000
= (125/1000) × 18000
= 2250

৭৭১.

A man buys a pen for 10% less than its value and sells it for 10% more than its value. His gain or loss percentage is-

ক
No profit, no loss
খ
20% profit
গ
Less than 20% profit
ঘ
More than 20% profit
ঙ
None of the above

সঠিক উত্তর: ঘ

More than 20% profit

উত্তর

সঠিক উত্তর: ঘ

More than 20% profit

ঘ

ব্যাখ্যা

Question: A man buys a pen for 10% less than its value and sells it for 10% more than its value. His gain or loss percentage is-

Solution:
Let, the value of pen is x taka

Buying price = x - 0.1x
= 0.9x taka

Selling price = x + 0.1x
= 1.1x taka

Profit = 1.1x - 0.9x = 0.2x taka

Profit percentage = (0.2x/0.9x) × 100%
= (200/9)%
= 22.22%

৭৭২.

A person has deposited Tk. 13200 in a bank which pays 14% interest. He withdraws the money and invests in Tk. 100 stock at Tk. 110 which pays a dividend of 15%. How much does he gain or lose?

ক
ক) Loses Tk. 48
খ
খ) Gains Tk. 48
গ
গ) Loses Tk. 132
ঘ
ঘ) Gains Tk. 132

সঠিক উত্তর: ক

ক) Loses Tk. 48

উত্তর

সঠিক উত্তর: ক

ক) Loses Tk. 48

ক

ব্যাখ্যা

Income from bank = 14% of Tk. 13200 = Tk. 1848
Number of shares purchased
= Tk. (13200/110)
= Tk. 120
Income from stock
= (15% of Tk. 100) × 120
= Tk. (15 × 20)
= Tk. 1800
∴ Loss = Tk. (1848 - 1800)
= Tk. 48

৭৭৩.

A man's salary was reduced by 30%, again the reduce salary was increased by 30%. Find the loss of in term of percentage.

ক
ক) 9%
খ
খ) 15%
গ
গ) 20%
ঘ
ঘ) 25%

সঠিক উত্তর: ক

ক) 9%

উত্তর

সঠিক উত্তর: ক

ক) 9%

ক

ব্যাখ্যা

Let the salary was Tk. 100

A man's salary was reduced by 30%.
So, salary will be Tk. (100 - 30) = Tk. 70

Again the reduce salary was increased by 30%.
So, salary will be Tk. (70 + 30% of 70) = Tk. (70 + 21) = Tk. 91

Loss of in term of percentage = Tk. (100 - 91) = Tk. 9

৭৭৪.

30% of 50 is what fraction of 75% of 80?

ক
ক) 1/2
খ
খ) 1/4
গ
গ) 1/5
ঘ
ঘ) 1/7

সঠিক উত্তর: খ

খ) 1/4

উত্তর

সঠিক উত্তর: খ

খ) 1/4

খ

ব্যাখ্যা

Question: 30% of 50 is what fraction of 75% of 80?

Solution:
30% of 50 = 50 × .3
= 15

75% of 80 = 80 × 0.75
= 60

fraction = 15/60
= 1/4

৭৭৫.

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
ক) 98%
খ
খ) 99%
গ
গ) 93%
ঘ
ঘ) 91%

সঠিক উত্তর: ক

ক) 98%

উত্তর

সঠিক উত্তর: ক

ক) 98%

ক

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

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

৭৭৬.

ক
ক) 13
খ
খ) 13.5
গ
গ) 12
ঘ
ঘ) None of these

সঠিক উত্তর: ঘ

ঘ) None of these

উত্তর

সঠিক উত্তর: ঘ

ঘ) None of these

ঘ

ব্যাখ্যা

(27/4) × (40/3) + 4 × x = (520 × 30)/100
90 + 4x = 156
4x = 156 - 90
4x = 66
x = 66/4
x = 16.5

৭৭৭.

At what profit percent must an article be sold so that by selling it at two-thirds of that price, there will be a loss of 20%?

ক
25%
খ
16.66%
গ
20%
ঘ
30.2%

সঠিক উত্তর: গ

20%

উত্তর

সঠিক উত্তর: গ

20%

গ

ব্যাখ্যা

Question: At what profit percent must an article be sold so that by selling it at two-thirds of that price, there will be a loss of 20%?

Solution:
Let,
Cost Price be x .
Selling Price be y.

Selling at 2/3 of y, causes 20% loss,
So, 2y/3 = x - 20% of x
⇒ 2y/3 = x - (20x/100)
⇒ 2y/3 = x{(1 - (20/100)}
⇒ 2y/3 = x × (80/100)
∴ y = 6x/5

Profit = Selling Price - Cost Price
= (6x/5) - x
= (6x - 5x)/5
= x/5

∴ Profit Percentage = (Profit/Cost Price) × 100%
= {(x/5)/x} × 100%
= 20%

৭৭৮.

University A charges Tk. 9,000 annually for tuition and Tk. 3,000 annually for room and board. University A charges 10% less than University B does for tuition and 20% more than University B does for room and board. The total annual cost of tuition, room and board is how much more or less at University A than it is at University B?

ক
Tk. 1,200 less
খ
Tk. 500 less
গ
Tk. 300 less
ঘ
Tk. 300 more
ঙ
The costs are equal.

সঠিক উত্তর: খ

Tk. 500 less

উত্তর

সঠিক উত্তর: খ

Tk. 500 less

খ

ব্যাখ্যা

Question: University A charges Tk. 9,000 annually for tuition and Tk. 3,000 annually for room and board. University A charges 10% less than University B does for tuition and 20% more than University B does for room and board. The total annual cost of tuition, room and board is how much more or less at University A than it is at University B?

Solution:
University A
tuition fees annually = Tk. 9000
Room and Boarding price annually Tk. 3000
Total fee for University A = Tk. 12000

University B
Tuition fees annually x
Room and Boarding price annually y

Tuition fee of A is 10% less than that of B
x - (10% of x) = 9000
⇒ 0.9x = 9000
∴ x = 10000

Boarding price of A is 20% more than B
y + (20% of y) = 3000
⇒ 1.2y = 3000
∴ y = 2500

Total fee for University B = 10000 + 2500 =12500

Total fee of A is less than that of B by = 12500 - 12000 = 500 annually

৭৭৯.

8% of the people eligible to vote are between 18 and 21 years of age. In an election, 85% of those eligible to vote, who were between 18 and 21, actually voted. In that election, the number of persons between 18 and 21, who actually voted, was what percent of those eligible to vote?

ক
7.2%
খ
6.8%
গ
5.9%
ঘ
7.6%
ঙ
8.2%

সঠিক উত্তর: খ

6.8%

উত্তর

সঠিক উত্তর: খ

6.8%

খ

ব্যাখ্যা

Question: 8% of the people eligible to vote are between 18 and 21 years of age. In an election, 85% of those eligible to vote, who were between 18 and 21, actually voted. In that election, the number of persons between 18 and 21, who actually voted, was what percent of those eligible to vote?

Solution:
Let x be the number of persons eligible to vote,
Hence the nuber eligible persons between 18 and 21 = 8 of x.
Number of persons between 18 and 21, who voted = 85 of (8 of x)

Implies that,
(85/100) × (8/100) × x = 6x/1000
Hence the required percentage,
(68x/100) × (1/x) × 100% = 6.8%

৭৮০.

A shopkeeper incurs a loss by selling an article for Tk 800. If he had sold it for Tk 1200, he would have made a profit which is three times the initial loss. At what price should he sell the article to make 25% profit?

ক
Tk. 1280
খ
Tk. 960
গ
Tk. 1020
ঘ
Tk. 1125

সঠিক উত্তর: ঘ

Tk. 1125

উত্তর

সঠিক উত্তর: ঘ

Tk. 1125

ঘ

ব্যাখ্যা

Question: A shopkeeper incurs a loss by selling an article for Tk 800. If he had sold it for Tk 1200, he would have made a profit which is three times the initial loss. At what price should he sell the article to make 25% profit?

Solution:
ধরি, পণ্যের ক্রয়মূল্য = x টাকা
800 টাকায় বিক্রি করলে ক্ষতি = x - 800 টাকা
1200 টাকায় বিক্রি করলে লাভ = 1200 - x টাকা

প্রশ্নমতে,
1200 - x = 3(x - 800)
⇒ 1200 - x = 3x - 2400
⇒ 1200 + 2400 = 3x + x
⇒ 3600 = 4x
⇒ x = 3600/4
∴ x = 900

এখন,
25% লাভে,
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য 125 টাকা
ক্রয়মূল্য 1 টাকা হলে বিক্রয়মূল্য (125/100) টাকা
∴ ক্রয়মূল্য ৯০০ টাকা হলে বিক্রয়মূল্য (125 × 900)/100 টাকা
= 1125 টাকা

৭৮১.

The total income of Habib in 2017, 2018 and 2019 was Tk 36,400. His income increased by 20% each year. What was his income in 2019?

ক
ক) 14,400
খ
খ) 12,000
গ
গ) 10,000
ঘ
ঘ) 8,000

সঠিক উত্তর: ক

ক) 14,400

উত্তর

সঠিক উত্তর: ক

ক) 14,400

ক

ব্যাখ্যা

Question: The total income of Habib in 2017, 2018 and 2019 was Tk 36,400. His income increased by 20% each year. What was his income in 2019?

Solution:
2017 সালে হাবিবের আয় ছিল = x টাকা
2018 সালে হাবিবের আয় ছিল = x + 20x/100 টাকা
= x + 1x/5
= 6x/5
2019 সালে হাবিবের আয় ছিল = 6x/5 + (6x/5) এর 20%
= (6x/5) + (6x/5) এর 20/100
= (6x/5) + (6x/25)
= (30x + 6x)/25
= 36x/25

প্রশ্নমতে,
x + (6x/5) + (36x/25) = 36400
(25x + 30x + 36x)/25 = 36400
91x/25 = 36400
x = (36400 × 25)/91
x = 10000

2019 সালে হাবিবের আয় ছিল = 36x/25
= (36 × 10000)/25
= 14400 টাকা

৭৮২.

An employer pays 3 workers X, Y and Z a total of Tk. 36600 a week. X is paid 125% of the amount Y is paid and 80% of the amount Z is paid. How much does X make a week?

ক
ক) 9000
খ
খ) 12000
গ
গ) 10800
ঘ
ঘ) 11700

সঠিক উত্তর: খ

খ) 12000

উত্তর

সঠিক উত্তর: খ

খ) 12000

খ

ব্যাখ্যা

x = 125% of y = 125y/100 = 5y/4
⇒ y = 4x/5
Again,
x = 80% of z = 80z/100 = 4z/5
⇒ z = 5x/4
x : y : z = x : 4x/5 : 5x/4 = 20 : 16 : 25
Sum of ratio = 20 + 16 + 25 = 61
So, x makes a week = 20/61 × 36600 = 20×600 = 12000 tk.

৭৮৩.

A shopkeeper buys 40 kg sugar at taka 45 per kg. and 60 kg rice at taka 50 per kg. At what price approximately in taka per kg should he sell to make profit 15% of cost?

ক
Tk. 55.20
খ
Tk. 65.50
গ
Tk. 58
ঘ
Tk. 50.20
ঙ
Tk. 55

সঠিক উত্তর: ক

Tk. 55.20

উত্তর

সঠিক উত্তর: ক

Tk. 55.20

ক

ব্যাখ্যা

Question: A shopkeeper buys 40 kg sugar at taka 45 per kg. and 60 kg rice at taka 50 per kg. At what price approximately in taka per kg should he sell to make profit 15% of cost?

Solution:
Cost of 40 kg sugar is = 40 × 45 = Tk. 1800
Cost of 60 kg sugar is = 60 × 50 = Tk. 3000

∴ Total cost = 1800 + 3000 = Tk. 4800
And total weight = 40 + 60 = 100 kg

Now, Total selling price = 4800 + 4800 of 15% = 4800 + 720 = Tk. 5520

∴ Selling price per kg = 5520 ÷ 100 = Tk. 55.20 per kg

৭৮৪.

What will be the profit percentage, if bananas purchased 10 for Tk. 100 and sold 8 for Tk. 100?

ক
ক) 20%
খ
খ) 30%
গ
গ) 15%
ঘ
ঘ) 25%

সঠিক উত্তর: ঘ

ঘ) 25%

উত্তর

সঠিক উত্তর: ঘ

ঘ) 25%

ঘ

ব্যাখ্যা

Question: What will be the profit percentage, if bananas purchased 10 for Tk. 100 and sold 8 for Tk. 100?

Solution:

১০ টি কলার ক্রয়মূল্য ১০০ টাকা
∴ ১ টি কলার ক্রয়মূল্য ১০ টাকা

৮ টি কলার বিক্রয়মূল্য ১০০ টাকা
∴ ১ টি কলার বিক্রয়মূল্য ২৫/২ টাকা

∴ লাভ = (২৫/২ - ১০) = ৫/২ টাকা

১০ টাকায় লাভ হয় ৫/২ টাকা

∴ ১০০ টাকায় লাভ হয় (৫ × ১০০)/(১০ × ২) = ২৫ টাকা।

৭৮৫.

In an examination, a student must score 35% of the total marks to pass. A student scores 189 marks and is declared failed by 7% marks. What is the maximum total marks in the exam?

ক
650
খ
675
গ
710
ঘ
750

সঠিক উত্তর: খ

675

উত্তর

সঠিক উত্তর: খ

675

খ

ব্যাখ্যা

Question: In an examination, a student must score 35% of the total marks to pass. A student scores 189 marks and is declared failed by 7% marks. What is the maximum total marks in the exam?

Solution:
Let
the maximum marks be x.

Then,
(35 - 7)% of x = 189
⇒ 28% of x = 189
⇒ 28x/100 = 189
⇒ 28x = (189 × 100)
⇒ x = (189 × 100)/28
∴ x = 675

৭৮৬.

At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 45 other employees of Company K, how many employees does Company K have?

ক
160
খ
180
গ
190
ঘ
200
ঙ
400

সঠিক উত্তর: খ

180

উত্তর

সঠিক উত্তর: খ

180

খ

ব্যাখ্যা

Question: At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 45 other employees of Company K, how many employees does Company K have?

Solution:
Let the total number of employees in the company be x
% of secretaries = 15%
% of salespeople = 60%
% of of employees other than secretaries and salespeople = 100 - 75 = 25%
But this number is given as 45
so 25% of x = 45
⇒ (25/100) × x = 45
⇒ (1/4)x = 45
∴x = 180

Therefore there a total of 180 employees in the company K

৭৮৭.

A shopkeeper sold a product at loss of 10%. He had sold it for Tk. 108 more, he would have earned a profit of 10%. Find the cost of the product.

ক
ক) Tk. 540
খ
খ) Tk. 580
গ
গ) Tk. 600
ঘ
ঘ) Tk. 650

সঠিক উত্তর: ক

ক) Tk. 540

উত্তর

সঠিক উত্তর: ক

ক) Tk. 540

ক

ব্যাখ্যা

At loss of 10%, if cost price is Tk. 100, selling price is Tk. (100 - 10) = Tk. 90
At profit of 10%, if cost price is Tk. 100, selling price is Tk. (100 + 10) = Tk. 110
More selling price = Tk. (110 - 90) = Tk. 20
if more selling price is Tk. 20, the cost price is Tk. 100
if more selling price is Tk. 108, the cost price is Tk. 100 × 108/20 = Tk. 540
-------------------------------------------------------------------------------------
Shortcut way:
more selling price = 10 - ( - 10) = 20
Therefore, 20% of cost price = More selling price
20% of cost price = 108
cost price = Tk. 100 × 108/20 = Tk. 540

৭৮৮.

Rafi sold a TV for Tk 12760 and gained a profit of 10%. If he sold it for Tk 12064, then what percentage of loss or gain he would have made?

ক
ক) 4% gain
খ
খ) 6% gain
গ
গ) 4% loss
ঘ
ঘ) 6% loss

সঠিক উত্তর: ক

ক) 4% gain

উত্তর

সঠিক উত্তর: ক

ক) 4% gain

ক

ব্যাখ্যা

Question: Rafi sold a TV for Tk 12760 and gained a profit of 10%. If he sold it for Tk 12064, then what percentage of loss or gain he would have made?

Solution:
Cost price = 12760 × (100/110) = 11600
Profit gained = 12064 - 11600 = 464
Profit percentage = (464/11600) × 100 = 4%

৭৮৯.

Mr. Anis is a trader. He mixes 26 kg of rice at Tk. 20 per kg with 30 kg of rice of other variety at Tk. 36 per kg and sells the mixture at Tk. 30 per kg. His profit percent is:

ক
5% profit
খ
1% profit
গ
4% profit
ঘ
no profit

সঠিক উত্তর: ক

5% profit

উত্তর

সঠিক উত্তর: ক

5% profit

ক

ব্যাখ্যা

Question: Mr. Anis is a trader. He mixes 26 kg of rice at Tk. 20 per kg with 30 kg of rice of other variety at Tk. 36 per kg and sells the mixture at Tk. 30 per kg. His profit percent is:

Solution:
C.P. of 56 kg rice = (26 × 20 + 30 × 36)
= (520 + 1080)
= 1600 taka

S.P. of 56 kg rice = (56 × 30)
= 1680 taka

∴ Profit = 1680 - 1600
= 80 taka

∴ Profit percentage = (80/1600) × 100%
= 5%

৭৯০.

What percentage of the whole week does Nazma spend in the office, if her office hours are 9 am to 5 pm from Monday to Friday?

ক
23.51%
খ
23.61%
গ
23.71%
ঘ
23.81%
ঙ
None

সঠিক উত্তর: ঘ

23.81%

উত্তর

সঠিক উত্তর: ঘ

23.81%

ঘ

ব্যাখ্যা

Question: What percentage of the whole week does Nazma spend in the office, if her office hours are 9 am to 5 pm from Monday to Friday?

Solution:
Time spent by Nazma in a day = 5 pm - 9 am = 8 hrs

Time spend by Nazma in a week = 8 × 5 = 40 hrs

Percentage time spent in a week
= [40/(24 × 7)] × 100
= (40/168) × 100
= 23.81%

৭৯১.

The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. It its present value is tk. 8748 its purchases price was-

ক
ক) Tk. 12500
খ
খ) Tk. 10000
গ
গ) Tk. 12000
ঘ
ঘ) Tk. 14000

সঠিক উত্তর: গ

গ) Tk. 12000

উত্তর

সঠিক উত্তর: গ

গ) Tk. 12000

গ

ব্যাখ্যা

Question: The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. It its present value is tk. 8748 its purchases price was-

Solution:
Let, purchased price = x

We know,
C = (1 - r)ⁿ
∴ Depreciated price = x(1 - 10%)³= x{(1 - 10/100)}³= x{1 - (1/10)}³ATQ,
x{1 - (1/10)}³ = 8748
⇒ x(9/10)³ = 8748
⇒ x = (8748 × 10 × 10 × 10)/(9 × 9 × 9)
∴ x = 12000

∴ Purchased price = Tk. 12000

৭৯২.

A train started with 540 passengers. At the first stop 1/9 of them got down and 24 got up. On its second stop 1/8 of the existing passengers got down and 9 got up. With how many passengers did it reach the third stop?

ক
ক) 420
খ
খ) 450
গ
গ) 480
ঘ
ঘ) 500

সঠিক উত্তর: খ

খ) 450

উত্তর

সঠিক উত্তর: খ

খ) 450

খ

ব্যাখ্যা

Question: A train started with 540 passengers. At the first stop 1/9 of them got down and 24 got up. On its second stop 1/8 of the existing passengers got down and 9 got up. With how many passengers did it reach the third stop?

Solution:
Number of passengers after first stop = {540 - (1/9 of 540) + 24} = 504
Number of passengers after second stop = {504 - (1/8 of 504) + 9} = 450

৭৯৩.

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

ক
Tk. 400
খ
Tk. 420
গ
Tk. 450
ঘ
Tk. 475

সঠিক উত্তর: ক

Tk. 400

উত্তর

সঠিক উত্তর: ক

Tk. 400

ক

ব্যাখ্যা

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

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

Selling price = 0.94x

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

৭৯৪.

By selling 90 ball pens for Tk. 160 a person loses 20%. How many ball pens should be sold for Tk. 96 so as to have a profit of 20%?

ক
30
খ
36
গ
42
ঘ
44

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: By selling 90 ball pens for Tk. 160 a person loses 20%. How many ball pens should be sold for Tk. 96 so as to have a profit of 20%?

Solution:

S.P. of 90 ball pens = Tk. 160

Loss % = 20%

∴ C.P. of 90 ball pens = [100/(100 - Loss%)] × Selling Price = [100/(100 - 20)] × 160

= (100 × 160)/80 = 200

C.P. of 1 ball pen = 20/9

Now we find how many pens should be sold for 96 to have a profit of 20%

Let us say, ‘x’ number of pens be sold for 96

Then, S.P. of x pens = 96

C.P of x pens = (20/9)x

Profit = S.P - C.P. = 96 - 20x/9
Profit% = (Profit/ C.P.) × 100
{96 - (20x/9)}/(20x/9) × 100 = 20
⇒ {96 - (20x/9)} × 5 = 20x/9
⇒ 96 - (20x/9) = 4x/9
⇒ 96 × 9 - 20x = 4x
⇒ 24x = 96 × 9

⇒ x = (96 × 9)/24 = 36

Therefore, 36 pens should be sold

৭৯৫.

The population of a village grew from 18,000 to 22,500 over a decade. What is the average annual percentage increase in population?

ক
2%
খ
2.5%
গ
1.57%
ঘ
None of the above

সঠিক উত্তর: খ

2.5%

উত্তর

সঠিক উত্তর: খ

2.5%

খ

ব্যাখ্যা

Question: The population of a village grew from 18,000 to 22,500 over a decade. What is the average annual percentage increase in population?

Solution:
The population rose in 10 years = (22500 - 18000) = 4500

Increase% of ten year = (4500/18000) × 100% = 25%

∴ Required average = (25/10)% = 2.5%

৭৯৬.

The population of a town is decreasing at a rate of 10% per annum. If the population two years ago was 20000, what is the present population?

ক
15000
খ
15200
গ
16000
ঘ
16200

সঠিক উত্তর: ঘ

16200

উত্তর

সঠিক উত্তর: ঘ

16200

ঘ

ব্যাখ্যা

Question: The population of a town is decreasing at a rate of 10% per annum. If the population two years ago was 20000, what is the present population?

Solution:
The present population = 20000(1 - 10/100)²
= 20000 × 0.9 × 0.9
= 16200

৭৯৭.

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

ক
ক) Tk. 6786.1
খ
খ) Tk. 6876.1
গ
গ) Tk. 8676.1
ঘ
ঘ) Tk. 7668.1

সঠিক উত্তর: খ

খ) Tk. 6876.1

উত্তর

সঠিক উত্তর: খ

খ) Tk. 6876.1

খ

ব্যাখ্যা

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

Solution:
Rebate = 6% of Tk.6650
= (6 × 6650)/100
= 399 Tk.
Tax = 10% of (6650 - 399)
= 10% of 6251
= (10 × 6251)/100
= 625.10
Total amount will have to pay =Tk. (6251 + 625.10)
= Tk. 6876.1

৭৯৮.

In recent survey of the students of a public university, it is found that 65% students are good in Mathematics and 45% students are good in Statistics. How many students are good in both Mathematics and Statistics of the public university?

ক
20%
খ
5%
গ
15%
ঘ
10%

সঠিক উত্তর: ঘ

10%

উত্তর

সঠিক উত্তর: ঘ

10%

ঘ

ব্যাখ্যা

Question: In recent survey of the students of a public university, it is found that 65% students are good in Mathematics and 45% students are good in Statistics. How many students are good in both Mathematics and Statistics of the public university?

Solution:
Good at Mathematics n(M) = 65
Good at Statistics n(S) = 45
good in both Mathematics and Statistics n(M ∩ S)

We know that
n(M ∪ S) = n(M) + n(S) - n(M ∩ S)
⇒ n(M ∩ S) = n(M) + n(S) - n(M ∪ S) = 65 + 45 - 100 = 110 - 100 = 10

৭৯৯.

A man sells two horses for tk 4000 each, neither losing nor gaining in the deal. If he sold 1 horse at a gain of 25%, the other horse is sold at a loss of:

ক
ক) 16.67
খ
খ) 18.33
গ
গ) 25%
ঘ
ঘ) 20%
ঙ
ঙ) 12.5%

সঠিক উত্তর: ক

ক) 16.67

উত্তর

সঠিক উত্তর: ক

ক) 16.67

ক

ব্যাখ্যা

ধরি প্রথম ঘোড়ার ক্রয়মূল্য = x টাকা
তাহলে, x + x এর 25/100 = 4000
বা, x = 3200 টাকা

তাহলে প্রথম ঘোড়ার ক্ষেত্রে মোট লাভ করেছে ৮০০ টাকা তাহলে দ্বিতীয় ঘোড়াতে ক্ষতি হয়েছে = ৮০০ টাকা

তাহলে দ্বিতীয় ঘোড়ার ক্রয়মূল্য = ৪০০০ + ৮০০ = ৪৮০০ টাকা।

তাহলে ক্ষতির শতকরা হার = (৮০০ × ১০০) / ৪৮০০ = ১৬.৬৭%

৮০০.

A retail fruit vendor buys pineapples at a score for Tk. 200, and retails them at a dozen for Tk. 156. What % was his gain or loss?

ক
loss 25%
খ
loss 30%
গ
gain 25%
ঘ
gain 30%

সঠিক উত্তর: ঘ

gain 30%

উত্তর

সঠিক উত্তর: ঘ

gain 30%

ঘ

ব্যাখ্যা

Question: A retail fruit vendor buys pineapples at a score for Tk. 200, and retails them at a dozen for Tk. 156. What % was his gain or loss?

Solution:
C.P of 1 pineapple = 220/score = 200/20 = 10 [Note: 1 score = 20 nos.]
S.P of 1 pineapple = 156/dozen = 156/12 = 13.
∴ Profit = 13 - 10 = 3
∴ % Profit = 100 × (3/10) = 30%