Percentage and Profit & Loss

PrepBank · পাতা ১১ / ১৭ · ১,০০১–১,১০০ / ১,৬৯৬

১,০০১.

A sells an article to B at gain of 25% B sells it to C at a gain of 20% and C sells it to D at a gain 10%. If D pays Tk. 660 for it, how much did it cost to A?

ক
Tk. 200
খ
Tk. 260
গ
Tk. 300
ঘ
Tk. 400

ব্যাখ্যা

Question: A sells an article to B at gain of 25% B sells it to C at a gain of 20% and C sells it to D at a gain 10%. If D pays Tk. 660 for it, how much did it cost to A?

Solution:
Let,
Cost Price for A was = 100

Then, CP for B = (100 + 25% of 100) = 125
CP for C = (125 + 20% of 125) = 150
CP for D = (150 + 10% of 150 )= 165

But, D pay Tk. 660. Then it must be equal to,
165 = 660
1 = 660/165
∴100 = {660 × (100/165)} = 400

So, CP for A = Tk. 400

১,০০২.

What percent of a is equal to 3a?

ক
100%
খ
150%
গ
300%
ঘ
350%

ব্যাখ্যা

Question: What percent of a is equal to 3a?

Solution:
Let x% of a = 3a
⇒ (x/100) × a = 3a
⇒ x/100 = 3a/a
⇒ x/100 = 3
⇒ x = 100 × 3
∴ x = 300

১,০০৩.

The population of Gotham City increases from 175,000 to 262,500. What is the percentage increase in the population?

ক
45%
খ
55%
গ
50%
ঘ
60%

ব্যাখ্যা

Question: The population of Gotham City increases from 175,000 to 262,500. What is the percentage increase in the population?

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

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

∴ জনসংখ্যা বৃদ্ধির শতকরা হার = 50%

১,০০৪.

On selling 17 balls at Tk. 840 there is a loss equal to the cost price of 5 balls. The cost price of a ball is-

ক
Tk. 85
খ
Tk. 50
গ
Tk. 60
ঘ
Tk. 70

ব্যাখ্যা

Question: On selling 17 balls at Tk. 840 there is a loss equal to the cost price of 5 balls. The cost price of a ball is-

Solution:
Let,
The cost price of 1 ball is = Tk. x
The cost price of 17 balls is = Tk. 17x

We know,
Cost price - Selling price = Loss
17x - 840 = 5x
⇒ 12x = 840
⇒ x = 840/12
∴ x = 70

∴ The cost price of 1 ball is Tk. 70

১,০০৫.

A person buys goods worth tk 600. He sells half of it at a gain of 10%. At what gain % must he sell the remaining goods to achieve an overall gain of 15%?

ক
15%
খ
20%
গ
25%
ঘ
30%

ব্যাখ্যা

Question: A person buys goods worth tk 600. He sells half of it at a gain of 10%. At what gain % must he sell the remaining goods to achieve an overall gain of 15%?

Solution:
To gain 15% on the whole, he must sell all goods for = 600 + 15% of 600
= 690 tk

He sells half at a 10% gain = 300 + 10% of 300
= 330 tk
Required balance = 690 - 330 = 360 tk
He must gain tk 60 on the remaining tk 300.

∴ % gain on remainder goods= (60 × 100) / 300 = 20%

১,০০৬.

After decreasing 24% in the price of an article the discounted price becomes Tk. 912. Find the actual price of the article?

ক
ক) Tk.1400
খ
খ) Tk.1300
গ
গ) Tk.1200
ঘ
ঘ) Tk.1100

ব্যাখ্যা

ধরি,
পণ্যটির প্রকৃত মূল্য x টাকা

প্রশ্নমতে,
x এর 76%= 912
76x /100 = 912
76x = 91200
x = 91200/76
x = 1200

পণ্যটির প্রকৃত মূল্য 1200 টাকা

১,০০৭.

The sum of the salaries of A and B is Tk. 2100. A spends 80% of his salary and B spends 70% of his salary. If their savings are in the proportion of 4 : 3, then the salary of A?

ক
ক) Tk.1700
খ
খ) Tk.1400
গ
গ) Tk.1600
ঘ
ঘ) Tk.1800

ব্যাখ্যা

A and B savings are 20% and 30%
Let the salaries of A and B be x and y respectively

Now
(20% of x)/(30% of y) = 4/3
(x/5)/(3y/10) = 4/3
(x/5)×(10/3y) = 4/3
2x/3y = 4/3
x/3y = 2/3
x/y = 2
x = 2y

Again
x + y = 2100
2y + y = 2100
3y = 2100
y = 700

A's salaries = x = 2y
= 2 × 700
=Tk.1400

১,০০৮.

A dress on sale in a shop is marked at Tk. Z. During the discount sale its price is reduced by 15%. Staffs are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of Z?

ক
0.75Z
খ
0.76Z
গ
0.765Z
ঘ
None

ব্যাখ্যা

Question: A dress on sale in a shop is marked at Tk. Z. During the discount sale its price is reduced by 15%. Staffs are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of Z?

Solution:
A dress on sale in a shop is marked at Tk. Z
After 15% discount the price is = Z - 15% of Z = Z - 0.15Z = 0.85Z

For staff member, further 10% reduction the final price will be = 0.85Z - 10% of 0.85Z = 0.85Z - 0.085Z = 0.765Z

১,০০৯.

The profit earned by selling an article for Tk 90 is double the loss incurred when the same article is sold for Tk 45. At what price should the article be sold to make 25% profit?

ক
Tk. 75
খ
Tk. 80
গ
Tk. 60
ঘ
Tk. 85

ব্যাখ্যা

Question: The profit earned by selling an article for Tk 90 is double the loss incurred when the same article is sold for Tk 45. At what price should the article be sold to make 25% profit?

Solution:
Let,
The cost price be Tk. x.

ATQ,
90 - x = 2(x - 45)
⇒ 90 - x = 2x - 90
⇒ 2x + x = 90 + 90
⇒ 3x = 180
⇒ x = 180/3
∴ x = 60

∴ Cost price = Tk. 60,
Profit = 25%

∴ The selling price of the article = Tk. (60 × 125)/100
= Tk. 75

১,০১০.

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

ক
ক) 50%
খ
খ) 54%
গ
গ) 60%
ঘ
ঘ) 64%

ব্যাখ্যা

Let number is 100.
Actual Multiplication = (100 × 5)/3 = 500/3.

Student multiplied = (100 × 3)/5 = 300/5.
Error,
= (500/3) - (300/5)
= (2500 - 900)/15
= 1600/15

%Error = (1600 ×100 ×3)/(15×500)% = 64%.

১,০১১.

In a survey about gym membership, 80 percent of people said they would join a new fitness center. Of those who said they would join, 75 percent actually joined, and of those who said they would not join, 10 percent ended up joining. What percent of the group joined the fitness center?

ক
56%
খ
60%
গ
58%
ঘ
62%
ঙ
None

ব্যাখ্যা

Question: In a survey about gym membership, 80 percent of people said they would join a new fitness center. Of those who said they would join, 75 percent actually joined, and of those who said they would not join, 10 percent ended up joining. What percent of the group joined the fitness center?

Solution:
Let's assume,
Total group = 100 people

Now,
75% of 80 = 80 × (75/100) = 60 people who said YES and actually joined
and, 10% of 20 = 20 × (10/100) = 2 people who said NO but actually joined

Total joined = Those who said YES and joined + Those who said NO but joined
= 60 + 2
= 62 people or 62%

১,০১২.

If x percent of 40 is y, then 10x equals?

ক
ক) 4y
খ
খ) 10y
গ
গ) 25y
ঘ
ঘ) 100y

ব্যাখ্যা

Given, x% of 40 = y
⇒ 40x/100 = y
⇒ x = 100y/40
⇒ x = 5y/2
∴ 10x = 25y

১,০১৩.

If a man was to sell his table for Tk. 750, he would lose 25%. To gain 25% he should sell it for:

ক
Tk. 1100
খ
Tk. 1225
গ
Tk. 1250
ঘ
Tk. 1200

ব্যাখ্যা

Question: If a man was to sell his table for Tk. 750, 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
⇒ 750 = x - (25x/100)
⇒ 750 = 75x/100
⇒ 75x = 75000
∴ x = 1000

To gain 25% = 1000 + 25% of 1000
= 1000 + 250
= Tk. 1250

১,০১৪.

A manufacturer sells an article to a wholesale dealer at a profit of 20% and the wholesale dealer sells it to retail merchant at a loss of 5%. Find the resultant loss or profit.

ক
ক) 10% loss
খ
খ) 14% profit
গ
গ) 18% loss
ঘ
ঘ) None of the above

ব্যাখ্যা

Question: A manufacturer sells an article to a wholesale dealer at a profit of 20% and the wholesale dealer sells it to retail merchant at a loss of 5%. Find the resultant loss or profit.

Solution:
Let, production cost = 100
Then first selling price after 20% profit = 120
Now, second selling price at 5% loss = 120 - (5% of 120)
⇒ 120 - 6 = 114
So, overall profit = 114 -100 = 14%

১,০১৫.

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

ক
40
খ
45
গ
50
ঘ
54

ব্যাখ্যা

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

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

ATQ,
(60 - q)/q = 20%
⇒ 100(60 - q)/q = 20
⇒ 6000 - 100q = 20q
⇒ 120q = 6000
∴ q = 50
Therefore, the value of 'q' is 50.

১,০১৬.

If a = 4b, what percentage of 2a is 2b?

ক
10%
খ
12%
গ
20%
ঘ
25%
ঙ
None

ব্যাখ্যা

প্রশ্ন: If a = 4b, what percentage of 2a is 2b?

সমাধান:
দেওয়া আছে,
a = 4b

ধরি,
x এর শতকরা 2a হলো 2b

প্রশ্নমতে,
(x/100) × 2a = 2b
⇒ x = (2b × 100)/2a
⇒ x = (2b × 100)/8b [a = 4b বসিয়ে]
∴ x = 25%

১,০১৭.

A man buys a fan for Tk. 1000 and sells it at a loss of 15%. What is the selling price of the fan?

ক
Tk. 950
খ
Tk. 850
গ
Tk. 890
ঘ
Tk. 915

ব্যাখ্যা

Question: A man buys a fan for Tk. 1000 and sells it at a loss of 15%. What is the selling price of the fan?

Solution:
Cost Price of the fan is Tk.1000

Loss percentage is 15%

As we know,
Loss percentage = (Loss/Cost Price) × 100

15 = (Loss/1000) × 100

∴ Loss = 150

As we know,

Loss = Cost Price - Selling Price

∴ Selling Price = Cost Price - Loss

= 1000 - 150

= 850

∴ Selling Price = Tk. 850

১,০১৮.

A reduction of 25% in the price of sugar enables a housewife to purchase 5 kg more for 600 Taka. What is the original price per kg of sugar?

ক
Tk. 48
খ
Tk. 28
গ
Tk. 32
ঘ
Tk. 40

ব্যাখ্যা

Question: A reduction of 25% in the price of sugar enables a housewife to purchase 5 kg more for 600 Taka. What is the original price per kg of sugar?

Solution:
Let original price per kg = p Taka
Reduced price = p - p of 25% = 0.75p
Original quantity for 600 Taka
Q₁ = 600/p kg

And
New quantity for 600 Taka
Q₂ = 600/0.75p = 800/p kg

Now, quantity difference,
Q₂ - Q₁ = 5
(800/p) - (600/p) = 5
200/p = 5
p = 200/5
p = 40

∴ Original price per kg = Tk. 40

১,০১৯.

By selling a product for 3500, a seller makes 15% profit. If the profit is decreased to 9%, then selling price will be:

ক
2850
খ
3815
গ
3043
ঘ
3317

ব্যাখ্যা

Question: By selling a product for 3500, a seller makes 15% profit. If the profit is decreased to 9%, then selling price will be:

Solution:
১৫% লাভে,
একটি পণ্যের ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য = (১০০ + ১৫) = ১১৫ টাকা

বিক্রয়মূল্য ১১৫ টাকা হলে ক্রয়মূল্য ১০০ টাকা
বিক্রয়মূল্য ১ টাকা হলে ক্রয়মূল্য (১০০/১১৫) টাকা
বিক্রয়মূল্য ৩৫০০ টাকা হলে ক্রয়মূল্য (১০০/১১৫) × ৩৫০০ টাকা
= ৩০৪৩.৪৮ টাকা

আবার,
৯% লাভে,
একটি পণ্যের ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য = (১০০ + ৯) = ১০৯ টাকা

ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য ১০৯ টাকা
ক্রয়মূল্য ১ টাকা হলে বিক্রয়মূল্য (১০৯/১০০) টাকা
ক্রয়মূল্য ৩০৪৩.৪৮ টাকা হলে বিক্রয়মূল্য (১০৯/১০০) × ৩০৪৩.৪৮ টাকা
= ৩৩১৭.৩৯ টাকা

∴ বিক্রয়মূল্য হবে ৩৩১৭.৩৯ টাকা।

১,০২০.

Sara sells his goods 20% cheaper than Rahim and 25% dearer than Monir. How much of the goods of Monir are cheaper than Rahim's?

ক
36%
খ
40%
গ
45%
ঘ
25%

ব্যাখ্যা

Question: Sara sells his goods 20% cheaper than Rahim and 25% dearer than Monir. How much of the goods of Monir are cheaper than Rahim's?

Solution:
Let,
Rahim sells at 100 taka
Sara sells at 80 taka

∴ Monir sells at = 80/1.25 = 64 taka

The goods of Monir are cheaper than Rahim's = (100 - 64) = 36 taka

Percentage cheaper = (36/100 ×100) = 36%

১,০২১.

A shopkeeper earns a profit of 12% on selling a book at 60% discount on the printed price. What is the ratio of the cost price and the printed price of the book?

ক
5 : 14
খ
7 : 18
গ
5 : 17
ঘ
7 : 28
ঙ
None

ব্যাখ্যা

Let the Cost Price be100 taka
selling price = 100 + 100 × 12% = 112 taka
After 60% discount on the printed price, then remaining = (100 - 60)% = 40%
If the market price is x, then 40% of x = 112
x = 112 × 100/40 = 280 taka
Required ratio = 100 : 280 = 5 : 14
--------------------------------------------------------------------------------------
Alternative way(easy way):
Let cost price be y taka
Profit = 12% of y taka = 12y/100 taka
Selling price = (y + 12y/100) taka
= 112y/100 taka
Discount = 60% of printed price
Selling price = printed price - discount
112y/100 = printed price - 60% of printed price
112y/100 = (1 - 60/100) × printed price
printed price × 40/100 = 112y/100
printed price = 112y/40
Cost price : Printed Price = y : 112y/40
= 40 : 112
= 5 : 14

১,০২২.

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

ব্যাখ্যা

30 % of 50 = 15
and 75% of 80 = 60.

∴ The fraction is = 15/60 = 1/4.

১,০২৩.

By selling a bicycle for 2,850 taka, a shopkeeper gains 14%. If the profit is reduced to 8%. What is the selling price?

ক
2600
খ
2700
গ
2780
ঘ
2820
ঙ
2950

ব্যাখ্যা

Let Cost Price was y.
or, y + 14% of y = 2850
or, y + 14y/100 = 2850
∴ y = 2500.
So, Cost Price = 2500 taka.
Now, When profit remains at 8%,
Selling Price = 2500 taka + 8% of 2500 taka
= 2700 taka.

১,০২৪.

A man bought some toys at the rate of 10 for Tk. 40 and sold them at 8 for Tk. 35. Find his gain or loss percent.

ক
ক) 10%
খ
খ) 9.5%
গ
গ) (75/8)%
ঘ
ঘ) (71/5)%

ব্যাখ্যা

প্রশ্ন: A man bought some toys at the rate of 10 for Tk. 40 and sold them at 8 for Tk. 35. Find his gain or loss percent.

সমাধান:
Cost price of 10 toys = Tk. 40
∴ CP of 1 toy = Tk. 4

Selling price of 8 toys = Tk. 35
∴ SP of 1 toy = Tk. 35/8

Therefore, Gain = 35/8 – 4 = 3/8.

Gain percent = {(3/8)/4} × 100% =(75/8)%

১,০২৫.

Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100 kg of fresh fruits?

ক
20 kg
খ
30 kg
গ
40 kg
ঘ
50 kg

ব্যাখ্যা

Question: Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100 kg of fresh fruits?

Solution:
The fruit content in both the fresh fruit and dry fruit is the same.

Given, fresh fruit has 68% water. So remaining 32% is fruit content. Weight of fresh fruits is 100kg

Dry fruit has 20% water. So remaining 80% is fruit content. Let weight of dry fruit be y kg.

Fruit % in freshfruit = Fruit% in dryfruit
(32/100) × 100 = (80/100 ) × y
⇒ 32 = (8/10) × y
⇒ y = (32 × 10)/8
∴ y = 40

We get, y = 40 kg

১,০২৬.

In a test, minimum passing percentage for girls and boys are 45% and 60% respectively. A boy scored 767 marks and failed by 313 marks. What are the minimum passing marks for girls?

ক
600
খ
500
গ
810
ঘ
300

ব্যাখ্যা

Question: In a test, minimum passing percentage for girls and boys are 45% and 60% respectively. A boy scored 767 marks and failed by 313 marks. What are the minimum passing marks for girls?

Solution:
Minimum pass percentage for Boys = 60%
Minimum pass percentage for girls = 45%

A boy gets 767 and failed by 313
∴ Passing marks for boys= 767 + 313 = 1080

Now
60% = 1080
⇒ 1% = 1080/60
⇒ 45% = (1080 × 45)/60
= 810

১,০২৭.

30% of a number when subtracted from 91, gives the number itself. Find the number.

ক
75
খ
70
গ
65
ঘ
60

ব্যাখ্যা

Question: 30% of a number when subtracted from 91, gives the number itself. Find the number.

Solution:
Let the number be x

According to the question,
91 - (30x/100) = x
⇒ 9100 - 30x = 100x
⇒ 9100 = 130x
⇒ x = 9100/130
∴ x = 70.

১,০২৮.

A dealer marks the price of all the goods at 30% above the cost price and assumes that he will make a profit of 15% if he offers a discount of 15%. Find what will be his actual profit on sales?

ক
ক) 15%
খ
খ) 30%
গ
গ) 12.50%
ঘ
ঘ) 10.50%

ব্যাখ্যা

Let cost-price goods be Tk. 100
Marked price (Selling Price) marked by the shopkeeper on goods = Tk. 130
He sells the goods at a discount of 15%

Therefore,
Selling price = 85% of Tk. 130
= Tk. 110.50
Gain = S.P. – C.P.
= 110.5 – 100
= 10.50%

১,০২৯.

Ms. Rahman's monthly salary is Tk. 8000.00 and she gets 15% commission on her salary. If her salary increased by 20%, by what percent will her commission increase?

ক
10%
খ
20%
গ
5%
ঘ
15%

ব্যাখ্যা

Question: Ms. Rahman's monthly salary is Tk. 8000.00 and she gets 15% commission on her salary. If her salary increased by 20%, by what percent will her commission increase?

Solution:
পূর্বের কমিশন = 8000 এর 15% টাকা
= 8000 × 15/100
= 1200 টাকা

২০% বৃদ্ধিতে বর্তমান বেতন = 8000 + 8000 এর 20%
= 8000 + 8000 × 20/100
= 8000 + 1600
=9600 টাকা

নতুন কমিশন = 9600 এর 15%
= 9600 × 15/100 = 1440 টাকা

কমিশন বৃদ্ধি পায় = 1440 - 1200 = 240 টাকা

শতকরা কমিশন বৃদ্ধি পায় = (240/1200) × 100%
= 20%

১,০৩০.

If a shopkeeper sells a watch for Tk. 600, he incurs a loss of 20%. At what price should he sell it to make a profit of 20%?

ক
Tk. 850
খ
Tk. 900
গ
Tk. 800
ঘ
Tk. 950

ব্যাখ্যা

Question: If a shopkeeper sells a watch for Tk. 600, he incurs a loss of 20%. At what price should he sell it to make a profit of 20%?

Solution:
Let the Cost Price (CP) of the watch be x.
Selling price = x - 20% of x
⇒ 600 = x - (20x/100)
⇒ 600 = 80x/100
⇒ 80x = 60000
⇒ x = 750 (This is the CP)

To gain 20% = 750 + 20% of 750
= 750 + (20 × 750)/100
= 750 + 150
= Tk. 900

১,০৩১.

A sells an article to B at a profit of 10% B sells the article back to A at a loss of 10%. In this transaction:

ক
A makes a profit of 20%
খ
B loses 20%
গ
A makes a profit of 11%
ঘ
A neither losses nor gains

ব্যাখ্যা

It could be easily shown by net percentage change graphic.
100(A) = 10%(Profit) ⇒110(B) = 10%(Loss) ⇒ 99(A)
In this transaction
A makes a profit of (110 - 99 = 11%) 11%
[10% on selling to B and 1% profit on buying back from B]

১,০৩২.

As the price of mango has reduced 20%, it is now possible to buy 2 more mangoes at Tk.12. What is the current price of 100 mangoes?

ক
ক) Tk.120
খ
খ) Tk.50
গ
গ) Tk.230
ঘ
ঘ) Tk.140

ব্যাখ্যা

Question: As the price of mango has reduced 20%, it is now possible to buy 2 more mangoes at Tk.12. What is the current price of 100 mangoes?

Solution:
ধরি,
1টি আমের পূর্বমূল্য = x টাকা
20% কমে
1টি আমের বর্তমানমূল্য = x - x এর 20%
= x - 20x /100
= 80x/100
= 0.8x

প্রশ্নমতে,
(12/0.8x) - (12/x) = 2
(15/x) - (12/x) = 2
(15 - 12)/x = 2
3/x = 2
2x = 3
x = 3/2
x = 1.5

1টি আমের বর্তমানমূল্য = 1.5 × 0.8 = 1.2 টাকা
100 টি আমের বর্তমানমূল্য = 1.2 × 100 টাকা
= 120 টাকা

১,০৩৩.

After decreasing 24% in the price of an article the discounted price becomes $912. Find the actual price of the article?

ক
ক) 1400
খ
খ) 1300
গ
গ) 1200
ঘ
ঘ) 1100

ব্যাখ্যা

Let the products actual price be x
ATQ, 76% of x = 912
Or, 76x/100 = 912
Or, x = (912 × 100) / 76
= 1200

১,০৩৪.

Jashim buys 10 CDs for BDT. 200. If DVDs cost BDT 20 more, how many DVDs can he buy for the same amount?

ক
ক) 4
খ
খ) 5
গ
গ) 6
ঘ
ঘ) 10

ব্যাখ্যা

Cost of a CD = 200/10 = 20
And, cost of a DVD = 20 + 20 = 40
∴ Number of DVD = 200/40 = 5

১,০৩৫.

A vendor bought toffees at 6 for a Taka. How many for a Taka must he sell to gain 20%?

ক
ক) 3
খ
খ) 4
গ
গ) 5
ঘ
ঘ) 6

ব্যাখ্যা

প্রশ্ন: A vendor bought toffees at 6 for a Taka. How many for a Taka must he sell to gain 20%?

সমাধান:
৬টি টফির ক্রয় মূল্য ১ টাকা

২০% লাভে,
ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য ১২০ টাকা
∴ ক্রয়মূল্য ১ টাকা হলে বিক্রয়মূল্য ১২০/১০০ টাকা
= ১.২ টাকা

১.২ টাকায় বিক্রয় হয় ৬টি
∴ ১ টাকায় বিক্রয় হয় ৬/১.২টি
= ৫টি

১,০৩৬.

If the cost price of an article is 80% of its selling price. Then find the profit%?

ক
ক) 20%
খ
খ) 25%
গ
গ) 30%
ঘ
ঘ) 50%

ব্যাখ্যা

Question: If the cost price of an article is 80% of its selling price. Then find the profit%?

Solution:
ধরি,
বিক্রয়মূল্য = ১০০ টাকা
ক্রয়মূল্য = ১০০ এর ৮০%
= ৮০ টাকা
লাভ = ১০০ - ৮০ = ২০ টাকা

শতকরা লাভ = {(২০/৮০) × ১০০}% = ২৫%

১,০৩৭.

Hemal bought a chair for Tk. 1540 and sold it to Tofail. If Hemal earned a profit of 25%, find the selling price of chair.

ক
Tk. 1875
খ
Tk. 1900
গ
Tk. 1925
ঘ
Tk. 1950

ব্যাখ্যা

Question: Hemal bought a chair for Tk. 1540 and sold it to Tofail. If Hemal earned a profit of 25%, find the selling price of chair.

Solution:
Cost Price of the chair = Tk. 1540
S.P. of the chair =?
Profit earned = 25%

∴ Selling Price = 1540 + 25% of 1540
= 1540 + (25 × 1540)/100
= 1540 + 385
= 1925

১,০৩৮.

Which number is 40% less than 90?

ক
ক) 60
খ
খ) 54
গ
গ) 52
ঘ
ঘ) 36

ব্যাখ্যা

প্রশ্ন: Which number is 40% less than 90?

সমাধান:
৯০ এর ৪০% কম যে সংখ্যাটি তা ৯০ এর ৬০% হবে।

∴ সংখ্যাটি = ৯০ এর ৬০/১০০
= ৫৪

১,০৩৯.

If an article is sold at 200 percent profit, then the ratio of its cost price to its selling price will be -

ক
ক) 1 : 3
খ
খ) 2 : 3
গ
গ) 1 : 2
ঘ
ঘ) 2 : 1

ব্যাখ্যা

Let
Cost price = Tk. 100
Sell price = 100 + 200% of 100
= 100 + (100 × 200)/100
= 100 + 200
= Tk. 300

Required ratio = 100 : 300 = 1 : 3

১,০৪০.

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

ক
210%
খ
110%
গ
100%
ঘ
50%

ব্যাখ্যা

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

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

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

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

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

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

১,০৪১.

A and B share profits in the ratio 2 : 3. If 20% of the total profit is given to charity and B's share is Tk. 4800, find the total profit.

ক
Tk. 8500
খ
Tk. 9000
গ
Tk. 10000
ঘ
Tk. 12000

ব্যাখ্যা

Question: A and B share profits in the ratio 2 : 3. If 20% of the total profit is given to charity and B's share is Tk. 4800, find the total profit.

Solution:
ধরি, মোট লাভ = Tk. x
20% দাতব্য প্রতিষ্ঠানে দেওয়ার পর বাকি থাকে = 100% - 20% = 80% of x
= 80x/100
A এবং B এর লাভের অনুপাত 2 : 3।
অর্থাৎ, B এর অংশ = 80x/100 এর 3/(2 + 3)
= 80x/100 এর 3/5

প্রশ্নমতে,
80x/100 × (3/5) = 4800
⇒ 4x/5 × (3/5) = 4800
⇒ 12x = 4800 × 25
⇒ x = 120000/12
⇒ x = 10000
সুতরাং, মোট লাভ হলো Tk. 10000।

১,০৪২.

Fahim sold a t-shirt for Tk. 810 and made a gain of 8%. What was the purchase price of the t-shirt?

ক
750 Tk.
খ
820 Tk.
গ
850 Tk.
ঘ
710 Tk.

ব্যাখ্যা

Question: Fahim sold a t-shirt for Tk. 810 and made a gain of 8%. What was the purchase price of the t-shirt?

Solution:
8% লাভে,
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য = 100 + 8 = 108 টাকা

বিক্রয়মূল্য 108 টাকা হলে ক্রয়মূল্য = 100 টাকা
বিক্রয়মূল্য 1 টাকা হলে ক্রয়মূল্য = 100 ÷ 108 টাকা
বিক্রয়মূল্য 810 টাকা হলে ক্রয়মূল্য = (100 × 810) ÷ 108 টাকা
= 750 টাকা

১,০৪৩.

In a store, shirts are sold for 25% less than the tag price. If a shirt costs Tk.480, what would be the tag price of the shirt to make a 25% profit on its cost?

ক
ক) 640
খ
খ) 720
গ
গ) 800
ঘ
ঘ) None

ব্যাখ্যা

No explanation added.

১,০৪৪.

An amount of Tk. 625 becomes Tk 1296 in 2 years if the interest is compounded half-yearly. What is the rate of compound interest?

ক
ক) 5%
খ
খ) 20%
গ
গ) 30%
ঘ
ঘ) 40%

ব্যাখ্যা

Question: An amount of tk.625 becomes Tk 1296 in 2 years if the interest is compounded half-yearly. What is the rate of compound interest?

solution:
let the rate be R%

Then,
625 {1 + R/(2 × 100)} ^{2 × 2} = 1296
⇒ (1 + R/200)⁴ = 1296/625
⇒ (1 + R/200)⁴ = (6/5)⁴
⇒ (1 + R/200) = 6/5
⇒ R/200 = 1/5
⇒ R = 40
∴ R = 40%

১,০৪৫.

Tanvir gets 20% more salary than Rakib. So, how much less salary does Rakib get than Tanvir?

ক
20%
খ
16.67%
গ
25%
ঘ
14.26%
ঙ
None of the above

ব্যাখ্যা

Question: Tanvir gets 20% more salary than Rakib. So, how much less salary does Rakib get than Tanvir?

Solution:
As Tanvir gets 20% more salary than Rakib
when, Rakib gets 100, Tanvir gets = (100 + 20% of 100)
= 120

120 of Tanvir's salary is 100 of Rakib's
100 of Tanvir's salary is {(100 × 100)/120} = 83.33

∴ Rakib gets (100 - 83.33) or, 16.67% less salary than Tanvir.

১,০৪৬.

A passenger paid 50% customs duty on accompanied baggage items. He paid another 20% sales tax on the total value of the items plus the custom duty paid. The total custom duty and sales tax is Tk. 350. what is the value of the item custom duty and sales tax?

ক
ক) Tk.400
খ
খ) Tk.450
গ
গ) Tk. 500
ঘ
ঘ) None of these

ব্যাখ্যা

Question: A passenger paid 50% customs duty on accompanied baggage items. He paid another 20% sales tax on the total value of the items plus the custom duty paid. The total custom duty and sales tax is Tk. 350. What is the value of the item custom duty and sales tax?

Solution:
ধরি,
পণ্যটির মূল্য = 100x টাকা
Customs duty = 100x এর 50%
= 100x এর 50/100
= 50x
Sales tax = 150x এর 20%
= 30x
Total custom duty and sales tax = 50x + 30x = 80x

প্রশ্নমতে,
80x = 350
x = 350/80
100x = (350 × 100)/80
= 437.5
পণ্যটির মূল্য = 437.50 টাকা

The value of the item custom duty and sales tax
= (437.5 + 350) টাকা
= 787.5 টাকা

অর্থাৎ, সঠিক উত্তর ঘ) none of these.

১,০৪৭.

A housewife saved Tk. 2.50 in buying n item on sale. If she spent Tk. 25 for the item, approximately how much percent she saved in the transaction?

ক
11%
খ
(100/11)%
গ
(113/11)%
ঘ
(123/11)%

ব্যাখ্যা

Question: A housewife saved Tk. 2.50 in buying n item on sale. If she spent Tk. 25 for the item, approximately how much percent she saved in the transaction?

Solution:
cost price = 25 + 2.5 = 27.5 taka

Approximate save = (2.5/27.5) × 100%
= (100/11)%

১,০৪৮.

In an examination 85% examinees passed in English. If total 75 examinees failed in English, then what is the total number of examinees?

ক
ক) 375
খ
খ) 500
গ
গ) 775
ঘ
ঘ) 600

ব্যাখ্যা

Question: In an examination 85% examinees passed in English. If total 75 examinees failed in English, then what is the total number of examinees?

Solution:
পরীক্ষায় পাশ করেছে = ৮৫%
ফেল করেছে = ১০০ - ৮৫
= ১৫%

মোট পরীক্ষার্থীর ১৫% = ৭৫
⇒ মোট পরীক্ষার্থী × ০.১৫ = ৭৫
∴ মোট পরীক্ষার্থী = ৭৫/০.১৫
= ৫০০ জন

১,০৪৯.

A shopkeeper sells his goods at a profit of 10%. If he had purchased it at 20% less and sells it at Tk. 10 more, he had a gain of 40%. Find the cost price of the goods.

ক
500
খ
600
গ
400
ঘ
200

ব্যাখ্যা

Question: A shopkeeper sells his goods at a profit of 10%. If he had purchased it at 20% less and sells it at Tk. 10 more, he had a gain of 40%. Find the cost price of the goods.

Solution:
Let the C.P of an article is 100.
ATQ,
S.P will be 110 ..............(1)
If he has purchased it at 20% less, the new C.P = 100 - 20= 80

If the C.P is 80, then he earns a profit of 40% and sells the article at Tk. 10 more than the previous price.
So, when he earns 40% on the new C.P then the profit = (40/100) × 80 = 32

That means if the C.P = 80, the S.P = 80 + 32 = 112 ............(2)

Compare equation 1 and 2, and we get,
The difference between S.P is = 2
But ATQ, it should be 10, i.e., multiple of 5
So, we need to multiply the actual value with 5 then we get actual cost price.
Hence, the C.P of the article is = 100 × 5 = 500

১,০৫০.

A retailer marked the price of a television at Taka 12000 and gave a discount of 15%. Calculate the selling price and the amount of discount.

ক
Taka 10200
খ
Taka 8000
গ
Taka 6000
ঘ
Taka 5800

ব্যাখ্যা

Question: A retailer marked the price of a television at Taka 12000 and gave a discount of 15%. Calculate the selling price and the amount of discount.

Solution:
Marked Price of the television = Taka 12000
Discount Percentage = 15%

∴ Discount Amount = Discount Percentage × Marked Price
= 15% × Taka 12000
= Taka 1800

∴ Selling Price = Marked Price - Discount Amount
= Taka 12000 - Taka 1800
= Taka 10200

১,০৫১.

A man deposits certain amount in his bank account. After a few days. he withdraws half of the money deposited and deposits Tk. 500 more. If he has a balance of Tk. 2000 in his bank account, find the amount deposited initially.

ক
Tk. 1500
খ
Tk. 2000
গ
Tk. 2500
ঘ
Tk. 3000

ব্যাখ্যা

Question: A man deposits certain amount in his bank account. After a few days. he withdraws half of the money deposited and deposits Tk. 500 more. If he has a balance of Tk. 2000 in his bank account, find the amount deposited initially.

Solution:
ধরি,
প্রথমে সে বিনিয়োগ করে ক টাকা

শর্তমতে,
ক - (ক/২) + ৫০০ = ২০০০
⇒ ক - (ক/২) = ১৫০০
⇒ ক/২ = ১৫০০
∴ ক = ৩০০০

১,০৫২.

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
Tk. 8
খ
Tk. 12
গ
Tk. 16
ঘ
Tk. 20

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 -

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

∴ Profit = Tk. (20 - x)

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

১,০৫৩.

A number reduced by 30% becomes 280. What percent should it be increased so that it becomes 500?

ক
35%
খ
20%
গ
25%
ঘ
30%

ব্যাখ্যা

Question: A number reduced by 30% becomes 280. What percent should it be increased so that it becomes 500?

Solution:
Let, the number be x

Now, x - 30% of x = 280
⇒ x - (30x/100) = 280
⇒ (100x - 30x)/100 = 280
⇒ 70x/100 = 280
⇒ 70x = (280 × 100)
⇒ x = (280 × 100)/70
⇒ x = 400

Required increase = 500 - 400 = 100
∴ Increase % = (100/400) × 100%
= 25%

১,০৫৪.

A fruit seller sells 20 apples for Tk. 900 and suffers a loss equal to the cost price of 5 apples. Find the cost price of one apple.

ক
Tk. 50
খ
Tk. 60
গ
Tk. 65
ঘ
Tk. 70

ব্যাখ্যা

Question: A fruit seller sells 20 apples for Tk. 900 and suffers a loss equal to the cost price of 5 apples. Find the cost price of one apple.

Solution:
Let,
cost price of 1 apple is = Tk. x
∴ cost price of 20 apples is = Tk. 20x
∴ cost price of 5 apples is = Tk. 5x

We know,
Cost price - Selling price = Loss
20x - 900 = 5x
⇒ 20x - 5x = 900
⇒ 15x = 900
⇒ x = 900/15
∴ x = 60

∴ Cost price of 1 apple is Tk. 60

১,০৫৫.

In an election between two candidates, 20% of the total votes cast were invalid. One candidate received 55% of the valid votes. If the total number of votes cast was 9,000, how many valid votes did the other candidate receive?

ক
3460
খ
3640
গ
3420
ঘ
3240
ঙ
None

ব্যাখ্যা

Question: In an election between two candidates, 20% of the total votes cast were invalid. One candidate received 55% of the valid votes. If the total number of votes cast was 9,000, how many valid votes did the other candidate receive?

Solution:
Number of valid votes = 80% of 9000 = 7200

Valid votes polled by other candidate = 45% of 7200
= (7200 × 45)/100
= 3240

১,০৫৬.

A bookstore purchased 120 textbooks for Taka 250 each and sold them at a profit of 15%. Calculate the total profit.

ক
6500
খ
4200
গ
3500
ঘ
4500

ব্যাখ্যা

Question: A bookstore purchased 120 textbooks for Taka 250 each and sold them at a profit of 15%. Calculate the total profit.

Solution:
Cost Price of 120 textbooks = 120 × Taka 250 = Taka 3,0000
Profit Percentage = 15%
Profit Amount = Profit Percentage × Cost Price = 15% × Taka 3,0000 = Taka 4500
Total Profit = Profit Amount = 4500

১,০৫৭.

The monthly income of a person was Tk. 13500 and his monthly expenditure was Tk. 9000. Next year, his income increased by 14% and his expenditure by 7%. Find the percentage increase in his savings.

ক
25%
খ
28%
গ
35%
ঘ
30%

ব্যাখ্যা

Question: The monthly income of a person was Tk. 13500 and his monthly expenditure was Tk. 9000. Next year, his income increased by 14% and his expenditure by 7%. Find the percentage increase in his savings.

Solution:
Savings before increased income = Tk. (13500 - 9000)
= Tk. 4500

Increased income = 114% of 13500 = Tk. (114/100) × 13500
= Tk. 15390

Increased expenditure = 107% of 9000 = Tk. (107/100) × 9000
= Tk. 9630

Saving after Increased income = Tk. (15390 - 9630) = Tk. 5760

Increased Savings = Tk. (5760 - 4500)
= Tk. 1260

∴ Increase % in savings = (1260/4500) × 100 %
= 28%

১,০৫৮.

If 5% is gained by selling an article for BDT 350 than selling it for BDT 340, the cost of the article is-

ক
ক) BDT 180
খ
খ) BDT 150
গ
গ) BDT 200
ঘ
ঘ) BDT 250

ব্যাখ্যা

Let, buying price is x Taka
ATQ, 5% of x = 350 - 340 = 10
⇒ x = (100 × 10) / 5
∴ x = 200

১,০৫৯.

Mr. Sihab sold two pipes at Tk. 120 each. Based on the cost, his profit on one of the pipes was 20% and his loss on the other was 20%. On the sale of the pipes, he_____.

ক
ক) Did not incur any net profit or loss
খ
খ) Lost 4 cents
গ
গ) Gained 4 cents
ঘ
ঘ) Lost 10 taka
ঙ
ঙ) None

ব্যাখ্যা

Question: Mr. Sihab sold two pipes at Tk. 120 each. Based on the cost, his profit on one of the pipes was 20% and his loss on the other was 20%. On the sale of the pipes, he_____.

Solution:
মনে করি, ক্রয়মূল্য = ১০০ টাকা
১ম ক্ষেত্রে, ২০% লাভে, বিক্রয়মূল্য ১২০ টাকা হলে ক্রয়মূল্য = ১০০ টাকা

২য় ক্ষেত্রে, ২০% ক্ষতিতে,

বিক্রয়মূল্য ৮০ টাকা হলে ক্রয়মূল্য = ১০০ টাকা
বিক্রয়মূল্য ১ টাকা হলে ক্রয়মূল্য = ১০০/৮০ টাকা
বিক্রয়মূল্য ১২০ টাকা হলে ক্রয়মূল্য = (১০০ × ১২০)/৮০ টাকা
= ১৫০ টাকা

মোট ক্রয়মূল্য = ১০০ + ১৫০ = ২৫০ টাকা
দুটি পাইপের বিক্রয়মূল্য = ১২০ × ২ = ২৪০ টাকা

ক্ষতি = ২৫০ - ২৪০ = ১০ টাকা

১,০৬০.

As the price of chocolate has decreased by 15%, 2 more chocolates are now available for tk 10 . What is the current price of 36 chocolates?

ক
21 tk
খ
23 tk
গ
26 tk
ঘ
27 tk

ব্যাখ্যা

প্রশ্ন: As the price of chocolate has decreased by 15%, 2 more chocolates are now available for tk 10 . What is the current price of 36 chocolates?

সমাধান:

১৫% কমায় ১০ টাকায় কমে = ১০ × (১৫/১০০) = ১.৫ টাকা

∴ ১.৫ টাকা কমায় ২ টি চকলেট বেশি পাওয়া যায়।

অর্থাৎ,

২টি চকলেটের বর্তমান মূল্য = ১.৫ টাকা

∴ ১টি চকলেটের বর্তমান মূল্য = ১.৫/২ টাকা

∴ ৩৬টি চকলেটের বর্তমান মূল্য = (১.৫/২) × ৩৬ টাকা

= ২৭ টাকা

১,০৬১.

A man spent 1/2 of his money and then lost 1/4 of the remainder. He was left with TK. 3,600. How much did he start with?

ক
ক) TK. 7200
খ
খ) TK. 8800
গ
গ) TK. 9600
ঘ
ঘ) TK. 10400

ব্যাখ্যা

Let,
he has TK. x
ATQ, x - x/2 - x/2×1/4 = 3600
or, x/2 - x/8 = 3600
or, (4x - x)/8 = 3600
∴ x = (3600×8)/3 = 9600

১,০৬২.

What is the profit of Tk. 650 in 6 years at the rate of profit Tk. 7.5 percent per annum?

ক
ক) Tk. 273.50
খ
খ) Tk. 292.50
গ
গ) Tk. 302.25
ঘ
ঘ) Tk. 283.50

ব্যাখ্যা

Required profit
= 6 × 650 × 7.5/100
= Tk. 292.50

১,০৬৩.

If the cost price is 25% of selling price, then what is the percentage of profit?

ক
ক) 300
খ
খ) 250
গ
গ) 180
ঘ
ঘ) 280

ব্যাখ্যা

ধরি,
বিক্রয়মূল্য = ১০০ টাকা
ক্রয়মূল্য = ১০০ এর ২৫%
= ২৫ টাকা
লাভ = ১০০ - ২৫ = ৭৫ টাকা

শতকরা লাভ = {(৭৫/২৫) × ১০০}% = ৩০০%

১,০৬৪.

A reduction of 20% in the price of sugar enables a housewife to purchase 6 kg more for 240 Taka. What is the original price per kg of sugar?

ক
8 Taka per kg
খ
10 Taka per kg
গ
12 Taka per kg
ঘ
6 Taka per kg

ব্যাখ্যা

Question: A reduction of 20% in the price of sugar enables a housewife to purchase 6 kg more for 240 Taka. What is the original price per kg of sugar?

Solution:
Reduction in the price of 20% amount of sugar will increase by 25%
It means, 25% = 6 Kg.

So, initially, total Sugar = 6 × 4 = 24 kg.

Thus, the original price of the sugar was = 240/24
= 10 Taka per kg.

১,০৬৫.

If 40% of a number is 120, what is 75% of the number?

ক
220
খ
275
গ
350
ঘ
420
ঙ
225

ব্যাখ্যা

Question: If 40% of a number is 120, what is 75% of the number?

Solution:
Let the number is x
Given that,
⇒ 40% of x =120
⇒ (40/100) × x = 120
⇒ x = (120 × 10)/4
⇒ x = 300

Now, find 75% of x,
75% of x = (75/100) × 300
= 225

১,০৬৬.

In a tournament, a player has a record of 40% wins, out of the number of games he has played so far which in turn is half of the total number of games he plays. What is the maximum percentage of the remaining games that the player can lose and still win 50% of all the games played?

ক
ক) 40%
খ
খ) 50%
গ
গ) 60%
ঘ
ঘ) 55%

ব্যাখ্যা

Question: In a tournament, a player has a record of 40% wins, out of the number of games he has played so far which in turn is half of the total number of games he plays. What is the maximum percentage of the remaining games that the player can lose and still win 50% of all the games played?

Solution:
Let the total number of games be 100
Number of games already played = 50
So, the remaining games to be played = 50

Games already lost = 60% of 50 = 30
Number of games that player can lose = 50% of 100 = 50

∴ Number of games that the player can still lose = (50 - 30) = 20

Hence, required percentage = (20 × 100)/50 = 40%

১,০৬৭.

A shopkeeper marks up his goods by 30% above the cost price. He then offers a discount of 10% on the marked price. What is the overall percentage profit?

ক
20%
খ
37%
গ
27%
ঘ
17%

ব্যাখ্যা

Question: A shopkeeper marks up his goods by 30% above the cost price. He then offers a discount of 10% on the marked price. What is the overall percentage profit?

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

Marked Price = 30% more than cost price
= 100 + 30
= Tk. 130

Discount = 10% of 130
= (10/100) × 130
= Tk. 13

Selling Price (SP) = 130 - 13 = Tk. 117

∴ Profit = SP - CP = 117 - 100 = Tk. 17

∴ Overall percentage profit = (profit / cost price) × 100%
= (17 / 100) × 100%
= 17%

১,০৬৮.

List price of an article at a showroom is 2000 taka and it is being sold at successive discount of 20% and 10%, what will be net selling price of it?

ক
1440 taka
খ
1240 taka
গ
1340 taka
ঘ
1140 taka
ঙ
1200 taka

ব্যাখ্যা

List price of an article = 2000 taka
After discount,
selling price = 2000 taka × 80% × 90% = 1440 taka

১,০৬৯.

If a man were to sell his bike for Tk. 67500, he would lose 25%. To gain 25% at what price should he sell it?

ক
Tk. 108500
খ
Tk. 110000
গ
Tk. 111800
ঘ
Tk. 112500

ব্যাখ্যা

Question: If a man were to sell his bike for Tk. 67500, he would lose 25%. To gain 25% at what price should he sell it?

Solution:
Let,
the cost price of the bike be x
Selling at Tk. 67,500 causes a 25% loss,

ATQ,
75% of cost price = 67500
⇒ cost price = 67500 ÷ 75%
⇒ cost price = 67500 ÷ (75/100)
⇒ cost price = {67500 × (100/75)}
∴ cost price = Tk. 90000

∴ To gain 25% he should sell it = (125/100) × 90000
= Tk. 112500

১,০৭০.

The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?

ক
ক) 50% increase
খ
খ) 25% increase
গ
গ) 50% decrease
ঘ
ঘ) 75% increase

ব্যাখ্যা

Let the original dimensions be x by y.
A₁ =xy
According to the question, new dimensions are x/2 and 3y
New area, A₂=3xy/2
A₁- A₂= xy/2
(A₁- A₂) / A₁= ( xy/2)/xy × 100% = 50% increase

১,০৭১.

A guy bought 10 pencils for Tk. 50 and sold them for Tk. 60. What is his gain in terms of percentage?

ক
20%
খ
10%
গ
12%
ঘ
5%

ব্যাখ্যা

Question: A guy bought 10 pencils for Tk. 50 and sold them for Tk. 60. What is his gain in terms of percentage?

Solution:
Profit = SP - CP = 60 - 50 = 10

Gain % = (Profit/CP) × 100% = (10/50) × 100% = 20%

১,০৭২.

If the price of the eraser is reduced by 25%, a person can buy 2 more erasers for a rupee. How many erasers are available for a rupee?

ক
6
খ
8
গ
10
ঘ
12
ঙ
None

ব্যাখ্যা

Question: If the price of the eraser is reduced by 25%, a person can buy 2 more erasers for a rupee. How many erasers are available for a rupee?

Solution:

Let 'p' be the erasers available for a rupee.

Reduced price = (75/100) × 1

= Tk. 3/4

Tk. 3/4 will fetch p erasers
Tk. 1 will fetch p × (4/3) erasers

Therefore,
4p/3 = p + 2
⇒ p = 6

১,০৭৩.

A hospital pharmacy charges $ 0.40 per fluidram of a certain medicine but allows a discount of 15 percent to Medicare patients. How much should the pharmacy charge a Medicare patient for 3 fluidounces of the medicine? (128 fluidrams = 16 fluidounces)

ক
$ 9.60
খ
$ 8.16
গ
$ 3.20
ঘ
$ 2.72

ব্যাখ্যা

Question: A hospital pharmacy charges $ 0.40 per fluidram of a certain medicine but allows a discount of 15 percent to Medicare patients. How much should the pharmacy charge a Medicare patient for 3 fluidounces of the medicine? (128 fluidrams = 16 fluidounces)

Solution:
16 fluidounces = 128 fluidrams
∴ 1 fluidounces = 128/16 fluidrams = 8 fluidrams
∴ 3 fluidounces = 3 × 8 = 24 fluidrams

Cost of 24 fluidrams = 24 × 0.40 = 9.6
Cost after 15% discount = 0.85 × 9.6 = 8.16

১,০৭৪.

100 oranges are bought at the rate of Tk. 350 and sold at the rate of Tk. 48 per dozen. The percentage of profit or loss is-

ক
ক) (100/7)% gain
খ
খ) (50/7)% loss
গ
গ) (80/7)% gain
ঘ
ঘ) (80/7)% loss

ব্যাখ্যা

Question: 100 oranges are bought at the rate of Tk. 350 and sold at the rate of Tk. 48 per dozen. The percentage of profit or loss is-

Solution:
C.P.of 1 orange = Tk.(350/100) = Tk.3.50
S.P.of 1 orange = Tk.(48/12 )= Tk. 4

Gain = Tk. (4 - 3.50) = Tk. 0.50
Gain% = {(0.50/3.50) × 100}% = (100/7)%

১,০৭৫.

Ahmed sold a T-shirt TK. 810 and gained 8%. How much did he purchase it for?

ক
ক) TK. 750
খ
খ) TK. 875
গ
গ) TK. 745
ঘ
ঘ) TK. 756

ব্যাখ্যা

ATQ, 108% = 810
Or, 100% = (100 × 810) / 108
= 750

১,০৭৬.

When a mobile is sold for Tk. 4250, the owner loses 15%. At what price must the mobile be sold to gain 15%?

ক
Tk. 6255
খ
Tk. 5750
গ
Tk. 5490
ঘ
Tk. 5060

ব্যাখ্যা

Question: When a mobile is sold for Tk. 4250, the owner loses 15%. At what price must the mobile be sold to gain 15%?

Solution:
Let,
the new S.P be Tk. x

ATQ,
85 : 4250 = 115 : x
⇒ 85/4250 = 115/x
⇒ 85x = 115 × 4250
⇒ x = (115 × 4250)/85
∴ x = 5750

১,০৭৭.

The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Tk. 4000. The total price of 12 chairs and 3 tables is:

ক
Tk.3000
খ
Tk.3200
গ
Tk.3600
ঘ
Tk.3900

ব্যাখ্যা

Let the cost of a chair and that of table be Rs. x and Rs. y respectively.
Then,10x = 4y or y = 5x/2
∴15x + 2y = 4000
⇒15x + 2 × 5x/2 = 4000
⇒20x = 4000
∴ x = 200
So, y = 5 × 200/2 = 500
Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Tk. (2400 + 1500) = Tk.3900

১,০৭৮.

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

ক
ক) 55
খ
খ) 50
গ
গ) 45
ঘ
ঘ) None

ব্যাখ্যা

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

Solution:
ধরি, ক্রয়মূল্য ১০০ টাকা
৩০% লাভে, বিক্রয়মূল্য = ১০০ + ৩০ টাকা
= ১৩০ টাকা

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

১০% লাভে,
ক্রয়মূল্য ৫০ টাকা হলে বিক্রয়মূল্য = ৫০ + ৫০ এর ১০%
= ৫০ + ৫
= ৫৫ টাকা

১,০৭৯.

একজন কর্মচারির বেতন ২০% বৃদ্ধির পর সাপ্তাহিক ১৮০ টাকা পেল। তার আগের সাপ্তাহিক বেতন কত ছিল?

ক
ক) ১৪৪ টাকা
খ
খ) ১৫০ টাকা
গ
গ) ১৬০ টাকা
ঘ
ঘ) ১৬৪ টাকা

ব্যাখ্যা

প্রশ্ন: একজন কর্মচারির বেতন ২০% বৃদ্ধির পর সাপ্তাহিক ১৮০ টাকা পেল। তার আগের সাপ্তাহিক বেতন কত ছিল?

সমাধান:
২০% বৃদ্ধিতে,
বর্তমান বেতন ১২০ টাকা হলে আগের বেতন ১০০ টাকা
বর্তমান বেতন ১৮০ টাকা হলে আগের বেতন (১০০ × ১৮০)/১২০ টাকা
= ১৫০ টাকা

১,০৮০.

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

ক
5
খ
0.05
গ
0.0005
ঘ
0.005

ব্যাখ্যা

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

Solution:
As we know,1% =1/100
Hence,
(1/2)% = (1/2) × (1/100)
= 1/200
= 0.005

১,০৮১.

If the salary of an employee is reduced by 20 percent for his late attendance and then increased by 20 percent on a pardon, how much does he loss?

ক
ক) 2%
খ
খ) 3%
গ
গ) 5%
ঘ
ঘ) 4%

ব্যাখ্যা

Question: If the salary of an employee is reduced by 20 percent for his late attendance and then increased by 20 percent on a pardon, how much does he loss?

Solution:
ধরি,
কর্মীর বেতন ছিল = 100 টাকা

20% হ্রাসে,
তার বর্তমান বেতন = 100 - 100 এর 20%
= 100 - 20
= 80 টাকা

আবার,
10% বৃদ্ধিতে,
তার বর্তমান বেতন = 80 + 80 এর 20%
= 80 + 16
= 96

তার মোটের উপর ক্ষতি = (100 - 96) = 4%

১,০৮২.

A company's profits have doubled for each of the last 5 years. If the total profits for the last 5 years were Tk. 62 lacs, what were the profits in the first year?

ক
Tk. 1,00,000
খ
Tk. 2,00,000
গ
Tk. 3,00,000
ঘ
Tk. 4,00,000
ঙ
Tk. 5,00,000

ব্যাখ্যা

Question: A company's profits have doubled for each of the last 5 years. If the total profits for the last 5 years were Tk. 62 lacs, what were the profits in the first year?

Solution:
ধরা যাক, প্রথম বছরের লাভ P টাকা। যেহেতু লাভ প্রতি বছর দ্বিগুণ হয়েছে,
সুতরাং, গত 5 বছরের লাভের পরিমাণ ছিল: P, 2P, 4P, 8P, এবং 16P।
প্রশ্ন অনুযায়ী, গত 5 বছরের মোট লাভ ছিল 62 লক্ষ টাকা।

∴ P + 2P + 4P + 8P + 16P = 62,00,000
⇒ 31P = 62,00,000
⇒ P = 62,00,000 / 31
⇒ P = 2,00,000
সুতরাং, প্রথম বছরে লাভ ছিল 2,00,000 টাকা।

১,০৮৩.

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

ক
33%
খ
37.5%
গ
40%
ঘ
42.5%

ব্যাখ্যা

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

Solution:
Let total marks = x

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

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

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

১,০৮৪.

The retail price of a pen is 40 taka. Asif got a discount of 25% over the retail price and he eventually saved taka 240 on his total purchase of the pens. How many pens did he buy?

ক
35 pens
খ
24 pens
গ
30 pens
ঘ
20 pens
ঙ
18 pens

ব্যাখ্যা

According to the question,
Retail price 40 Tk. (per pen).
20% discount = 40 × (25/100)
= 10 Tk.
অর্থ্যাৎ,
প্রতি pen এ save হয় = 10 Tk.
Total savings = 240 Tk.
∴ Number of pen = 240/10
= 24 pens.

১,০৮৫.

120 boys and 80 girls appeared in an examination. If 60% of the boys and 40% of the girls passed the examination, what is the percentage of candidates who failed in the examination?

ক
48%
খ
52%
গ
45%
ঘ
42%
ঙ
None of these

ব্যাখ্যা

Question: 120 boys and 80 girls appeared in an examination. If 60% of the boys and 40% of the girls passed the examination, what is the percentage of candidates who failed in the examination?

Solution:
Number of students failed = 40% of boys (120) + 60% of girls (80)
= (40 × 120)/100 + (60 × 80)/100
= 48 + 48
= 96

Total number of students = 120 + 80 = 200

∴ Percentage of candidates failed = (96/200) × 100
= 48%

১,০৮৬.

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

ক
ক) 52.30%
খ
খ) 35.00%
গ
গ) 34.48%
ঘ
ঘ) 30.00%

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%

১,০৮৭.

A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is:

ক
45 : 51
খ
45 : 56
গ
47 : 51
ঘ
47 : 56

ব্যাখ্যা

Question: A shopkeeper carns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is:

Solution:
let, marked price 100 tk

selling price 90 taka

cost price = 90/1.12

ratio = (90/1.12) : 100
= 90 : 112
= 45 : 56

১,০৮৮.

A person having bought goods for Tk. 400 sells half of it at a gain of 5%, at what gain % must he sell the remainder so as to gain 20% on the whole?

ক
ক) 30%
খ
খ) 32%
গ
গ) 34%
ঘ
ঘ) 35%
ঙ
ঙ) 39%

ব্যাখ্যা

To gain 20% on whole he must sell all good for,
Tk. 400 + 20% of 400 = 480
As he get 5% gain on half of the goods i.e. 200 + 5% of 200 = 210
So required balance = 480 - 210 = 270
He must gain Tk. 70 on rest Tk. 200
% gain on remainder goods = (70×100)/200
= 35%

১,০৮৯.

A certain amount of money earning simple interest becomes 7/5^th of the initial amount in 4 years. What is the interest rate?

ক
4%
খ
6%
গ
8%
ঘ
10%
ঙ
None of these

ব্যাখ্যা

Question: A certain amount of money earning simple interest becomes 7/5^th of the initial amount in 4 years. What is the interest rate?

Solution:
ধরি,
আসল P = 100 টাকা
মুনফা-আসল A = 100 এর 7/5
= 140 টাকা

মুনাফা I = 140 - 100 = 40 টাকা
সময় n = 4 বছর
মুনাফার হার r = ?

আমরা জানি,
I = Pnr
⇒ r = I/Pn
= (40 × 100)/(100 × 4)
= 10%

১,০৯০.

A souvenir vendor purchased 1,000 shirts for a special event at a price of Tk. 500 each. The vendor sold 600 of the shirts on the day of the event for Tk. 1200 each and 300 of the shirts in the week following the event for Tk. 400 each. The vendor was unable to sell the remaining shirts. What was the vendor's gross profit on the sale of these shirts?

ক
Tk. 100000
খ
Tk. 220000
গ
Tk. 270000
ঘ
Tk. 300000
ঙ
Tk. 340000

ব্যাখ্যা

Question: A souvenir vendor purchased 1,000 shirts for a special event at a price of Tk. 500 each. The vendor sold 600 of the shirts on the day of the event for Tk. 1200 each and 300 of the shirts in the week following the event for Tk. 400 each. The vendor was unable to sell the remaining shirts. What was the vendor's gross profit on the sale of these shirts?

Solution:
purchased 1000 shirts each for 500, we have a total cost of 500000

600 shirts were sold for 1200 each so 600 × 1200 = 720000

300 shirts were sold for 400 each so 300 × 400 = 120000

total revenue= 720000 + 120000 = 840000

∴ gross profit = 840000 - 500000 = 340000

১,০৯১.

10 pens costs Tk. 100 each. If half of the pens are sold at 10% loss then find at what price remaining each pen should be sold for making no loss and no profit.

ক
Tk. 110
খ
Tk. 112
গ
Tk. 120
ঘ
Tk. 90

ব্যাখ্যা

Question: 10 pens costs Tk. 100 each. If half of the pens are sold at 10% loss then find at what price remaining each pen should be sold for making no loss and no profit.

Solution:
Total cost price of 10 pens = 10 × 100 = Tk. 1000

Selling price of 1 pen = 100 - (100 × 10%) = Tk. 90
Hence, selling price of 5 pens = Tk. 450

Now, selling price of remaining 5 pens = 1000 - 450 = Tk. 550
Hence, selling price of 1 pen = Tk. 110

১,০৯২.

A person buys certain number of gems 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
5% gain
খ
3% gain
গ
4% loss
ঘ
None of the above is correct

ব্যাখ্যা

Question: A person buys certain number of gems 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:
The cost price of each gem is 20 per Tk. = Tk. 1/20
The price of each gem is 30 per Tk. = Tk. 1/30

∴ Average cost of gem = {(1/20) + (1/30)}/2
= (3 + 2)/(2 × 60)
= 5/120
= 1/24

The selling price of mixed gem = 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 a loss of 4%

১,০৯৩.

A shopkeeper purchased 70 kg of potatoes for Tk. 420 and sold the whole potatose at the rate of 7 tk per kg. What will be his gain percent?

ক
16.28%
খ
15%
গ
11.50%
ঘ
16.67%
ঙ
None of these

ব্যাখ্যা

Question: A shopkeeper purchased 70 kg of potatoes for Tk. 420 and sold the whole potatose at the rate of 7 tk per kg. What will be his gain percent?

Solution:
70 কেজি আলুর বিক্রয়মূল্য = (70 × 7) = 490 টাকা

∴ লাভ = 490 - 420 = 70

420 টাকা লাভ হয় = 70 টাকা
1 টাকা লাভ হয় = 70/420 টাকা
100 টাকা লাভ হয় = {(70 × 100)/420} টাকা
= 100/6
= 16.67 টাকা

১,০৯৪.

z% of z is the same as 10% of

ক
z³/10
খ
z²/10
গ
z⁵/10
ঘ
z^{- 2}/10
ঙ
None

ব্যাখ্যা

Question: z% of z is the same as 10% of

Solution:
Let z% of z = 10% of p
⇒ (z/100) × z = (10/100) × p
⇒ p = (z²/100) × 10
⇒ p = z²/10

১,০৯৫.

The price of raw materials has gone up by 15%, labor cost has also increased from 25% of the cost of raw material to 30% of the cost of raw material. By how much percentage should there be reduction in the usage of raw materials so as to keep the cost same?

ক
ক) 28%
খ
খ) 17%
গ
গ) 27%
ঘ
ঘ) 24%

ব্যাখ্যা

Let the initial cost of raw material be 100. So, initial labor cost was 25 and net cost was 125
Now,
15% increment in raw materials cost and labor cost has gone up to 30% from 25 %
So, Raw material cost = 115 And Labor cost = (115 × 30%) = 34.5
New net cost = 115 + 34.5 = 149.5
Difference of labor cost = 149.5 - 125 = 24.5
Price has to be reduced by = (24.5×100) / 149.5 = 16.387
∴ Price has to be reduced by approximately 17%

১,০৯৬.

A student bought a bag for Tk. 350 and later sold it for Tk. 400. Find the profit percentage he earned.

ক
17.29%
খ
14.29%
গ
16.57%
ঘ
11.11%

ব্যাখ্যা

Question: A student bought a bag for Tk. 350 and later sold it for Tk. 400. Find the profit percentage he earned.

Solution:
Here,
CP = 350, and SP = 400

As SP > CP,

∴ Profit = SP - CP = 400 - 350 = 50.

Profit% = (50/350) ×100%

=100/7 %
= 14.29%

১,০৯৭.

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

ক
ক) 116%
খ
খ) 166.66%
গ
গ) 60%
ঘ
ঘ) 100%

ব্যাখ্যা

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

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

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

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

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

১,০৯৮.

Discussing grocery rates with her husband, a wife says, Rice is 30% cheaper than wheat. Now, find out how much percent is the price of wheat more than that of rice?

ক
ক) 37.5%
খ
খ) 40.65%
গ
গ) 42.85%
ঘ
ঘ) 45%

ব্যাখ্যা

Suppose, 1 Kg Wheat = Tk. 100
So, 1 Kg Rice will be Tk. 100 - (30% of 100)
= 100 - 30
= Tk. 70

According to the question,
(100/70) × 100 = 142.85%
So, Wheat is 142.85% of Rice
⇒ It is (142.85 - 100)
= 42.85% more than that of Rice.

১,০৯৯.

(75% of 320) + (40% of 150) - ? = 170

ক
140
খ
130
গ
125
ঘ
120

ব্যাখ্যা

Question: (75% of 320) + (40% of 150) - ? = 170

Solution:
Let,
(75% of 320) + (40% of 150) - x = 170
⇒ {(75 × 320)/100} + {( 40 × 150)/100} - x = 170
⇒ 240 + 60 - x = 170
⇒ - x = 170 - 300
∴ x = 130

১,১০০.

Hamid, Jobayer and Sumon start a shop by investing Tk. 27,000. Tk. 72,000 and Tk. 81,000 respectively. At the end of the year, the profit was distributed among them and Sumon earned the share of Tk. 36,000. Find the total profit.

ক
Tk. 1,10,000
খ
Tk. 1,2,5000
গ
Tk. 98,000
ঘ
Tk. 80,000

ব্যাখ্যা

The ratio of shares of Hamid, Jobayer, and Sumon = Ratio of their investments
Hamid : Jobayer : Sumon = 27000 : 72000 : 81000 = 3 : 8 : 9

Given share of profit earned by Smith =Tk. 36,000
Total no. of shares = 3 + 8 + 9 = 20 shares
Sumon's share = 9/20
Let total profit = Tk. X
36000/X = 9/20
X = (36000 × 20)/9 = 80,000.