Percentage and Profit & Loss

PrepBank · পাতা ৬ / ১৭ · ৫০১–৬০০ / ১,৬৯৬

৫০১.

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

ক
ক) 5 : 3
খ
খ) 7 : 5
গ
গ) 8 : 7
ঘ
ঘ) 11 : 9

সঠিক উত্তর: গ

গ) 8 : 7

উত্তর

সঠিক উত্তর: গ

গ) 8 : 7

গ

ব্যাখ্যা

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

Solution:
CP = Tk. x
SP= (175/2)% of x
= (175/2) × (1/100) × x
= 7x/8

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

৫০২.

Two tailors X and Y are paid a total of Tk. 550 per week by their employer. If X is paid 20 percent more than the sum paid to Y, how much is Y paid per week?

ক
ক) Tk. 200
খ
খ) TK. 250
গ
গ) TK. 300
ঘ
ঘ) Tk 400

সঠিক উত্তর: খ

খ) TK. 250

উত্তর

সঠিক উত্তর: খ

খ) TK. 250

খ

ব্যাখ্যা

Let,
the sum paid to Y per week be Tk. x
Then, sum paid to X per week
= 120% of Tk. x
= Tk. (120/100) × x
= Tk. (6/5) x.
∴ x + (6x/5) = 550
⇒ 11x/5 = 550
⇒ x = (550 × 5)/11
= Tk. 250.

৫০৩.

Kamrul bought a house, whose sale price was Tk. 8 lakh. He availed 20% discount as an early bird offer and then 10% discount due to cash payment. After that he spent 10% of the cost price in interior decoration and the lawn of the house. At what price should he sell the house to earn a profit of 25%?

ক
7,90,000 Tk
খ
8,90,000 Tk
গ
8,92,000 Tk
ঘ
7,92,000 Tk

সঠিক উত্তর: ঘ

7,92,000 Tk

উত্তর

সঠিক উত্তর: ঘ

7,92,000 Tk

ঘ

ব্যাখ্যা

Question: Kamrul bought a house, whose sale price was Tk. 8 lakh. He availed 20% discount as an early bird offer and then 10% discount due to cash payment. After that he spent 10% of the cost price in interior decoration and the lawn of the house. At what price should he sell the house to earn a profit of 25%?

Solution:
Here, original price = 8,00,000 Tk

After 20% early bird discount,
8,00,000 × (1 - 0.20) = 6,40,000 Tk

After 10% cash discount,
6,40,000 × (1 - 0.10) = 5,76,000 Tk

Renovation cost = 10% of 5,76,000
= (10/100) × 5,76,000
= 57,600 Tk

∴ Total CP = 5,76,000 + 57,600 = 6,33,600 Tk

Now,
Profit amount = 25% of 6,33,600
= (25/100) × 6,33,600
= 1,58,400 Tk

∴ Required SP = 6,33,600 + 1,58,400 = 7,92,000 Tk

৫০৪.

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
15%
খ
18%
গ
19%
ঘ
20%

সঠিক উত্তর: গ

19%

উত্তর

সঠিক উত্তর: গ

19%

গ

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

৫০৫.

A shopkeeper sells a badminton racket, whose marked price is 200 taka, at a discount of 15% and gives a shuttle cock costing 20 taka free with each racket. Even then he makes a profit of 25%. His cost price per racket is-

ক
90 Tk
খ
100 Tk
গ
120 Tk
ঘ
150 Tk

সঠিক উত্তর: গ

120 Tk

উত্তর

সঠিক উত্তর: গ

120 Tk

গ

ব্যাখ্যা

Question: A shopkeeper sells a badminton racket, whose marked price is 200 taka, at a discount of 15% and gives a shuttle cock costing 20 taka free with each racket. Even then he makes a profit of 25%. His cost price per racket is-

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

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

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

His cost price per racket is 120 Tk.

৫০৬.

In 1985, 45 percent of a document storage facility's 60 customers were banks, and in 1987, 25 percent of its 144 customers were banks. What was the percent increase from 1985 to 1987 in the number of bank customers the facility had?

ক
10.7%
খ
20%
গ
25%
ঘ
33.33%
ঙ
58.33%

সঠিক উত্তর: ঘ

33.33%

উত্তর

সঠিক উত্তর: ঘ

33.33%

ঘ

ব্যাখ্যা

Question: In 1985, 45 percent of a document storage facility's 60 customers were banks, and in 1987, 25 percent of its 144 customers were banks. What was the percent increase from 1985 to 1987 in the number of bank customers the facility had?

Solution:
No of bank customers in 1985 = 45% of 60 = 0.45 × 60 = 27
No of bank customers in 1987 = 25% of 144 = 0.25 × 144 = 36

∴ Custeomer increase 36 - 27 = 9

∴ increase in % = (9/27) × 100% = (100/3)% = 33.33%

৫০৭.

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

ক
ক) 13%
খ
খ) 15%
গ
গ) 16%
ঘ
ঘ) 17%

সঠিক উত্তর: ঘ

ঘ) 17%

উত্তর

সঠিক উত্তর: ঘ

ঘ) 17%

ঘ

ব্যাখ্যা

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

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

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

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

৫০৮.

Sabuj sold an item for Tk. 6,384 and incurred a loss of 30%. At what price should he have sold the item to have gained a profit of 30%?

ক
Tk. 10,879
খ
Tk 12,065
গ
Tk. 11,856
ঘ
Tk. 21,654
ঙ
Tk. 15,400

সঠিক উত্তর: গ

Tk. 11,856

উত্তর

সঠিক উত্তর: গ

Tk. 11,856

গ

ব্যাখ্যা

30% ক্ষতিতে দাম, 70% = 6384
30% লাভে দাম, 130% = (6384 × 130)/70
= 11856

৫০৯.

A box contains 200 marbles, 25% of which are of black colour. Babu took some marbles from the box and found that 30% of them are black. Of the remaining marbles, 10% were black marbles. How many marbles did Babu take?

ক
120
খ
125
গ
150
ঘ
None of these

সঠিক উত্তর: গ

150

উত্তর

সঠিক উত্তর: গ

150

গ

ব্যাখ্যা

Question: A box contains 200 marbles, 25% of which are of black colour. Babu took some marbles from the box and found that 30% of them are black. Of the remaining marbles, 10% were black marbles. How many marbles did Babu take?

Solution:
বাক্সে মার্বেল আছে = 200 টি
কালো মার্বেল আছে = 200 এর 25%
= 200 এর 25/100
= 50 টি

ধরি
বাবু বাক্স হতে মার্বেল তুলে ছিলো x টি

প্রশ্নমতে
x এর 30% + (200 - x) এর 10% = 50
⇒ 30x/100 + 10(200 - x)/100 = 50
⇒ (30x + 2000 - 10x)/100 = 50
⇒ 20x + 2000 = 5000
⇒ 20x = 5000 - 2000
⇒ 20x= 3000
∴ x = 150

বাবু বাক্স হতে মার্বেল তুলে ছিলো 150 টি

৫১০.

The cost price of 19 articles is the same as the selling price of 29 articles. What is the loss percentage?

ক
ক) 52.30%
খ
খ) 35.00%
গ
গ) 34. 48%
ঘ
ঘ) 30.00%

সঠিক উত্তর: গ

গ) 34. 48%

উত্তর

সঠিক উত্তর: গ

গ) 34. 48%

গ

ব্যাখ্যা

ধরি,
19 টি জিনিসের ক্রয়মূল্য x টাকা
∴ 29 টি জিনিসের বিক্রয়মূল্য x টাকা
∴ ক্ষতি = (x/19) - (x/29)
= (29x - 19x)/551 = 10x/551 টাকা
∴ শতকরা ক্ষতির পরিমাণ = (10x/551)/(x/19) × 100%
= (10x/551) × (19/x) × 100%
= 34.48%

৫১১.

Of 3,600 employees of company, 1/3 are clerks. If the clerical staff were to be reduced by 1/3, what percent of the total number of remaining employess would be clerical staff?

ক
25%
খ
22.2%
গ
20%
ঘ
12.5%

সঠিক উত্তর: ক

25%

উত্তর

সঠিক উত্তর: ক

25%

ক

ব্যাখ্যা

Question: Of 3,600 employees of company, 1/3 are clerks. If the clerical staff were to be reduced by 1/3, what percent of the total number of remaining employess would be clerical staff?

Solution:
clerks এর সংখ্যা = 3600/3 = 1200 জন
clerk চাকরিচ্যুত করা হয় = 1200/3 = 400 জন
clerk চাকরিচ্যুত করা করার পর
অফিসে কর্মকর্তা থাকে = (3600 - 400) = 3200 টাকা
clerk চাকরিচ্যুত করা করার পর
clerk থাকে = 1200 - 400 = 800 জন

3200 জনের মধ্যে clerk = 800 জন
1 জনের মধ্যে clerk = 800/3200 জন
100 জনের মধ্যে clerk = (800 × 100)/3200 জন
= 25%

৫১২.

An employee is paid a salary of Tk. 300 per month and earns a 6% commission on all her sales. What must her annual sales be in order for her to have a gross annual salary of exactly Tk. 21600?

ক
Tk. 22896
খ
Tk. 26712
গ
Tk. 300000
ঘ
Tk. 330000
ঙ
Tk. 360000

সঠিক উত্তর: গ

Tk. 300000

উত্তর

সঠিক উত্তর: গ

Tk. 300000

গ

ব্যাখ্যা

Question: An employee is paid a salary of Tk. 300 per month and earns a 6% commission on all her sales. What must her annual sales be in order for her to have a gross annual salary of exactly Tk. 21600?

Solution:
Annual salary Tk. 300 × 12 = Tk. 3600
Subtracting the annual salary Tk. 3600 from Tk. 21600, we get Tk. 21600 - Tk. 3600 = Tk.18000.

For 6% commission,
For Tk. 6 her annual sales Tk. 100
For Tk. 1 her annual sales Tk. 100/6
For Tk. 18000 her annual sales Tk. (100 × 18000)/6
= Tk. 300000

৫১৩.

A tradesman fixed his selling price of goods at 25% above the cost price. He sells half the stock at this price, one-quarter of his stock at a discount of 20% on the original selling price, and the rest at a discount of 40% on the original selling price. Find the gain percentage altogether?

ক
4%
খ
6.25%
গ
7.50%
ঘ
10%

সঠিক উত্তর: খ

6.25%

উত্তর

সঠিক উত্তর: খ

6.25%

খ

ব্যাখ্যা

Question: A tradesman fixed his selling price of goods at 25% above the cost price. He sells half the stock at this price, one-quarter of his stock at a discount of 20% on the original selling price, and the rest at a discount of 40% on the original selling price. Find the gain percentage altogether?

Solution:
Let C.P = 100;
then S.P = 100 + 25 = 125 Tk

Now, revenue
= [(1/2) × 125] + [(1/4) × (80/100) × 125] + [(1/4) × (60/100) × 125]
= 62.5 + 25 + 18.75
= 106.25

∴ Gain = 106.25 - 100
= 6.25 Tk

Gain percentage = (6.25 × 100)/100
= 6.25%

৫১৪.

2100 Taka is lent at compound interest of 10% per annum for 2 years. Find the amount after two years.

ক
ক) Tk. 2520
খ
খ) Tk. 420
গ
গ) Tk. 2541
ঘ
ঘ) Tk. 441

সঠিক উত্তর: গ

গ) Tk. 2541

উত্তর

সঠিক উত্তর: গ

গ) Tk. 2541

গ

ব্যাখ্যা

Question: 2100 Taka is lent at compound interest of 10% per annum for 2 years. Find the amount after two years.

Solution:
চক্রবৃদ্ধি মূলধন = P (1 + r)ⁿ
= 2100 (1 + 10/100)²
= 2100 × (110/100) × (110/100)
= 21 × 11 × 11
= 2,541

৫১৫.

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

ক
100
খ
150
গ
200
ঘ
240

সঠিক উত্তর: গ

200

উত্তর

সঠিক উত্তর: গ

200

গ

ব্যাখ্যা

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

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

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

৫১৬.

The Ratio of the cost price of a pencil and a pen is 3 : 7. The ratio of the selling price is 1 : 4. If the loss incurred is equal after selling both products, then what is the ratio of the cost price and selling price of a pen?

ক
11 : 16
খ
21 : 16
গ
21 : 11
ঘ
21 : 76

সঠিক উত্তর: খ

21 : 16

উত্তর

সঠিক উত্তর: খ

21 : 16

খ

ব্যাখ্যা

Question: The Ratio of the cost price of a pencil and a pen is 3:7. The ratio of the selling price is 1:4. If the loss incurred is equal after selling both products, then what is the ratio of the cost price and selling price of a pen?

Answer:
Let, cost price of a pencil = 3x
pen = 7x
Selling price of a pencil = y
pen = 4y
According to the question,
3x- y = 7x- 4y
→ 4y-y =7x -3x
→ 3 y = 4x
∴ y = 4/3 x

The ratio of the cost price of a pen: the selling price of a pen = 7x : 4 (4/3 x)
= 21 : 16

৫১৭.

If Profit = 25 Taka and Cost Price = 125 Taka, what is the profit percentage?

ক
15%
খ
20%
গ
25%
ঘ
30%

সঠিক উত্তর: খ

20%

উত্তর

সঠিক উত্তর: খ

20%

খ

ব্যাখ্যা

Question: If Profit = 25 Taka and Cost Price = 125 Taka, what is the profit percentage?

Solution: Here,
- Cost Price = 100 Tk
- Profit = 25 Tk

- Now, Cost Price is 125 and Profit is 25 Taka
- Cost Price is 1 Taka so the Profit is = 25/125 Taka
- Cost Price is 100 Taka so the Profit is = (25× 100)/ 125 Taka = 20%

৫১৮.

If 64% of a number is 2592. What is 88% of that number?

ক
3201
খ
3448
গ
3564
ঘ
None of these

সঠিক উত্তর: গ

3564

উত্তর

সঠিক উত্তর: গ

3564

গ

ব্যাখ্যা

Question: If 64% of a number is 2592. What is 88% of that number?

Solution:
let the number be x

64% of x = 2592
⇒ 64x/100 = 2592
⇒ x = (2592 × 100)/64
= 4050

88% of that number = 4050 × 88/100 = 3564

৫১৯.

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. 6000
খ
Tk. 5600
গ
Tk. 4850
ঘ
Tk. 5000

সঠিক উত্তর: ঘ

Tk. 5000

উত্তর

সঠিক উত্তর: ঘ

Tk. 5000

ঘ

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:
At 16% loss,
Selling price Tk. 84 when cost price Tk. 100
Selling price Tk. 1 when cost price Tk. 100/84
Selling price Tk. 3360 when cost price Tk. (100 × 3360)/84
= Tk. 4000

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. 4000 when selling price Tk. (115 × 4000)/100
= Tk. 4600

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. 4600 when marked price Tk. (100 × 4600)/92
= Tk. 5000

∴ The marked price of the saree should be Tk. 5000.

৫২০.

A product is sold at a profit of 20%. If the cost price is increased by 10% and sale price by Tk. 26, then the percentage of profit reduce by 5%, cost price is

ক
ক) 400
খ
খ) 500
গ
গ) 600
ঘ
ঘ) 700

সঠিক উত্তর: ক

ক) 400

উত্তর

সঠিক উত্তর: ক

ক) 400

ক

ব্যাখ্যা

Let, the cost price be Tk. x
Selling price at 20% profit
= x + 20% of x
= x + 20x/100
= 120x/100
= Tk. 6x/5

The cost price is increased by 10%.
So, new cost price
= (x + 10% of x)
= Tk. 11x/10

Therefore, new selling price = Tk. (6x/5 + 26)

New profit = (6x/5 + 26) - 11x/6
= Tk. (x/10 + 26)

According to the question,
(x/10 + 26) ÷ 11x/10 × 100 = 15
⇒ (x + 260) × 100/11x = 15
⇒ 65x = 26,000
∴ x = 400

৫২১.

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

ক
ক) 17%
খ
খ) 16%
গ
গ) 15%
ঘ
ঘ) 14%

সঠিক উত্তর: ক

ক) 17%

উত্তর

সঠিক উত্তর: ক

ক) 17%

ক

ব্যাখ্যা

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

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

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

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

৫২২.

If a man were to sell his chair for 930 taka, he would lose 25%. To gain 25%, what amount should he sell it?

ক
1400
খ
1600
গ
1280
ঘ
930
ঙ
None

সঠিক উত্তর: ঙ

None

উত্তর

সঠিক উত্তর: ঙ

None

ঙ

ব্যাখ্যা

Let the Cost price of the Chair be y taka.
Selling price = y - 25% of y
= y - 25y/100
= 75y/100
= 3y/4
Therefore 3y/4 = 930
or, y = 1240
So, To gain 25%, Selling Price would be
= 1240 + 25% of 1280
= 1240 + 310
= 1550
= 1600 taka

৫২৩.

The market value of a certain machine decreased by 30 percent of its purchase price each year. If the machine was purchased in 1982 for its market value of Tk. 8000, what was its market value two years later?

ক
Tk. 8000
খ
Tk. 3200
গ
Tk. 5600
ঘ
Tk. 2400

সঠিক উত্তর: খ

Tk. 3200

উত্তর

সঠিক উত্তর: খ

Tk. 3200

খ

ব্যাখ্যা

Question: The market value of a certain machine decreased by 30 percent of its purchase price each year. If the machine was purchased in 1982 for its market value of Tk. 8000, what was its market value two years later?

Solution:

Total price reduce after 2 years = 60% of purchase price = 60% of 8000

= 4800

Market value after 2 years = 8000 - 4800

= 3200

৫২৪.

Hasibul bought an AC for Tk.12160 and paid Tk.340 for transportation. Then he sold it for Tk.12875. Find his profit %.

ক
ক) 3%
খ
খ) 4%
গ
গ) 5%
ঘ
ঘ) 6%

সঠিক উত্তর: ক

ক) 3%

উত্তর

সঠিক উত্তর: ক

ক) 3%

ক

ব্যাখ্যা

প্রশ্ন: Hasibul bought an AC for Tk.12160 and paid Tk.340 for transportation. Then he sold it for Tk.12875. Find his profit %.

সমাধান:
হাসিবুলের AC বাবদ মোট খরচ ১২১৬০ + ৩৪০ টাকা
= ১২৫০০ টাকা

লাভ হয় = (১২৮৭৫ - ১২৫০০) টাকা
= ৩৭৫ টাকা

১২৫০০ টাকায় লাভ হয় ৩৭৫ টাকা
∴ ১০০ টাকায় লাভ হয় (৩৭৫ × ১০০)/১২৫০০ টাকা
= ৩%

৫২৫.

By selling an umbrella for Tk. 300, a shopkeeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is-

ক
ক) 4%
খ
খ) 8%
গ
গ) 6%
ঘ
ঘ) 10%

সঠিক উত্তর: খ

খ) 8%

উত্তর

সঠিক উত্তর: খ

খ) 8%

খ

ব্যাখ্যা

Marked price = Tk. 300
C.P = (100/120) × 300 = Tk. 250

Sale price = 90% of Tk. 300
= 300 × (90/100)
= Tk. 270

Required gain% = {(20/250) × 100}% = 8%

৫২৬.

A cricket team has won 40 games out of 60 played. It has 30 more games to play. How many of these must the team win to make a record 70% win for them?

ক
ক) 20
খ
খ) 25
গ
গ) 23
ঘ
ঘ) 32

সঠিক উত্তর: গ

গ) 23

উত্তর

সঠিক উত্তর: গ

গ) 23

গ

ব্যাখ্যা

Team won 40 games out of 60 and the remaining games were 30.
Total games = 60 + 30
= 90
70% of 90 = 63
Team has to win 63 games in total.
Team has already won 40.
∴ Games to win = 63 - 40
= 23

৫২৭.

একটি পণ্য ২০% লাভে বিক্রি করা হয়েছে। যদি ক্রয়মূল্য ১০% বৃদ্ধি করা হয় এবং বিক্রয়মূল্য ২৬ টাকা বাড়ানো হয়, তাবে লাভের হার ৫% কমে যায়। পণ্যটির ক্রয়মূল্য কত?

ক
৪০০ টাকা
খ
৪৬৬ টাকা
গ
৪৮০ টাকা
ঘ
৫০০ টাকা
ঙ
কোনোটিই নয়

সঠিক উত্তর: ক

৪০০ টাকা

উত্তর

সঠিক উত্তর: ক

৪০০ টাকা

ক

ব্যাখ্যা

প্রশ্ন: একটি পণ্য ২০% লাভে বিক্রি করা হয়েছে। যদি ক্রয়মূল্য ১০% বৃদ্ধি করা হয় এবং বিক্রয়মূল্য ২৬ টাকা বাড়ানো হয়, তাবে লাভের হার ৫% কমে যায়। পণ্যটির ক্রয়মূল্য কত?

সমাধান:
মনে করি,
ক্রয়মূল্য = ক টাকা

২০% লাভে বিক্রয়মূল্য = (ক × ১২০)/১০০ = (১২০ক/১০০) = ৬ক/৫ টাকা

দেওয়া আছে,
ক্রয়মূল্য ১০% বৃদ্ধি করা হয় এবং বিক্রয়মূল্য ২৬ টাকা বাড়ানো হয়
∴ নতুন ক্রয়মূল্য = (ক × ১১০)/১০০ = (১১০ক/১০০) = ১১ক/১০ টাকা
নতুন বিক্রয়মূল্য = {(৬ক/৫) + ২৬} টাকা
= (৬ক + ১৩০)/৫ টাকা

∴ লাভ = [{(৬ক + ১৩০)/৫} - (১১ক/১০)] টাকা
= (১২ক + ২৬০ - ১১ক)/১০ টাকা
= (ক + ২৬০)/১০ টাকা
= {(ক/১০) + ২৬} টাকা

প্রশ্নমতে,
{(ক/১০) + ২৬} × (১০/১১ক) × ১০০ = ১৫
⇒ ১০০(ক + ২৬০) = ১৬৫ক
⇒ ১০০ক + ২৬০০ = ১৬৫ক
⇒ ৬৫ক = ২৬০০
⇒ ক = ৪০০

সুতরাং, ক্রয়মূল্য ৪০০ টাকা

৫২৮.

If 0.06 is x% of 0.6, then the value of x is

ক
ক) 6
খ
খ) 60
গ
গ) 10
ঘ
ঘ) 5

সঠিক উত্তর: গ

গ) 10

উত্তর

সঠিক উত্তর: গ

গ) 10

গ

ব্যাখ্যা

x% of 0.6 = 0.06
⇒ (x/100) × 0.6 = 0.06
⇒ x = 0.06 × 100/0.60
⇒ x = 10

৫২৯.

Income tax is raised from 4% to 5% but the revenue is increased by 10% only. Find the decreased percentage in the amount taxed.

ক
ক) 8
খ
খ) 10
গ
গ) 12
ঘ
ঘ) 15

সঠিক উত্তর: গ

গ) 12

উত্তর

সঠিক উত্তর: গ

গ) 12

গ

ব্যাখ্যা

ধরি,
প্রথম আয়কর ছিল x টাকা
নতুন আয়কর ছিল y টাকা

ধরি,
প্রথম রাজস্ব ছিলো = 100 টাকা

x এর 4% = 100
4x/100= 100
x/25 = 100
x = 2500

আবার ,
রাজস্ব 10% বৃদ্ধিতে নতুন রাজস্ব = 100 + 10 = 110 টাকা
y এর 5% = 110
5y/100 =110
y/20 = 110
y = 2200

আয়কর কমেছে = (2500 - 2200) টাকা = 300 টাকা

আয়কর শতকরা কমেছে = {(300/2500) × 100}% = 12%

৫৩০.

In a certain store, the profit is 320% of the cost, If the cost increase by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?

ক
ক) 60%
খ
খ) 70%
গ
গ) 50%
ঘ
ঘ) 30%

সঠিক উত্তর: খ

খ) 70%

উত্তর

সঠিক উত্তর: খ

খ) 70%

খ

ব্যাখ্যা

Question: In a certain store, the profit is 320% of the cost, If the cost increase by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?

Solution:

Let the cost price be 100x
so, Profit = 320% of 100x = 320x
then, selling price = 100x + 320x = 420x

Now, cost price increased by 25%
New, Cost price = 125x
New Profit = 420x - 125x = 295x

Profit percent on selling price = (295x/420x) × 100 = 70%

∴ The required percentage is 70%

৫৩১.

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

ক
180%
খ
200%
গ
250%
ঘ
280%

সঠিক উত্তর: খ

200%

উত্তর

সঠিক উত্তর: খ

200%

খ

ব্যাখ্যা

Question: Arif bought a ticket of a cricket match for Tk. 25 and later sold the ticket to Rafi 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

শতকরা লাভ 200%

৫৩২.

A number is mistakenly divided by 2 instead of being multiplied by 2. Find the percentage change in the result.

ক
25%
খ
40%
গ
55%
ঘ
75%

সঠিক উত্তর: ঘ

75%

উত্তর

সঠিক উত্তর: ঘ

75%

ঘ

ব্যাখ্যা

Question: A number is mistakenly divided by 2 instead of being multiplied by 2. Find the percentage change in the result.

Solution:
Let the number be N.
2N is the correct outcome.
0.5N is the mistakenly calculated outcome.

Change in the number= 2N - 0.5N = 1.5N

Percentage change= (1.5N/2N) × 100 = 75%

৫৩৩.

What is the minimum percentage increase in the mean of set X {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes?

ক
50%
খ
80%
গ
100%
ঘ
150%

সঠিক উত্তর: গ

100%

উত্তর

সঠিক উত্তর: গ

100%

গ

ব্যাখ্যা

Question: What is the minimum percentage increase in the mean of set X {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes?

Solution:
old mean = - 4 - 1 + 6 + 9 /5 = 2

-4, -1 will be replaced by 2, 3

new mean = 2 + 3 + 6 + 9 /5 = 4

%increase = {(4 - 2)/2} × 100%
= 100%

৫৩৪.

If a is 10% less than b and c is 40% less than d, then ac is what percent less than bd?

ক
37%
খ
40%
গ
46%
ঘ
54%

সঠিক উত্তর: গ

46%

উত্তর

সঠিক উত্তর: গ

46%

গ

ব্যাখ্যা

Suppose, b = 100
a = 100 - 10 = 90

Suppose, d = 100
c = 100 - 40 = 60

ac = 90 × 60
= 5400;

bd
= 100 × 100
= 10,000

ac is less than bd in percentage
= (10,000 - 5400)/10,000
= 4600/10,000 × 100%
= 46%

৫৩৫.

A book vendor sold a book at loss of 10%. Had he sold it for Tk. 108 more, he would have earned a profit of 10%. Find the cost of the book = ?

ক
ক) Tk. 442
খ
খ) Tk. 540
গ
গ) Tk. 648
ঘ
ঘ) Tk. 740

সঠিক উত্তর: খ

খ) Tk. 540

উত্তর

সঠিক উত্তর: খ

খ) Tk. 540

খ

ব্যাখ্যা

Given loss = 10% profit = 10%
Difference of overall profit and loss = 10 - (-10) = 20%
20% of cp = sp
20/ 100×cp = 108
20 × cp = 108 × 100
cp = 10800/20
∴ cp = 540

৫৩৬.

45% of 750 - 25% of 480 = ?

ক
217.50
খ
376.21
গ
120
ঘ
337.50

সঠিক উত্তর: ক

217.50

উত্তর

সঠিক উত্তর: ক

217.50

ক

ব্যাখ্যা

Question: 45% of 750 - 25% of 480 = ?

Solution:
Given that,
= 45 × (750/100) - 25 × (480/100)
= (45 × 7.5) - (25 × 4.8)
= 337.5 - 120
= 217.50

৫৩৭.

If Adnan’s salary is 60% higher than Bina’s salary, by what percentage is Bina’s salary less than Adnan’s?

ক
27.5% lower
খ
35.5% lower
গ
30.5% lower
ঘ
37.5% lower

সঠিক উত্তর: ঘ

37.5% lower

উত্তর

সঠিক উত্তর: ঘ

37.5% lower

ঘ

ব্যাখ্যা

Question: If Adnan’s salary is 60% higher than Bina’s salary, by what percentage is Bina’s salary less than Adnan’s?

Solution:
Let,
Bina’s Salary is Tk. 100.
Then,
∴ Adnan’s Salary = (100 + 60% of 100)
= 100 + (60× 100)/100
= 100 + 60
= 160

∴ Difference between Adnan’s Salary and Bina’s Salary = 160 - 100 = 60

∴ lower = (60/160) × 100 = 37.5%

∴ Bina’s salary is 37.5% lower than Adnan’s salary.

৫৩৮.

Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?

ক
ক) 16 : 5
খ
খ) 14 : 5
গ
গ) 16 : 7
ঘ
ঘ) 19 : 5

সঠিক উত্তর: ঘ

ঘ) 19 : 5

উত্তর

সঠিক উত্তর: ঘ

ঘ) 19 : 5

ঘ

ব্যাখ্যা

Quantity of alcohol in vessel P = 62.5/100 × 2 = 5/4 litres
Quantity of alcohol in vessel Q = 87.5/100 × 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed
= 4.75 : 1.25 = 19 : 5.

৫৩৯.

In order to maintain the price line, a trader allows a discount of 12 % on the marked price of goods in his ship. However, he still makes a gross profit of 32 % on the cost price. Find the profit percent he would have made on the selling price had he sold at the marked price.

ক
40%
খ
42%
গ
50%
ঘ
52%

সঠিক উত্তর: গ

50%

উত্তর

সঠিক উত্তর: গ

50%

গ

ব্যাখ্যা

Question: In order to maintain the price line, a trader allows a discount of 12 % on the marked price of goods in his ship. However, he still makes a gross profit of 32 % on the cost price. Find the profit percent he would have made on the selling price had he sold at the marked price.

Solution:
Let,
CP = 100
SP = 132
This is after a discount of 12%
Thus the marked price must be = 132 + {(132 × 12)/88} = 150

∴ Profit Percent = {(150 - 100)/100} × 100% = 50%
Therefore he is marking the product 50% above the cost price. Hence the profit will be 50%

৫৪০.

The price of a phone is Tk. 8000. Its price is first increased by 25% and then decreased by 20%. What is the present price of the phone?

ক
Tk. 5000
খ
Tk. 5550
গ
Tk. 5900
ঘ
Tk. 8000

সঠিক উত্তর: ঘ

Tk. 8000

উত্তর

সঠিক উত্তর: ঘ

Tk. 8000

ঘ

ব্যাখ্যা

Question: The price of a phone is Tk. 8000. Its price is first increased by 25% and then decreased by 20%. What is the present price of the phone?

Solution:
Initial Cost = Tk. 8000
After 25% increase in the cost, it becomes,
(8000 + 25% of 8000)
= 8000 + 2000
= Tk. 10000

Now, cost is decreased by 20%, so cost will become,
(10000 - 20% of 10000)
= 10000 - 2000
= Tk. 8000

So, present cost is Tk. 8000.

৫৪১.

Tanvir has 450 coins of 50 paisa and 500 coins of 1 Tk. If he gives 46% of 50 paisa coins and 54% of 1 Tk. coins his brother, the amount of money remaining with Tanvir will be -

ক
ক) 416.5
খ
খ) 414.5
গ
গ) 313.5
ঘ
ঘ) 301.5
ঙ
ঙ) None

সঠিক উত্তর: ঙ

ঙ) None

উত্তর

সঠিক উত্তর: ঙ

ঙ) None

ঙ

ব্যাখ্যা

Question: Tanvir has 450 coins of 50 paisa and 500 coins of 1 Tk. If he gives 46% of 50 paisa coins and 54% of 1 Tk. coins his brother, the amount of money remaining with Tanvir will be -

Solution:
তানভীরের নিকট ৫০ পয়সা আছে = 450 × 50 = 225 টাকা
তানভীরের নিকট 1 টাকা আছে = 500 × 1 = 500 টাকা

তানভীরের নিকট ৫০ পয়সা থাকবে = 225 এর 54%
= 225 এর 54/100
= 121.5

তানভীরের নিকট 1 টাকা থাকবে = 500 এর 46%
= 500 এর 46/100
= 230

মোট থাকবে = 121.5 + 230 = 351.5 টাকা

৫৪২.

A man buys doughnuts at the rate of Tk. 35 per 100 pieces and sells them at Tk. 7.20 per dozen. If the profit is Tk. 30, how many doughnuts did he buy?

ক
ক) 60
খ
খ) 120
গ
গ) 180
ঘ
ঘ) 210

সঠিক উত্তর: খ

খ) 120

উত্তর

সঠিক উত্তর: খ

খ) 120

খ

ব্যাখ্যা

Cost price of one doughnut = 35/100 = 0.35
Selling price of one doughnuts = 7.20/12 = 0.6 tk
Profit in one doughnuts = 0.6 - 0.35 = 0.25 tk
So, Total doughnuts bought = 30 / 0.25 = 120

৫৪৩.

A number is decreased by 10% and then increased by 10%. The number so obtained is 10 less than the original number. What was the original number?

ক
ক) 1000
খ
খ) 2000
গ
গ) 3000
ঘ
ঘ) 4000
ঙ
ঙ) 5000

সঠিক উত্তর: ক

ক) 1000

উত্তর

সঠিক উত্তর: ক

ক) 1000

ক

ব্যাখ্যা

x + y + xy/100
= 10 - 10 - (100/100)
= -1%
so, 1% = 10
and 100% = 10 × 100
= 1000

৫৪৪.

A candidate has to obtain a minimum of 40% of the total marks to pass. He got 30% of the total marks and failed by 50 marks. What are the maximum marks?

ক
400
খ
425
গ
475
ঘ
500

সঠিক উত্তর: ঘ

500

উত্তর

সঠিক উত্তর: ঘ

500

ঘ

ব্যাখ্যা

Question: A candidate has to obtain a minimum of 40% of the total marks to pass. He got 30% of the total marks and failed by 50 marks. What are the maximum marks?

Solution:
Let the maximum marks be x.

Then,
40% of x - 30% of x = 50
⇒ 10% of x = 50
⇒ 10x/100 = 50
⇒ x= (50 × 100)/10
∴ x = 500

৫৪৫.

Three candidates, Salman, Parimal & Maruf contested an election and received 1800, 3300 and votes 3900 respectively. What percent of the total votes did Salman get?

ক
20%
খ
40%
গ
45%
ঘ
70%

সঠিক উত্তর: ক

20%

উত্তর

সঠিক উত্তর: ক

20%

ক

ব্যাখ্যা

Question: Three candidates, Salman, Parimal & Maruf contested an election and received 1800, 3300 and votes 3900 respectively. What percent of the total votes did Salman get?

Solution:
Total no. of votes polled = (1800 + 3300 + 3900) = 9000.
Required percentage = (1800/9000) × 100% = 20%.

৫৪৬.

The bus fare was recently raised from Tk. 3.70 to Tk. 4.00 per kilometer. What is the approximate percentage increase?

ক
8%
খ
5%
গ
6%
ঘ
10%

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: The bus fare was recently raised from Tk. 3.70 to Tk. 4.00 per kilometer. What is the approximate percentage increase?

Solution:
বাস ভাড়া বাড়ে = (4.00 - 3.70) টাকা
= 0.30 টাকা

বাস ভাড়া শতকরা বাড়ে = (0.30/3.70) × 100%
= 8.1 %
≈ 8%

৫৪৭.

A toaster machine is priced at Tk. 25,000 and sold with two successive discounts of 15% and 10%. What is its final selling price?

ক
Tk. 19,125
খ
Tk. 15,125
গ
Tk. 18,125
ঘ
Tk. 19,000

সঠিক উত্তর: ক

Tk. 19,125

উত্তর

সঠিক উত্তর: ক

Tk. 19,125

ক

ব্যাখ্যা

Question: A toaster machine is priced at Tk. 25,000 and sold with two successive discounts of 15% and 10%. What is its final selling price?

Solution:
Given,
Marked Price = Tk. 25000
Price after 15% discount
= 25000 - (15% of 25000)
= 25000 - 3750
= Tk. 21,250

Price after 10% discount
= 21250 - (10% of 21250)
= 21250 - 2125
= Tk. 19,125

∴ Final Selling Price = Tk. 19,125

৫৪৮.

If the salary of an employee is reduced by 10 percent for his late attendance and then increased by 10 percent on a pardon, how much does he lose?

ক
ক) 1%
খ
খ) (1/2)%
গ
গ) 99%
ঘ
ঘ) 90%

সঠিক উত্তর: ক

ক) 1%

উত্তর

সঠিক উত্তর: ক

ক) 1%

ক

ব্যাখ্যা

At 10% decrease,
salary = 100 - 10 = 90

And a 10% increase,
the salary = 90 + 90×10/100 = 99

∴ He is at = 100 - 99 = 1% loss

৫৪৯.

A shirt with a list price of Tk. 150 is sold for Tk. 105 after two successive discounts. If the second discount is 12.5%, what was the rate of the first discount?

ক
20%
খ
30%
গ
25%
ঘ
33%

সঠিক উত্তর: ক

20%

উত্তর

সঠিক উত্তর: ক

20%

ক

ব্যাখ্যা

Question: A shirt with a list price of Tk. 150 is sold for Tk. 105 after two successive discounts. If the second discount is 12.5%, what was the rate of the first discount?

Solution:
Let the first discount be x%.

∴ After the first discount,
∴ the price = (100 − x)% of 150
= (100 − x)/100 × 150

After the second discount of 12.5%,
the selling price = 87.5% of the first discounted price
= 87.5/100 × (100 − x)/100 × 150

Given selling price = 105,
ATQ,
87.5/100 × (100 − x)/100 × 150 = 105
⇒ 100 − x = (105 × 100 × 100) / (87.5 × 150)
⇒ 100 − x = 80

∴ x = 100 − 80
= 20

∴ The first discount is 20%.

৫৫০.

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

ক
ক) 125
খ
খ) 150
গ
গ) 175
ঘ
ঘ) 200

সঠিক উত্তর: খ

খ) 150

উত্তর

সঠিক উত্তর: খ

খ) 150

খ

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

৫৫১.

40% boys in a school. If 30% of the boys and 20% of the girls went to the debate club, what percentage of the students went to the debate club?

ক
21%
খ
27%
গ
25%
ঘ
24%
ঙ
20%

সঠিক উত্তর: ঘ

24%

উত্তর

সঠিক উত্তর: ঘ

24%

ঘ

ব্যাখ্যা

ধরি, মোট ছাত্র-ছাত্রী ১০০ জন।
৪০% ছাত্র হলে ছাত্রী ৬০%।
ছাত্র অংশ নেয় ৪০×৩০%= ১২ জন।
ছাত্রী অংশ নেয় ৬০×২০%= ১২ জন।
∴ শতকরা মোট অংশগ্রহণকারী ছাত্র-ছাত্রী = ২৪%।

৫৫২.

Which of the number below is not equivalent to 4%?

ক
ক) 1/25
খ
খ) 4/100
গ
গ) 0.40
ঘ
ঘ) 0.04

সঠিক উত্তর: গ

গ) 0.40

উত্তর

সঠিক উত্তর: গ

গ) 0.40

গ

ব্যাখ্যা

আমরা অপশন গুলো বিবেচনা করি -
A. 1/25 = 1/25 × 100% = 4%
B. 4/100 = 1/25 = 4%
C. .04 = 4/100 = 40/100 × 100% = 40%
D. 0.04 = 4/100 = 1/25 = 4%
সুতরাং, অপশন গ) 40% সঠিক উত্তর।

৫৫৩.

Mr. Tamal purchased stocks for Tk.1,500 and sold 2/3 of it after its value doubled. He sold the remaining stock at 5 times of its purchase price. What is the total profit?

ক
ক) Tk. 2,000
খ
খ) Tk. 2,500
গ
গ) Tk. 3,000
ঘ
ঘ) Tk. 6,000

সঠিক উত্তর: গ

গ) Tk. 3,000

উত্তর

সঠিক উত্তর: গ

গ) Tk. 3,000

গ

ব্যাখ্যা

Question: Mr. Tamal purchased stocks for Tk.1,500 and sold 2nd/3 of it after its value doubled. He sold the remaining stock at 5 times of its purchase price. What v. as the total profit?

Solution:
স্টকের মূল্য = ১৫০০ টাকা
দ্বিগুণ বাড়ার পর , এর মূল্য = ১৫০০ × ২
= ৩০০০ টাকা

৩০০০ এর ২/৩ অংশ
= ২০০০ টাকা
বাকি আছে = ১ - ২/৩
= ১/৩ অংশ

বৃদ্ধি পাবার আগে ১/৩ অংশের দাম = ১৫০০ ×১/৩ টাকা
= ৫০০ টাকা

১/৩ অংশের নতুন দাম = ৫০০ × ৫
= ২৫০০ টাকা

মোট বিক্রয়মূল্য = ২০০০ + ২৫০০ টাকা
= ৪৫০০ টাকা

∴ মোট লাভ = ৪৫০০ - ১৫০০ টাকা
= ৩০০০ টাকা

৫৫৪.

80% of a smaller number is 4 less than 40% of a larger number. The larger number is 85 greater than the smaller one. The sum of these two number is-

ক
ক) 160
খ
খ) 235
গ
গ) 280
ঘ
ঘ) 290

সঠিক উত্তর: খ

খ) 235

উত্তর

সঠিক উত্তর: খ

খ) 235

খ

ব্যাখ্যা

Question: 80% of a smaller number is 4 less than 40% of a larger number. The larger number is 85 greater than the smaller one. The sum of these two number is-

Solution:
Let the smaller number be x and larger number be y
According to the question,
80% of x + 4 = 40% of y
80x/100 + 4 = 40y/100
(8x/10) + 4= 4y/10
(8x + 40)/10 =4y/10
4y - 8x = 40
y - 2x = 10 --------- (1)
y - x = 85 ----------- (2)
By using (1) and (2), we get
x = 75
y = 160

Now
x + y = 160 + 75
= 235

৫৫৫.

A salesman receives daily wage of Tk. 250 and earns a commission of 15% on all sales he makes. How much taka worth of sales does he need to make in order to bring his total daily income of Tk. 1,000?

ক
ক) Tk. 6,000
খ
খ) Tk. 5,500
গ
গ) Tk. 5,000
ঘ
ঘ) Tk. 4,500

সঠিক উত্তর: গ

গ) Tk. 5,000

উত্তর

সঠিক উত্তর: গ

গ) Tk. 5,000

গ

ব্যাখ্যা

Question: A salesman receives daily wage of Tk. 250 and earns a commission of 15% on all sales he makes. How much taka worth of sales does he need to make in order to bring his total daily income of Tk. 1,000?

Solution:
1000 টাকার মজুরি পেতে কমিশন লাগবে = 1000 - 250 = 750 টাকা

15 টাকা কমিশন হলে মোট বিক্রয় = 100 টাকা
1 টাকা কমিশন হলে মোট বিক্রয় = 100/15 টাকা
750 টাকা কমিশন হলে মোট বিক্রয় = (100 × 750)/15 টাকা
= 5000 টাকা

৫৫৬.

When a plot is sold for Tk. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?

ক
Tk. 21,000
খ
Tk. 22,500
গ
Tk. 25,300
ঘ
Tk. 25,800

সঠিক উত্তর: গ

Tk. 25,300

উত্তর

সঠিক উত্তর: গ

Tk. 25,300

গ

ব্যাখ্যা

Question: When a plot is sold for Tk. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?

Solution:
15% ক্ষতিতে
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য (100 - 15) টাকা বা 85 টাকা

বিক্রয়মূল্য 85 টাকা হলে ক্রয়মূল্য 100 টাকা
বিক্রয়মূল্য 1 টাকা হলে ক্রয়মূল্য 100/85 টাকা
বিক্রয়মূল্য 18700 টাকা হলে ক্রয়মূল্য (100 × 18700)/85 টাকা
= 22000 টাকা

15% লাভে
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য (100 + 15) টাকা বা 115 টাকা

ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য 115 টাকা
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য 115/100 টাকা
ক্রয়মূল্য 22000 টাকা হলে বিক্রয়মূল্য (115 × 22000)/100 টাকা
= 25300 টাকা

৫৫৭.

The price of a model M camera is $209 and the price of a special lens is $69. When the camera and lens are purchased together, the price is $239. The amount saved by purchasing the camera and lens together is approximately what percent of the total price of the camera and lens when purchased separately?

ক
14%
খ
16%
গ
33%
ঘ
86%

সঠিক উত্তর: ক

14%

উত্তর

সঠিক উত্তর: ক

14%

ক

ব্যাখ্যা

Question: The price of a model M camera is $209 and the price of a special lens is $69. When the camera and lens are purchased together, the price is $239. The amount saved by purchasing the camera and lens together is approximately what percent of the total price of the camera and lens when purchased separately?

Solution:
Price of the camera and lens when purchased separately = 209 + 69 = 278
Total price when purchased together = 239

Discount in $ = 278 - 239 = 39

Discount % = (39/278) × 100% = 14.02% ≅ 14%

Hence the correct answer is A

৫৫৮.

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

ক
ক) 56. 25%
খ
খ) 25.56 %
গ
গ) 50.25%
ঘ
ঘ) 54.25%v

সঠিক উত্তর: ক

ক) 56. 25%

উত্তর

সঠিক উত্তর: ক

ক) 56. 25%

ক

ব্যাখ্যা

ধরি,
দ্রব্যটির ক্রয়মূল্য 100 টাকা
25% লাভে দ্রব্যটির বিক্রয়মূল্য = 100 + 25 = 125 টাকা
অর্থাৎ দ্রব্যটি দামের 80% হলো = 125 টাকা
∴ দ্রব্যটি দামের 100% হলো = (125 × 100)/80
= 156.25 টাকা
∴ শতকরা লাভ হতো = 156.25 - 100 = 56.25%

৫৫৯.

A shopkeeper buys a mobile phone for Tk. 8,000 and sells it to a retailer at a profit of 15%. The retailer then sells it to a customer at a profit of 10%. How much does the customer pay for the mobile phone?

ক
Tk. 10,120
খ
Tk. 9,900
গ
Tk. 10,000
ঘ
Tk. 10,240
ঙ
Tk. 9,840

সঠিক উত্তর: ক

Tk. 10,120

উত্তর

সঠিক উত্তর: ক

Tk. 10,120

ক

ব্যাখ্যা

Question: A shopkeeper buys a mobile phone for Tk. 8,000 and sells it to a retailer at a profit of 15%. The retailer then sells it to a customer at a profit of 10%. How much does the customer pay for the mobile phone?

Solution:
দোকানদারের 15% লাভে বিক্রয়মূল্য = 8000 + 8000 এর 15%
= 8000 + (8000 × 15 / 100)
= 8000 + 1200
= Tk. 9200

দোকানদারের বিক্রয়মূল্য = খুচরা বিক্রেতার ক্রয়মূল্য

খুচরা বিক্রেতার 10% লাভে বিক্রয়মূল্য = 9200 + 9200 এর 10%
= 9200 + (9200 × 10 / 100)
= 9200 + 920
= Tk. 10120

সুতরাং, খুচরা বিক্রেতার বিক্রয়মূল্য = ক্রেতার ক্রয়মূল্য = Tk. 10,120

৫৬০.

In an election between two candidates, the winner got 65% of the total votes cast and won the election by a majority of 2748 votes. What is the total number of votes cast if no vote is declared invalid?

ক
ক) 8580
খ
খ) 8720
গ
গ) 9000
ঘ
ঘ) 9160

সঠিক উত্তর: ঘ

ঘ) 9160

উত্তর

সঠিক উত্তর: ঘ

ঘ) 9160

ঘ

ব্যাখ্যা

Winner gets 65% 0f valid votes and loser gets 35% of votes.
Difference between this two = 2748
(65-35)% = 2748
30% = 2748
Total number of voters, 100%
= (2748×100)/30
= 9160

৫৬১.

The number 25 is 2.5% of which of the following?

ক
10
খ
62.5
গ
100
ঘ
625
ঙ
1000

সঠিক উত্তর: ঙ

1000

উত্তর

সঠিক উত্তর: ঙ

1000

ঙ

ব্যাখ্যা

Question: The number 25 is 2.5% of which of the following?

Solution:
Let,
25 is 2.5% of x

2.5% of x = 25
⇒ (2.5/100) × x = 25
⇒ 2.5x = 2500
⇒ x = 2500/2.5
∴ x = 1000

৫৬২.

The marked price is 20% higher than cost price. A discount of 20% is given on the marked price. By this type of sale, there is = ?

ক
ক) 4% loss
খ
খ) 2% loss
গ
গ) No loss no gain
ঘ
ঘ) 4% gain

সঠিক উত্তর: ক

ক) 4% loss

উত্তর

সঠিক উত্তর: ক

ক) 4% loss

ক

ব্যাখ্যা

Let the cost price = 100 units
Marked price = 120 units
Selling price = 120 × 80/100 = 96 units
There will be loss
Loss% = 100−96 /100 × 100 = 4%

৫৬৩.

One-fourth percent, written as a decimal, is-

ক
0.25
খ
0.00025
গ
0.025
ঘ
0.0025

সঠিক উত্তর: ঘ

0.0025

উত্তর

সঠিক উত্তর: ঘ

0.0025

ঘ

ব্যাখ্যা

Question: One-fourth percent, written as a decimal, is-

Solution:
As we know,1% =1/100
Hence,
(1/4)% = (1/4) × (1/100)
= 1/400
= 0.0025

৫৬৪.

7 is 5 percent of what number?

ক
ক) 35
খ
খ) 140
গ
গ) 75
ঘ
ঘ) 49

সঠিক উত্তর: খ

খ) 140

উত্তর

সঠিক উত্তর: খ

খ) 140

খ

ব্যাখ্যা

question: 7 is 5 percent of what number?

solution:
let the number is X

So,
5% of X = 7
X = 7 × 20
X = 140

৫৬৫.

60% of 200 is what percent of 160?

ক
ক) 20
খ
খ) 50
গ
গ) 60
ঘ
ঘ) 75

সঠিক উত্তর: ঘ

ঘ) 75

উত্তর

সঠিক উত্তর: ঘ

ঘ) 75

ঘ

ব্যাখ্যা

Let 60% of 200 be x percent of 160.
that means, 60% of 200 = x% of 160.
⇒ 60 × 200/100 = 160x/100
⇒ 120 = 8x/5
⇒ 8x = 600
⇒ x = 75

৫৬৬.

If Amina’s salary is 60% more than Bina’s salary, then Bina’s salary is what percent less than Amina’s salary?

ক
37.5%
খ
40%
গ
24.5%
ঘ
50%

সঠিক উত্তর: ক

37.5%

উত্তর

সঠিক উত্তর: ক

37.5%

ক

ব্যাখ্যা

Question: If Amina’s salary is 60% more than Bina’s salary, then Bina’s salary is what percent less than Amina’s salary?

Solution:
Let,
Bina’s Salary is Tk. 100. Then,
Amina’s Salary = (100 + 60% of 100)
= 100 + (60× 100)/100
= 100 + 60
= 160

Difference between Amina’s Salary and Bina’s Salary = 160 - 100 = 60

∴ lower = (60/160) × 100 = 37.5%

∴ Bina’s salary is 37.5% lower than Amina’s salary.

৫৬৭.

A trader allows two successive discounts of 30% and 15% on selling an article. If he gets Tk. 476 for that article, find its marked price = ?

ক
ক) 700
খ
খ) 400
গ
গ) 900
ঘ
ঘ) 800

সঠিক উত্তর: ঘ

ঘ) 800

উত্তর

সঠিক উত্তর: ঘ

ঘ) 800

ঘ

ব্যাখ্যা

Let, Marked price = Tk. x
∴x× 70/100 × 85/100 =476
⇒ x = 476 × 100/70 ×100/85
⇒ x= Tk. 800

৫৬৮.

If 16% of 40% of a number is 8, then find the number.

ক
115
খ
120
গ
125
ঘ
130

সঠিক উত্তর: গ

125

উত্তর

সঠিক উত্তর: গ

125

গ

ব্যাখ্যা

Question: If 16% of 40% of a number is 8, then find the number.

Solution:

Let X be the required number.

Therefore, as per the given question,

(16/100) × (40/100) × X = 8

⇒ X = (8 × 100 × 100)/(16 × 40)

∴ X = 125

৫৬৯.

A, B and C enter into partnership with investment in the ratio of 5:7:8. If at the end of the year A's share of profit is Tk. 42360, how much is the total profit?

ক
ক) Tk 169,440
খ
খ) Tk 183,000
গ
গ) Tk 196,700
ঘ
ঘ) Tk. 168,440

সঠিক উত্তর: ক

ক) Tk 169,440

উত্তর

সঠিক উত্তর: ক

ক) Tk 169,440

ক

ব্যাখ্যা

Let, A's profit = 42,360 = 5x
So, x = 42,360/5 = 8472
total profit = 5x + 7x + 8x = 20x = 20×8472
∴ The total profit is tk. 1,69,440

৫৭০.

Which one of the following is equal to 1/4 of 0.01 percent?

ক
ক) 0.025
খ
খ) 0.0025
গ
গ) 0.00025
ঘ
ঘ) 0.000025

সঠিক উত্তর: ঘ

ঘ) 0.000025

উত্তর

সঠিক উত্তর: ঘ

ঘ) 0.000025

ঘ

ব্যাখ্যা

Question: Which one of the following is equal to 1/4 of 0.01 percent?

Solution:
1/4 of 0.01%
= (1/4) × 0.01/100
=0.25 × 1/10000
= 0.000025

৫৭১.

The cost price of 19 articles is same as the selling price of 29 articles. What is loss percentage?

ক
52.30%
খ
35.00%
গ
34.48%
ঘ
30.00%

সঠিক উত্তর: গ

34.48%

উত্তর

সঠিক উত্তর: গ

34.48%

গ

ব্যাখ্যা

Let the cost price of 19 articles be y taka
Therefore, the cost price of 1 article = y/19 taka
The selling price of 29 articles = y taka
Therefore, the selling price of 1 article = y/29 taka
Therefore, loss = (y/19 - y/29) taka
= 10y/551 taka
Percentage loss = (10y/551) ÷ (y/19) × 100%
= 34.48%

৫৭২.

In an election contested by two parties, Party D secured 12% of the total votes more than party R. If party R got 132,000 votes, by how many votes did it lose the election?

ক
ক) 36,000
খ
খ) 240,000
গ
গ) 300,000
ঘ
ঘ) 24,000

সঠিক উত্তর: ক

ক) 36,000

উত্তর

সঠিক উত্তর: ক

ক) 36,000

ক

ব্যাখ্যা

Question: In an election contested by two parties, Party D secured 12% of the total votes more than party R. If party R got 132,000 votes, by how many votes did it lose the election?

Solution:
ধরি
মোট ভোটার সংখ্যা 100 জন

প্রশ্নমতে,
D + R = 100............(1)
D - R = 12...............(2)

(1) + (2) ⇒
2D = 112
D = 112/2
D = 56%

(1) ⇒
D + R = 100
56 + R = 100
R = 100 - 56
R = 44%

44% ভোট = 132000
1% ভোট = 132000/44
100 % ভোট =(132000 × 100)/44
= 300,000
মোট ভোটার = 300,000 টি
D দল ভোট পায় = (300000 - 132000) টি
= 168000 টি

ব্যবধান = (168000 - 132000) টি = 36000টি

৫৭৩.

A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons?

ক
1600 gallons
খ
1625 gallons
গ
1650 gallons
ঘ
1675 gallons

সঠিক উত্তর: খ

1625 gallons

উত্তর

সঠিক উত্তর: খ

1625 gallons

খ

ব্যাখ্যা

Question: A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons?

Solution:
let, the capacity of the pool is x gallons

.3 of initial water = 300
⇒ initial water = 300/.3
= 1000 gallons

ATQ,
0.8x =1000 + 300
⇒ x = (1300 × 10)/( 8)
= 1625 gallons

৫৭৪.

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

ক
18
খ
20
গ
15
ঘ
16

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

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

Answer: Let Cost Price of each article be Taka 1
- Cost Price of x articles = x Taka
- Selling Price of x articles = 20 Taka
- Profit = (20 - x) Taka

x টাকায় লাভ হয় 20 - x টাকা
1 টাকায় লাভ হয় (20 - x)/ x টাকা
100 টাকায় লাভ হয়

প্রশ্নমতে,

100(20-x)=25x
125x=2000
∴x= 16

৫৭৫.

A man buys a field of agricultural land for Tk. 3,60,000. He sells one-third at a loss of 20% and two-fifths at a gain of 25%. At what price must he sell the remaining field so as to make an overall profit of 10%?

ক
Tk.1,00,000
খ
Tk. 1,15,000
গ
Tk. 1,25,000
ঘ
Tk. 1,20,000

সঠিক উত্তর: ঘ

Tk. 1,20,000

উত্তর

সঠিক উত্তর: ঘ

Tk. 1,20,000

ঘ

ব্যাখ্যা

Question: A man buys a field of agricultural land for Tk. 3,60,000. He sells one-third at a loss of 20% and two-fifths at a gain of 25%. At what price must he sell the remaining field so as to make an overall profit of 10%?

Solution:
১০% লাভে,
ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য ১১০ টাকা
∴ ক্রয়মূল্য ৩৬০০০০ টাকা হলে বিক্রয়মূল্য (১১০ × ৩৬০০০০)/১০০ টাকা
= ৩৯৬০০০ টাকা

সম্পূর্ণ জমির ক্রয়মূল্য ৩৬০০০০ টাকা
১/৩ অংশ জমির ক্রয়মূল্য (৩৬০০০০ ÷ ৩) টাকা
= ১২০০০০ টাকা

২/৫ অংশ জমির ক্রয়মূল্য (৩৬০০০০ × ২)/৫ টাকা
= ১৪৪০০০ টাকা

২০% ক্ষতিতে,
১২০০০০ টাকার জমির বিক্রয়মূল্য = (৮০ × ১২০০০০)/১০০ টাকা
= ৯৬০০০ টাকা

২৫% লাভে,
১৪৪০০০ টাকার জমির বিক্রয়মূল্য = (১২৫ × ১৪৪০০০)/১০০ টাকা
= ১৮০০০০ টাকা

∴ অবশিষ্ট জমি বিক্রয় করতে হবে =(৩৯৬০০০ - ৯৬০০০ - ১৮০০০০) টাকা
= ১২০০০০ টাকা

৫৭৬.

The population of a certain town increases by 50% every 50 years. If the population in 1950 was 810, in what year was the population 160?

ক
ক) 1650
খ
খ) 1800
গ
গ) 1700
ঘ
ঘ) 1750

সঠিক উত্তর: ঘ

ঘ) 1750

উত্তর

সঠিক উত্তর: ঘ

ঘ) 1750

ঘ

ব্যাখ্যা

If the population increases by 50% then you're multiplying the previous number by 3/2. So to work backwards, divide by 3/2 (which is the same as multiplying by 2/3).

So we have:

1950: 810
1900: 810×(2/3) = 540
1850: 540×(2/3) = 360
1800: 360×(2/3) = 240
1750: 240×(2/3) = 160

৫৭৭.

If (30% of 80)/y = 24, then what is the value of y?

ক
3/10
খ
1
গ
2/11
ঘ
2

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: If (30% of 80)/y = 24, then what is the value of y?

Solution:
(30% of 80)/y = 24
⇒ (.3 × 80)/y = 24
⇒ y = 24/24 = 1

৫৭৮.

A trader owes a merchant 10,028 Tk due 1 year hence. The trader wants to settle the account after 3 months. If the rate of interest is 12% per annum, how much cash should he pay

ক
ক) Tk. 9025.20
খ
খ) Tk. 9200
গ
গ) Tk. 9600
ঘ
ঘ) Tk. 9560

সঠিক উত্তর: খ

খ) Tk. 9200

উত্তর

সঠিক উত্তর: খ

খ) Tk. 9200

খ

ব্যাখ্যা

Required money = Present Worth of Tk. 10028 due 9 months hence
= Tk. [{10028 × 100}/{100 +(12 × 9/12)}]
= Tk. 9200

৫৭৯.

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

ক
Tk. 2200
খ
Tk. 1200
গ
Tk. 1280
ঘ
Tk. 3260
ঙ
None

সঠিক উত্তর: খ

Tk. 1200

উত্তর

সঠিক উত্তর: খ

Tk. 1200

খ

ব্যাখ্যা

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

Solution:

Let the cost price of the table be x.

Selling price = x - 25% of x

⇒ 720 = x - (25x/100)

⇒ 720 = 75x/100

⇒ 75x = 72000

∴ x = 960

To gain 25%, the selling price should be = 960 + 25% of 960

= Tk. 1200

৫৮০.

Manajir bought an AC for Tk. 12160 and paid Tk. 340 for transportation. Then he sold it for Tk. 12875. Find his profit %.

ক
4%
খ
4.5%
গ
3%
ঘ
5%

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: Manajir bought an AC for Tk. 12160 and paid Tk. 340 for transportation. Then he sold it for Tk. 12875. Find his profit %.

Solution:

CP of AC = Actual CP + Transportation cost = 12160 + 340 = 12500

SP of AC = 12875

∴ Profit = 12875 - 12500 = 375

Profit % = (375/12500) × 100 = 3%

৫৮১.

In an examination 80% of the boys passed in English and 85% passed in Mathematics, while 75% passed in both. If 45 boys failed in both, the number of boys who sat for the examination was-

ক
345
খ
400
গ
450
ঘ
500

সঠিক উত্তর: গ

450

উত্তর

সঠিক উত্তর: গ

450

গ

ব্যাখ্যা

Question: In an examination 80% of the boys passed in English and 85% passed in Mathematics, while 75% passed in both. If 45 boys failed in both, the number of boys who sat for the examination was-

Solution:
Successful boys in English or Maths or both = 80 + 85 - 75 = 90%
Unsuccessful boys = 10%

∴ Total number of boys = (100/100 × 45
= 450

৫৮২.

A man buys an article for 20% less than its value and sells it for 20% more than its value. What is his gain or loss percentage?

ক
No profit, no loss
খ
40% profit
গ
50% profit
ঘ
More than 50% Profit

সঠিক উত্তর: গ

50% profit

উত্তর

সঠিক উত্তর: গ

50% profit

গ

ব্যাখ্যা

Questjion: A man buys an article for 20% less than its value and sells it for 20% more than its value. What is his gain or loss percentage?

Solution:
Let, the value of article is x Tk.

Buying price at 20% less,
= x - 20% of x
= x - (20x/100)
= x - 0.2x
= 0.8x Tk.

Selling Price at 20% more,
= x + 20% of x
= x + 0.2x
= 1.2x Tk.

Profit = 1.2x - 0.8x
= 0.4x Tk.

∴ Profit Percentage = (0.4x/0.8x) × 100%
= (40/0.8)%
= 50%

∴ The gain percentage is 50%.

৫৮৩.

The population of a town increases by 10% in the first year and decreases by 10% in the next year. What is the overall percentage change?

ক
0%
খ
1% increase
গ
1% decrease
ঘ
2% increase

সঠিক উত্তর: গ

1% decrease

উত্তর

সঠিক উত্তর: গ

1% decrease

গ

ব্যাখ্যা

Question: The population of a town increases by 10% in the first year and decreases by 10% in the next year. What is the overall percentage change?

Solution:
Let the initial population = 100

Population after 1st year (10% increase)
Population = 100 + 10% of 100 = 100 + 10 = 110

Population after 2nd year (10% decrease)
Population = 110 - 10% of 110 = 110 - 11 = 99

Overall change = Final population - Initial population
= 99 - 100
= - 1

Overall percentage change = (- 1/100) × 100% = - 1%

∴ Population decreased by 1%

৫৮৪.

15% monthly salary increase resulted in a Tk. 14400 per year increase in salary for an employee. What was his monthly salary before the increase?

ক
Tk. 7850
খ
Tk. 8980
গ
Tk. 6000
ঘ
Tk. 8000
ঙ
Tk. 7500

সঠিক উত্তর: ঘ

Tk. 8000

উত্তর

সঠিক উত্তর: ঘ

Tk. 8000

ঘ

ব্যাখ্যা

Question: 15% monthly salary increase resulted in a Tk. 14400 per year increase in salary for an employee. What was his monthly salary before the increase?

Solution:
Increasing in 12 months = 14400 taka
So, Increasing in 1 month = (14400/12) = Tk. 1200

Now,
15% of original salary = 1200
1% of original salary = 1200/15
∴ 100% of original salary = (1200 × 100)/15 = 8000 taka.

So the monthly salary before the increase was Tk. 8,000.

৫৮৫.

Himel is throwing a bachelorette party for his best friend with x guests total. All of the guests plan to split the cost of renting a limo for y taka. The day before, z guests cancel. Which of the following represents the percent increase in the amount each guest must pay towards the limo rental?

ক
{100x/y(z - x)}%
খ
{100z/(x - z)}%
গ
(y/x)%
ঘ
None of these

সঠিক উত্তর: খ

{100z/(x - z)}%

উত্তর

সঠিক উত্তর: খ

{100z/(x - z)}%

খ

ব্যাখ্যা

Question: Himel is throwing a bachelorette party for his best friend with x guests total. All of the guests plan to split the cost of renting a limo for y taka. The day before, z guests cancel. Which of the following represents the percent increase in the amount each guest must pay towards the limo rental?

Solution:
first, each guest pays y/x taka

after z guests cancel, y/(x - z) taka

increase = { y/(x - z)} - (y/x)
= yz/x(x - z)

%increase = (yz/x(x - z)) × (x/y) × 100%
= 100z/(x - z) %

৫৮৬.

A book sold at a discounted price. If it had a regular price of tk. 300 and was sold for tk. 276, how much discount was applied?

ক
7%
খ
8%
গ
9%
ঘ
10%
ঙ
None

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

প্রশ্ন: A book sold at a discounted price. If it had a regular price of tk. 300 and was sold for tk. 276, how much discount was applied?

সমাধান:
দেওয়া আছে,
বইয়ের প্রকৃত মূল্য = 300 টাকা
বিক্রয়মূল্য = 276 টাকা
ছাড়ের পরিমাণ = 300 - 276 = 24 টাকা

300 টাকায় ছাড় দেয় = 24 টাকা
1 টাকায় ছাড় দেয় = 24/300 টাকা
∴ 100 টাকায় ছাড় দেয় = (24 × 100)/300 টাকা
= 8 টাকা বা 8%

৫৮৭.

Due to reduction in the bus price by 15%, the number of passengers on a certain route increased by 40%. What will be the percentage increase in revenue?

ক
ক) 17
খ
খ) 18
গ
গ) 19
ঘ
ঘ) 20
ঙ
ঙ) None

সঠিক উত্তর: গ

গ) 19

উত্তর

সঠিক উত্তর: গ

গ) 19

গ

ব্যাখ্যা

ধরি,১০০ জন যাত্রী পরিবহন হত যখন ভাড়া ছিল ১০০ টাকা।
রাজস্ব = ১০০×১০০ = ১০০০০ টাকা
ভাড়া কমার পরে,
১৪০ জন যাত্রী পরিবহন হত যখন ভাড়া ৮৫ টাকা।
রাজস্ব = ১৪০×৮৫ = ১১৯০০ টাকা
রাজস্ব বৃদ্ধি = (১১৯০০ - ১০০০০) টাকা = ১৯০০ টাকা
১০০০০ টাকায় রাজস্ব বৃদ্ধি = ১৯০০ টাকা
১ টাকায় রাজস্ব বৃদ্ধি = ১৯০০/১০০০০ টাকা
১০০ টাকায় রাজস্ব বৃদ্ধি = ১৯০০×১০০/১০০০০ টাকা
= ১৯ টাকা বা ১৯%

৫৮৮.

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

ক
ক) 88%
খ
খ) 65%
গ
গ) 85%
ঘ
ঘ) 78%

সঠিক উত্তর: ক

ক) 88%

উত্তর

সঠিক উত্তর: ক

ক) 88%

ক

ব্যাখ্যা

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

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

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

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

৫৮৯.

What percentage of the whole week does Sagor spend in school except lunch time, if his school times are 8 am to 4 pm from Monday to Saturday, with 2 hours for lunch each day?

ক
11%
খ
20%
গ
21%
ঘ
25%

সঠিক উত্তর: গ

21%

উত্তর

সঠিক উত্তর: গ

21%

গ

ব্যাখ্যা

Question: What percentage of the whole week does Sagor spend in school except lunch time, if his school times are 8 am to 4 pm from Monday to Saturday, with 2 hours for lunch each day?

Solution:
Time spent by Sagor in a day = 4 pm - 8 am = 8 hours

Except lunch time, Sagor spends in a day = 8 - 2 = 6 hours

Number of school days in a week = 6

Total school hours in a week = 6 × 6 = 36 hours

Total hours in a week = 7 × 24 = 168 hours

Percentage time spent in a week = (36/168) × 100%
= 21%

৫৯০.

If an article is sold for Tk. 178 at a loss of 11%, what should be its selling price in order to earn a profit of 11%?

ক
Tk. 222
খ
Tk. 224
গ
Tk. 228
ঘ
Tk. 232

সঠিক উত্তর: ক

Tk. 222

উত্তর

সঠিক উত্তর: ক

Tk. 222

ক

ব্যাখ্যা

Question: If an article is sold for Tk. 178 at a loss of 11%, what should be its selling price in order to earn a profit of 11%?

Solution:

SP of the article = Tk. 178

Loss % = 11%

∴ CP = {100/(100 - 11)} × 178

= (178 × 100)/89 = 200

Now CP = Tk. 200 and Profit% = 11%

∴ New SP = {(100 + 11)/100} × 200 = (111 × 200)/100 = 222

Therefore, the article should be sold at Tk. 222

৫৯১.

If the monthly salary of an employee is increased by (8/3)%, he gets tk.88 more. His monthly salary (in TK.) is

ক
ক) 2700
খ
খ) 2800
গ
গ) 3000
ঘ
ঘ) 3300

সঠিক উত্তর: ঘ

ঘ) 3300

উত্তর

সঠিক উত্তর: ঘ

ঘ) 3300

ঘ

ব্যাখ্যা

Let
The monthly salary be x

Now
(8/3)% of x = 88
(8/3) × (1/100) × x = 88
8x/(3 × 100) = 88
x = (88 × 3 × 100)/8
x = 3300

৫৯২.

বিক্রয় করসহ একটি দ্রব্যের বিক্রয়মূল্য ৩০৮ টাকা। বিক্রয় করের হার ১০%। যদি দ্রব্যটি বিক্রয়ে দোকানদারের ১২% লাভ হয়, তবে দ্রব্যটির ক্রয়মূল্য কত?

ক
২৩০ টাকা
খ
২২০ টাকা
গ
২৫০ টাকা
ঘ
২৬০ টাকা
ঙ
২৪০ টাকা

সঠিক উত্তর: গ

২৫০ টাকা

উত্তর

সঠিক উত্তর: গ

২৫০ টাকা

গ

ব্যাখ্যা

প্রশ্ন: বিক্রয় করসহ একটি দ্রব্যের বিক্রয়মূল্য ৩০৮ টাকা। বিক্রয় করের হার ১০%। যদি দ্রব্যটি বিক্রয়ে দোকানদারের ১২% লাভ হয়, তবে দ্রব্যটির ক্রয়মূল্য কত?

সমাধান:
বিক্রয় কর ১০% হলে, কর সংযোজন মূল্য = ১০০ + ১০ = ১১০ টাকা

কর সংযোজন মূল্য ১১০ টাকা হলে কর বাদে মূল্য = ১০০ টাকা
∴ কর সংযোজন মূল্য ১ টাকা হলে কর বাদে মূল্য = ১০০/১১০ টাকা
∴ কর সংযোজন মূল্য ৩০৮ টাকা হলে কর বাদে মূল্য = (১০০ × ৩০৮)/১১০ টাকা
= ২৮০ টাকা

১২% লাভে, বিক্রয়মূল্য = ১০০ + ১২ = ১১২ টাকা

বিক্রয়মূল্য ১১২ টাকা হলে ক্রয়মূল্য = ১০০ টাকা
∴ বিক্রয়মূল্য ১ টাকা হলে ক্রয়মূল্য = ১০০/১১২ টাকা
∴ বিক্রয়মূল্য ২৮০ টাকা হলে ক্রয়মূল্য = (১০০ × ২৮০)/১১২ টাকা
= ২৫০ টাকা

৫৯৩.

If on a Sale there is 40% discount on the marked price of Tk. 1000, but the sale is done at Tk. 510 only then what additional discount % did the customer get?

ক
ক) 10%
খ
খ) 15%
গ
গ) 28%
ঘ
ঘ) 9%

সঠিক উত্তর: খ

খ) 15%

উত্তর

সঠিক উত্তর: খ

খ) 15%

খ

ব্যাখ্যা

Question: If on a Sale there is 40% discount on the marked price of Tk. 1000, but the sale is done at Tk. 510 only then what additional discount % did the customer get?

Solution:

Marked price = Tk. 1000
First discount = 40%
After first discount selling price is = 1000 - (40% of 100) = 600

Let the second discount is = x%

ATQ,
600 - (x% of 600) =510
⇒ 600 - 6x = 510
⇒ 6x = 90
⇒ x = 15

৫৯৪.

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

ক
70%
খ
65%
গ
50%
ঘ
25%

সঠিক উত্তর: গ

50%

উত্তর

সঠিক উত্তর: গ

50%

গ

ব্যাখ্যা

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

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

Discount = 2400 - 1200
= 1200 taka

%discount = (1200/2400) × 100%
= 50%

৫৯৫.

A trader 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
ক) 5%
খ
খ) 15%
গ
গ) 12%
ঘ
ঘ) 8%

সঠিক উত্তর: ক

ক) 5%

উত্তর

সঠিক উত্তর: ক

ক) 5%

ক

ব্যাখ্যা

প্রশ্ন: A trader 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:

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

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

∴ Profit = 1680 - 1600
= 80

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

৫৯৬.

How many litres of water must be evaporated from 50 litres of a 3% sugar solution to get a 5% sugar solution?

ক
ক) 6
খ
খ) 8
গ
গ) 10
ঘ
ঘ) 20
ঙ
ঙ) None

সঠিক উত্তর: ঘ

ঘ) 20

উত্তর

সঠিক উত্তর: ঘ

ঘ) 20

ঘ

ব্যাখ্যা

3% sugar solution = 50×(3/100) = 1.5 Liters of sugar
This amount must be 5% of a reduced final amount (50 - x)
ATQ,
1.5 = 5% × (50-x)
⇒ 50 - x = 150/5 = 30
∴ x = 20

৫৯৭.

A trader, while selling a pen, was asking for such a price that will enable him to offer a 10% discount and still make a profit of 20% on cost. If the cost of the pen was Tk. 30, what was his asking price?

ক
Tk. 70
খ
Tk. 60
গ
Tk. 80
ঘ
Tk. 50
ঙ
Tk. 40

সঠিক উত্তর: ঙ

Tk. 40

উত্তর

সঠিক উত্তর: ঙ

Tk. 40

ঙ

ব্যাখ্যা

Question: A trader, while selling a pen, was asking for such a price that will enable him to offer a 10% discount and still make a profit of 20% on cost. If the cost of the pen was Tk. 30, what was his asking price?

Solution:
If the cost price was Tk. 30
then at 20% profit selling price is Tk. (30 + 30 × 20%) = 30 + (600/100) = Tk. 36

Again at 10% discount,
If the selling price is Tk. 90 then asking price is Tk. 100
If the selling price is Tk. 1 then asking price is Tk. 100/90 = 10/9
If the selling price is Tk. 36 then asking price is Tk. (10 × 36)/9 = Tk. 40

So the asking price is Tk. 40

৫৯৮.

A bicycle is purchased for Tk. 200 and sold at a 10% loss. Find the selling price and the total loss incurred.

ক
Taka 100, Loss Incurred: Tk. 20
খ
Taka 180, Loss Incurred: Tk. 20
গ
Taka 800, Loss Incurred: Tk. 20
ঘ
Taka 380, Loss Incurred: Tk. 20

সঠিক উত্তর: খ

Taka 180, Loss Incurred: Tk. 20

উত্তর

সঠিক উত্তর: খ

Taka 180, Loss Incurred: Tk. 20

খ

ব্যাখ্যা

Question: A bicycle is purchased for Tk. 200 and sold at a 10% loss. Find the selling price and the total loss incurred.

Solution:
Cost Price of the bicycle = Taka 200
Loss Percentage = 10%

∴ Loss Amount = Loss Percentage × Cost Price
= 10% × Taka 200
= Taka 20

∴ Selling Price = Cost Price - Loss Amount
= Taka 200 - Taka 20
= Taka 180

Total Loss Incurred: Tk. 20

৫৯৯.

What is 450% of 0.001?

ক
0.045
খ
0.45
গ
0.0045
ঘ
45

সঠিক উত্তর: গ

0.0045

উত্তর

সঠিক উত্তর: গ

0.0045

গ

ব্যাখ্যা

Let x be 450% of 0.001
x = 450% of 0.001
= 450/100 × 0.001
= 0.0045

৬০০.

If the length and width of a rectangular garden plot were each increased by 20 percent, what would be the percent increase in the area of the plot?

ক
ক) 44%
খ
খ) 24%
গ
গ) 36%
ঘ
ঘ) 40%
ঙ
ঙ) None of these

সঠিক উত্তর: ক

ক) 44%

উত্তর

সঠিক উত্তর: ক

ক) 44%

ক

ব্যাখ্যা

Question: If the length and width of a rectangular garden plot were each increased by 20 percent, what would be the percent increase in the area of the plot?

Solution:
Let,
x and y be the sides of rectangle A.
Area of rectangle A = xy
If x and y, the sides of rectangle A, are each increased by 20% to form the sides of rectangle B,
the sides of rectangle B are 1.2x and 1.2y.
Hence, area of rectangle B is: (1.2x) × (1.2y) = 1.44xy

∴ we have = 1.44 xy - xy = 0.44xy

the percent increase in the area of the plot = {(0.44xy × 100)/xy} %
= 44%