Percentage and Profit & Loss

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

১.

A teacher says, 15% of the first number is equal to 21% of the second number. So, 18% of the first number will be what percent of the second number?

ক
ক) 18%
খ
খ) 20%
গ
গ) 24%
ঘ
ঘ) 25.2%

ব্যাখ্যা

According to the question,
15% of 1st no. =21% of 2nd no.
1% of 1st no.= (21/15) % of 2nd no.
18% of 1st no.= {(21/15) × 18} % of 2nd no.
=25.2%

২.

Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:

ক
42, 33
খ
47, 38
গ
68, 59
ঘ
75, 66

ব্যাখ্যা

প্রশ্ন: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:

সমাধান:
ধরি,
একজন পায় ক নম্বর
অপরজন পায় ক + ৯ নম্বর

শর্তমতে,
ক + ৯ = (ক + ক + ৯) × (৫৬/১০০)
বা, ১০০(ক + ৯) = ৫৬(২ক +৯)
বা, ১০০ক + ৯০০ = ১১২ক + ৫০৪
বা, ১২ক = ৩৯৬
∴ ক = ৩৩

∴ একজন পায় ৩৩ নম্বর
অপরজন পায় ৩৩ + ৯ = ৪২ নম্বর

৩.

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

ক
4%
খ
6.69%
গ
10.02%
ঘ
8%

ব্যাখ্যা

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

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

let second discount is x%

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

৪.

Roni bought an old cycle for Tk. 1200 and spent Tk. 200 on its repair. He sold it for Tk. 1680. His profit percent is =?

ক
12%
খ
20%
গ
24%
ঘ
30%

ব্যাখ্যা

Question: Roni bought an old cycle for Tk. 1200 and spent Tk. 200 on its repair. He sold it for Tk. 1680. His profit percent is =?

Solution:
Total cost = 1200 + 200 taka
= 1400 taka

profit = 1680 - 1400
= 280 taka

%profit = (280/1400) × 100%
= 20%

৫.

If a woman sells her table for Tk. 2,400, she loses 20%. To gain 20%, at what price should she sell it?

ক
Tk. 3000
খ
Tk. 3400
গ
Tk. 3600
ঘ
Tk. 4000

ব্যাখ্যা

Question: If a woman sells her table for Tk. 2,400, she loses 20%. To gain 20%, at what price should she sell it?

Solution:
Let the Cost price of the Table is x.
Selling price = x - 20% of x
⇒ 2400 = x - (20x/100)
⇒ 2400 = 80x/100
⇒ 80x = 240000
∴ x = 3000

To gain 20% = 3000 + 20% of 3000
= 3000 + 600
= Tk. 3600

To gain 20%, she should sell the table for Tk. 3600.

৬.

If both the length and the breadth of a rectangle are increased by 20%, what is the percentage increase in its area?

ক
22%
খ
44%
গ
33%
ঘ
38%

ব্যাখ্যা

Question: If both the length and the breadth of a rectangle are increased by 20%, what is the percentage increase in its area?

Solution:
মনে করি,
দৈর্ঘ্য = x একক এবং
প্রস্থ = y একক
∴ ক্ষেত্রফল = xy বর্গ একক

২০% বৃদ্ধিতে,
নতুন দৈর্ঘ্য = x + x এর ২০%
= ১২x /১০ একক

২০% বৃদ্ধিতে,
প্রস্থ = y + y এর ২০%
= ১২y /১০ একক

∴ নতুন ক্ষেত্রফল = (১২x/১০) ×( ১২y/১০) = ১৪৪xy/১০০ বর্গ একক

∴ ক্ষেত্রফল বৃদ্ধি =১৪৪xy/১০০ - xy
=(১৪৪xy - ১০০xy)/১০০
= ৪৪xy/১০০
∴ শতকরা ক্ষেত্রফল বৃদ্ধি = {(৪৪xy/১০০) × (১/xy) × ১০০}%
= ৪৪%

৭.

In an election 2 candidates participate, 20% of the votes are declared invalid, and the winner gets 70% of the valid votes and wins the election by 3200 votes. Find the valid votes.

ক
10000
খ
8000
গ
5620
ঘ
12000

ব্যাখ্যা

Question: In an election 2 candidates participate, 20% of the votes are declared invalid, and the winner gets 70% of the valid votes and wins the election by 3200 votes. Find the valid votes.

Solution:
Let total votes = 100
Then, 80 votes are valid only.
As per question, the winner gets = 80 × (70/100) = 56 (valid votes),
So, the loser's votes = 80 - 56 = 24
Difference = 56 - 24 = 32, but ATQ, it is 3200
i.e., 32 × 100 = 3200
Hence 80 × 100= 8000
So, we have to multiply 32 by 100 to make it equal to 3200.
So, 80 is also multiplied with 100.
Therefore, the total valid votes = 80 × 100= 8000

৮.

By selling 100 notebooks, a shopkeeper gains the selling price of 20 notebooks. What is his gain percentage?

ক
15%
খ
20%
গ
25%
ঘ
10%

ব্যাখ্যা

Question: By selling 100 notebooks, a shopkeeper gains the selling price of 20 notebooks. What is his gain percentage?

Solution:

Let the SP of 1 notebook be Tk. 1

SP of 100 notebooks = Tk. 100

Now,
gain = selling price of 20 notebooks = Tk. 20

Then
CP = SP - Gain = 100 - 20 = 80

Gain% = (20/80) × 100% = 25%

৯.

If 25% of a = b, then b% of 16 is equal to- ?

ক
2% of a
খ
8% of a
গ
6% of a
ঘ
4% of a

ব্যাখ্যা

Question: If 25% of a = b, then b% of 16 is equal to- ?

Solution:
Given that,
⇒ 25% of a = b
⇒ (25/100) × a = b
⇒ a/4 = b
∴ b = a/4

Now,
b% of 16
= (b/100) × 16
= (a/4) × (16/100)
= 4a/100
= 4% of a

১০.

A dishonest dealer sells the goods at 6(1/4)% loss on cost price but uses 12(1/2)% less weight. What is the percentage profit or loss?

ক
7(1/2)%
খ
7(5/7)%
গ
7(1/7)%
ঘ
7(2/5)%

ব্যাখ্যা

Let, the C.P (cost price) of 1 kg goods be 1 tk
Then, S.P. of ⟮100 - (25/2%) of 1 kg} i.e., g 875 g goods = .9375 tk
S.P of 1 kg goods = (.9375/875 × 1000) tk = 1 (1/14) tk
& there4; Profit % = (1/14 × 100)% = 7(1/7)%
Answer : 7(1/7)%

১১.

Salman bought 1600 eggs at Tk. 3.75 a dozen. He sold 900 of them at 2 for Tk.1 and the remaining at 5 for Tk. 2. His percent gain or loss is-

ক
ক) 26% gain
খ
খ) 46% gain
গ
গ) 36% loss
ঘ
ঘ) 16% loss

ব্যাখ্যা

C. P of 1600 eggs =Tk. (3.75/12) × 1600
= Tk. 500
S. P of 1600 eggs =Tk. {(1/2) × 900 + (2/5) × 700}
= Tk. (450 + 280)
= Tk. 730

Gain = Tk. (730 - 500)
= TK.230
Gain% = {(230/500) × 100}% = 46%

১২.

The cost price of a product is 64% of the market price. How much is the gain in percent if the product is sold allowing a discount of 12%

ক
ক) 37.5%
খ
খ) 38.5%
গ
গ) 42.5%
ঘ
ঘ) 27.5%

ব্যাখ্যা

Question: The cost price of a product is 64% of the market price. How much is the gain in percent if the product is sold allowing a discount of 12%

Solution:
ধরি
পণ্যটির তালিকামূল্য 100 টাকা
পণ্যটির ক্রয়মূল্য = 64 টাকা
12% হ্রাসে
পণ্যটির মূল্য = (100 - 12) টাকা = 88 টাকা
লাভ = 88 - 64 = 24 টাকা
শতকরা লাভ = {(24/64) × 100%}
= 37.5%

১৩.

A vendor buys mangoes at a score for Tk. 300 and retails them at a dozen for Tk. 240. Did he gain or lose in the transaction, and what percentage was his gain or loss?

ক
27.67% loss
খ
27.67% gain
গ
33.33% loss
ঘ
33.33% gain

ব্যাখ্যা

Question: A vendor buys mangoes at a score for Tk. 300 and retails them at a dozen for Tk. 240. Did he gain or lose in the transaction, and what percentage was his gain or loss?

Solution:
Cost Price (C.P) of 1 mango = Tk. 300/score
= 300/20 = 15 (Note: 1 score = 20)

Selling Price (S.P) of 1 mango = Tk. 240/dozen
= 240/12
= 20

∴ Profit on 1 mango = 20 - 15 = 5

∴ % Profit = (5/15) × 100 % = 33.33%

১৪.

Some articles were bought at 6 articles for TK. 5 and sold at 5 articles for Tk. 6. Gain percent is:

ক
ক) 20%
খ
খ) 30%
গ
গ) 33.33%
ঘ
ঘ) 35%
ঙ
ঙ) 44%

ব্যাখ্যা

Suppose, number of articles bought = L.C.M. of 6 and 5 = 30.
C.P. of 30 articles = TK.(5/6)x 30 = Tk. 25.
S.P. of 30 articles = Tk. (6/5)x 30 = Tk. 36.
Gain % = (11/25)x 100 = 44%.

১৫.

The price of cooking oil is reduced by 10%. A family buys 4 litres more for Tk. 720 after the reduction. What was the original price per litre?

ক
45 Tk/litre.
খ
40 Tk/litre.
গ
20 Tk/litre.
ঘ
35 Tk/litre.

ব্যাখ্যা

Question: The price of cooking oil is reduced by 10%. A family buys 4 litres more for Tk. 720 after the reduction. What was the original price per litre?

Solution:
Let
Original price of cooking oil = x Tk/litre.
Original quantity = 720/x litre

New price = 0.90x Tk/litre
New quantity = 720/0.90x = 720/(9x/10) = (720 × 10)/9x = 800/x litre

ATQ,
(800/x) - (720/x) = 4
⇒ (800 - 720)/x = 4
⇒ 80/x = 4
⇒ x = 80/4
∴ x = 20

∴ Original price of cooking oil = 20 Tk/litre.

১৬.

Selling price of first article is Tk. 960 and cost price of second article is Tk. 960. If there is a profit of 20% on first article and loss of 20% on second article, then, what will be the total loss?

ক
ক) Tk. 38
খ
খ) Tk. 36
গ
গ) Tk. 34
ঘ
ঘ) Tk. 32

ব্যাখ্যা

SP of first article = Tk. 960
CP of 2nd article = Tk.960
Profit on first article = 20%
Loss on 2nd article = 20%

After profit of 20%, CP of first article = 960 × (100/120)
= Tk. 800
After loss of 20%, SP of 2nd article = 960 × (80/100)
=Tk. 768
Total CP of both article = 800 + 960 = Tk.1760
Total SP of both article = 960 + 768 = Tk.1728

∴ Total loss = 1760 – 1728 = Tk. 32

১৭.

Abir and Babul invest in a business in the ratio 5 : 4. If 10% of the total profit goes to charity and abir’s share is Tk 945, the total profit is -

ক
1500 tk
খ
2100 tk
গ
1890 tk
ঘ
2400 tk

ব্যাখ্যা

Question: Abir and Babul invest in a business in the ratio 5 : 4. If 10% of the total profit goes to charity and abir’s share is Tk 945, the total profit is -

Solution:
Let,
The total profit = 100 tk

After paying 10% to charity,
Abir’s share = 90 × (5/9)
= 50 tk

Now,
If abir’s share is tk 50, total profit = 100 tk
If abir’s share is tk 1, total profit = 100/50 tk
If abir’s share is tk 945, total profit = (100/50) × 945
= 1890 tk

So, the total profit is 1890 tk.

১৮.

There is a shopkeeper whose claim is that he sells a certain product at a cost of Tk 23/kg, which actually costs him Tk 25/kg. The shopkeeper says that he is taking the loss to let his customers get a better deal. When examined thoroughly, the constabulary find that the shopkeeper is actually using an 800 gms weight in place of a 1 kg weight. How much does he gain or lose?

ক
10% loss
খ
15% profit
গ
20% loss
ঘ
12.5% profit

ব্যাখ্যা

Question: There is a shopkeeper whose claim is that he sells a certain product at a cost of Tk 23/kg, which actually costs him Tk 25/kg. The shopkeeper says that he is taking the loss to let his customers get a better deal. When examined thoroughly, the constabulary find that the shopkeeper is actually using an 800 gms weight in place of a 1 kg weight. How much does he gain or lose?

Solution:
Selling price of 0.8 kg = 23 taka

Now,
Selling price of 1 kg = 23/0.8 taka
= 115/4 taka
= 28.75 taka

∴ Percentage profit = {(28.75 - 25)/25} × 100%
= (3.75/25) × 100%
= 15%

১৯.

A dealer has 1000 kg sugar and he sells a part of it at 8% profit and the rest of it at 18% profit. The overall profit he earns is 14%. What is the quantity which is sold at 18% profit?

ক
ক) 250 kg
খ
খ) 600 kg
গ
গ) 620 kg
ঘ
ঘ) 400 kg

ব্যাখ্যা

The basic formula which is used to find the ratio in which the ingredients are mixed is :

As per the rule of Allegation,

Quantity of Cheaper : Quantity of Dearer = (18-14) : (14-8) = 4:6 = 2:3
Quantity of sugar sold at 18% profit = 3/5 × 1000 = 600kg

২০.

An uneducated retailer marks all his goods at 50% above the cost price and thinking that he will still make 25% profit, offers a discount of 25% on the marked price. What is his actual profit on the sales?

ক
10%
খ
12.5%
গ
15.8%
ঘ
20%

ব্যাখ্যা

Question: An uneducated retailer marks all his goods at 50% above the cost price and thinking that he will still make 25% profit, offers a discount of 25% on the marked price. What is his actual profit on the sales?

Solution:
Let, cost price is 100 taka

After 50% increase = 100 + 100 × .5
= 150 taka

25% discounted price = 150 - 150 × .25
= 112.5 taka

Actual profit percentage = (112.5 - 100) × 100%/100
= 12.5%

২১.

Which number is 60% less than 80?

ক
30
খ
32
গ
35
ঘ
40

ব্যাখ্যা

Question: Which number is 60% less than 80?

Solution:
let, the number is x

x = 80 - 80 × . 6
= 80 - 48
= 32

২২.

40% of 265 + 35% of 180 = 50% of ?

ক
238
খ
300
গ
338
ঘ
454

ব্যাখ্যা

Question: 40% of 265 + 35% of 180 = 50% of ?

Solution:
40% of 265 + 35% of 180 = 50% of x
⇒ (265 × 40)/100 + (35 × 180)/100 = x/2
⇒ 106 + 63 = x/2
⇒ 169 = x/2
∴ x = 338

২৩.

On increasing the price of tickets for a show by 20 % the audience decreases by 30%. What is the effect on revenue?

ক
16% increase
খ
16% decrease
গ
4% increase
ঘ
4% decrease

ব্যাখ্যা

Question: On increasing the price of tickets for a show by 20 % the audience decreases by 30%. What is the effect on revenue?

Solution:
Effect on revenue
= percent increase - percent decrease - (percent increase × percent decrease)/100
= 20 - 30 - (20 × 30)/100
= - 10 - 600/100
= -10 - 6
= - 16 %

'-' sign shows decrease in revenue.

২৪.

The total population of a city is 6500.The number of males and females increases by 5% and 10% respectively and consequently the population becomes 7000. Find the number of males in the village.

ক
ক) 4000
খ
খ) 3000
গ
গ) 3500
ঘ
ঘ) 2950

ব্যাখ্যা

We are given that,
1) Total population of city = 6500
2) Increase in male and female population = 5% & 10% respectively.
3) Final population of city = 7000

Hence,
Let’s assume that number of males = x
Number of female = 6500 – x

Therefore, after an increase in 5% male and 10% female, the population becomes 7000
5% male +10% female = Difference between new and original population
⇒ (5/100)x + (10/100) (6500 - x) = 7000 - 6500
⇒ 5x + 65000 - 10x = 50000
⇒ 5x = 15000
⇒ x = 3000

Number of males = 3000
Number of females = 3500.

২৫.

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

ক
10%
খ
15%
গ
18%
ঘ
20%

ব্যাখ্যা

Numbers from 1 to 70 has 1 or 9 in the unit digits
= 1, 9, 11, 19, 21, 29, 31, 39, 41, 49
= 10 Numbers

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

২৬.

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
7560
খ
8900
গ
9160
ঘ
9250
ঙ
None

ব্যাখ্যা

Question: 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?

Solution:
Winner gets 65% of 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

২৭.

The income of ‘A’ is 20% higher than that of ‘B’. The income of ‘B’ is 25% less than of ‘C’. What percent less is A’s income from C’s income?

ক
ক) 7%
খ
খ) 8%
গ
গ) 9%
ঘ
ঘ) 10%

ব্যাখ্যা

Let,
C's income = 100
So, B's income = 100-25 = 75
And,
A's income = 75 + 75×(20/100) = 75+15 = 90
∴ A’s income less from C’s income is = {(100 - 90)/100}×100 = 10%

২৮.

A fruit salad is made by mixing 3 kgs of mango costing Tk 120 per kg and 2 kgs of papaya costing Tk 100 per kg and 2 kgs of grapes costing Tk 140 per kg. At what price (in Taka) per kg should the mixture be sold to make profit of 25 percent?

ক
125
খ
150
গ
175
ঘ
None of these

ব্যাখ্যা

Question: A fruit salad is made by mixing 3 kgs of mango costing Tk 120 per kg and 2 kgs of papaya costing Tk 100 per kg and 2 kgs of grapes costing Tk 140 per kg. At what price (in Taka) per kg should the mixture be sold to make profit of 25 percent?

Solution:
3 কেজি আমের মূল্য = 120 × 3 = 360 টাকা
2 কেজি পেঁপের মূল্য = 100 × 2 = 200 টাকা
2 কেজি আঙ্গুরের মূল্য = 140 × 2 = 280 টাকা

মোট = 360 + 200 + 280 = 840 টাকা

25% লাভে
বিক্রয়মূল্য = 840 + 840 এর 25%
= 840 + 840 এর 25/100
= 840 + 210
= 1,050

7 কেজি বিক্রয় করতে হবে = 1050 টাকা
1 কেজি বিক্রয় করতে হবে = 1050/7 টাকা
= 150 টাকা

২৯.

A book was sold for Tk. 144. If the percentage of profit was numerically equal to the cost price, the cost of the clock was -

ক
Tk. 60
খ
Tk. 70
গ
Tk. 80
ঘ
Tk. 100

ব্যাখ্যা

Question: A book was sold for Tk. 144. If the percentage of profit was numerically equal to the cost price, the cost of the clock was -

Solution:
Let, the percentage of profit be x%
cost of the clock was x taka.

x + x × x/100 = 144
⇒ x + (x²/100) = 144
⇒ (x² + 100x) = 14400
⇒ x²+ 100x - 14400 = 0
⇒ x²+ 180x - 80x - 14400 = 0
⇒ x(x + 180) - 80 (x + 180) = 0
⇒ (x + 180) (x - 80) = 0
∴ x = 80

৩০.

A book was sold at a loss of 15%. If the selling price had been increased by 75 Taka, there would have been a profit of 10%. What is the cost price of the book?

ক
Tk. 350
খ
Tk. 300
গ
Tk. 280
ঘ
Tk. 400
ঙ
None of these

ব্যাখ্যা

Question: A book was sold at a loss of 15%. If the selling price had been increased by 75 Taka, there would have been a profit of 10%. What is the cost price of the book?

Solution:
ধরি,
বইটির ক্রয়মূল্য ১০০ টাকা হলে,

১৫% ক্ষতিতে বিক্রয়মূল্য = (১০০ - ১৫) টাকা = ৮৫ টাকা
১০% লাভে বিক্রয়মূল্য = (১০০ + ১০) টাকা = ১১০ টাকা

∴ বিক্রয়মূল্যের পার্থক্য = (১১০ - ৮৫) = ২৫ টাকা

এখন,
বিক্রয়মূল্যের পার্থক্য ২৫ টাকা হলে ক্রয়মূল্য = ১০০ টাকা
∴ বিক্রয়মূল্যের পার্থক্য ১ টাকা হলে ক্রয়মূল্য = ১০০/২৫ টাকা
∴ বিক্রয়মূল্যের পার্থক্য ৭৫ টাকা হলে ক্রয়মূল্য = (১০০ × ৭৫)/২৫ টাকা
= ৩০০ টাকা

∴ বইটির ক্রয়মূল্য = ৩০০ টাকা।

৩১.

The price of a loaf of bread was increased by 20%. How many that used to buy 300 loaves?

ক
ক) 240
খ
খ) 250
গ
গ) 280
ঘ
ঘ) 320

ব্যাখ্যা

Let the price of one loaf of bread is 100x
So, price of 300 loaves of bread is 30000x

At 20% increase,
Price of one loaf of bread is 120x
So, with 30000x taka = 30000x/120x = 250 loaves of bread can be purchased

৩২.

The ratio of the cost price and selling price is 5 : 4, the loss percent is =?

ক
20%
খ
22%
গ
25%
ঘ
30%

ব্যাখ্যা

Question: The ratio of the cost price and selling price is 5 : 4, the loss percent is =?

Solution:
let, cost price 5x
selling price 4x taka

loss = {(5x - 4x)/5x} × 100%
= (1/5) × 100%
= 20%

৩৩.

A merchant sells one table for Tk. 1200, making a profit of 25%, and another table for Tk. 1500, incurring a loss of 10%. What is his overall gain or loss percentage?

ক
3.14% gain
খ
2.78% gain
গ
4.82% loss
ঘ
1.73% loss
ঙ
None

ব্যাখ্যা

Question: A merchant sells one table for Tk. 1200, making a profit of 25%, and another table for Tk. 1500, incurring a loss of 10%. What is his overall gain or loss percentage?

Solution:
C.P. of 1st table = Tk.(100 × 1200)/125 = Tk. 960
C.P. of 2nd table = Tk.(100 × 1500)/90 = Tk. 1667
So, total C.P. = Tk.(960 + 1667) = Tk. 2627
Total S.P. = Tk.(1200 + 1500) = Tk. 2700

∴ Gain% = {(2700 - 2627) × 100}/2627%
= (73 × 100)/2627%
= 2.78%

৩৪.

A dishonest trader mixes 2 kg of vegetable ghee costing Tk. 45 a kg with 3 kg of standard ghee costing Tk. 70 per kg. He sells the mixed ghee at Tk. 65 per kg. What is his percentage of profit?

ক
ক) 16.67%
খ
খ) 8.33%
গ
গ) 6%
ঘ
ঘ) 21%

ব্যাখ্যা

Question: A dishonest trader mixes 2 kg of vegetable ghee costing Tk 45 a kg with 3 kg of standard ghee costing Tk. 70 per kg. He sells the mixed ghee at Tk. 65 per kg. What is his percentage of profit?

Solution:
2 কেজি Vegetable ঘি'র ক্রয়মূল্য = 2 × 45 = 90 টাকা
আবার, 3 কেজি Standard ঘি'র ক্রয়মূল্য
= (3 × 70) = 210 টাকা

∴ (2 + 3) = 5 কেজি ঘি'র মোট ক্রয়মূল্য = 90 + 210 = 300 টাকা।

আবার, 5 কেজি ঘি'র বিক্রয়মূল্য = 5 × 65 = 325 টাকা

∴ লাভ = (325 - 300) টাকা = 25 টাকা
300 টাকায় লাভ হয় 25 টাকা
100 টাকায় লাভ হয় (25 × 100)/300 টাকা
= 8.33%

৩৫.

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

ক
400%
খ
300%
গ
200%
ঘ
100%

ব্যাখ্যা

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

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

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

ATQ,
3(x - 100) = 2x - 100
⇒ 3x - 300 = 2x - 100
⇒ 3x - 2x = 300 - 100
∴ x = 200

Then the Profit = (200 - 100) = 100
Hence the profit percentage is = (100 × 100)/100 %
= 100%

৩৬.

A's savings and expenditures are in the ratio of 1 : 4. His income increases by 10 % and expenditure also increases by 15%. How much percent does his savings increase or decrease?

ক
ক) increased by 10%
খ
খ) increased by 12%
গ
গ) decreased by 10%
ঘ
ঘ) decreased by 12%

ব্যাখ্যা

Question: A's savings and expenditures are in the ratio of 1 : 4. His income increases by 10 % and expenditure also increases by 15%. How much percent does his savings increase or decrease?

Solution:
let A's savings = x
and expenditures = 4x

his total income = x + 4x = 5x

his increased income = 110% of 5x = 5.5x
his Increased expenditure = 115% of 4x = 4.6x
so, savings = 5.5x - 4.6x = 0.9x

now, decreased savings = x - 0.9x = 0.1x

∴ decreased % = (0.1 × 100)/1 = 10%

৩৭.

Bananas are bought at Tk. 36 per dozen and sold at a profit of 20%. How much is the selling price of twenty bananas?

ক
ক) Tk. 75
খ
খ) Tk. 72
গ
গ) Tk. 68
ঘ
ঘ) None of the Above

ব্যাখ্যা

Question: Bananas are bought at Tk. 36 per dozen and sold at a profit of 20%. How much is the selling price of twenty bananas?

Solution:
৩৬ টাকায় ক্রয় করে ১২ টি কলা
∴ ১ টাকায় ক্রয় করে ১২/৩৬ টি কলা
∴ ১০০ টাকায় ক্রয় করে (১২ × ১০০)/৩৬ টি কলা
= ১০০/৩ টি কলা

২০% লাভে বিক্রয়মূল্য = (১০০ + ২০) টাকা = ১২০ টাকা

২০% লাভ করতে হলে,
১০০/৩ টি কলার বিক্রয়মূল্য ১২০ টাকা
∴ ১ টি কলার বিক্রয়মূল্য (১২০ × ৩)/১০০ টাকা
∴ ২০ টি কলার বিক্রয়মূল্য (১২০ × ৩ × ২০)/১০০ টাকা
= ৭২ টাকা

৩৮.

In an election, the winning candidate secured 70% of the total votes and won by a majority of 60,000 votes. What is the total number of votes polled?

ক
145,000
খ
150,000
গ
155,000
ঘ
160,000

ব্যাখ্যা

Question: In an election, the winning candidate secured 70% of the total votes and won by a majority of 60,000 votes. What is the total number of votes polled?

Solution:
Let, The winning candidate secured 0.70x votes,
and the losing candidate secured 0.30x votes.

ATQ,
0.70x - 0.30x = 60,000
⇒ 0.40x = 60,000
⇒ x = 60,000 / 0.40
= 150,000

Thus, the total number of votes polled is 150,000.

৩৯.

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

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

ব্যাখ্যা

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

Therefore,
130 % of 125 % of 120 % of x = 50.50
⇒ (120/100) × (125/100) × (130/100) × x = 5050/100
⇒ (195/100) x = 5050/100
⇒ x = (5050 × 100)/(195 × 100)
⇒ x = 25.89

Cost price of shoes = Tk. 25.89.

৪০.

0.57 expressed as a percent of 3.8 is-

ক
15%
খ
30%
গ
40%
ঘ
None of the above

ব্যাখ্যা

Question: 0.57 expressed as a percent of 3.8 is-

Solution:
Required Percentage = (0.57 ×100)/3.8
= (57 × 100 × 10)/(38 × 100)
= 15%

৪১.

If one number is 20% smaller than another number, and that second number is 10% greater than 150, what is the value of the first number?

ক
133
খ
132
গ
152
ঘ
140.55
ঙ
None

ব্যাখ্যা

Question: If one number is 20% smaller than another number, and that second number is 10% greater than 150, what is the value of the first number?

Solution:
Let,
First number x
Second number y

ATQ,
y is 10% more than 150
⇒ y = 150 + [(150 × 10)/100]
= 165

and x is 20% less than y
⇒ x = 165 - [(165 × 20)/100]
= 165 - 33
= 132

∴ First number 132

৪২.

Three-eighth of 320 chairs was sold at a profit of Tk. 50 each and the rest for Tk. 33600. If the seller makes a profit of 20% on the whole transaction, what is the cost price of each of the chair?

ক
Tk. 150
খ
Tk. 175
গ
Tk. 120
ঘ
Tk. 125

ব্যাখ্যা

Question: Three-eighth of 320 chairs was sold at a profit of Tk. 50 each and the rest for Tk. 33600. If the seller makes a profit of 20% on the whole transaction, what is the cost price of each of the chair?

Solution:
Three-eighth of 320 = (320 × 3)/8 = 120

120 chairs were sold at a profit of Tk. 50 each.
Profit on these 120 chairs = 6000.

S.P. of all 320 chairs = (C.P. of 120 chairs + Profit on 120 chairs) + S.P. of 200 chairs
= (120 × C.P) + 6000 + 33600
= (120 × C.P.) + 39600

But these 320 chairs were sold at a profit of 20%.
∴ S. P. of 320 chair is = (120/100) ×(320 × C.P.) = 1.2 × 320 × C.P. = 384 × C.P.

Now,
384 × C.P = 120 × C. P. + 39600
⇒ 384 C.P. = 120 C.P. + 39600
⇒ 264 C.P. = 39600
⇒ C. P. = 150.

৪৩.

If the total payroll expense of a certain business in year Y was Tk. 84000, which was 20 percent more than in year X, what was the total payroll expense in year X?

ক
Tk. 70000
খ
Tk. 68320
গ
Tk. 64000
ঘ
Tk. 60000
ঙ
Tk. 52320

ব্যাখ্যা

Question: If the total payroll expense of a certain business in year Y was Tk. 84000, which was 20 percent more than in year X, what was the total payroll expense in year X?

Solution:
Total payroll expense in year Y was Tk. 84000, that is 20% more than year X = 120% of X

∴ 120% of X = 84000
⇒ (120/100) × X = 84000
⇒ X = (84000 × 100)/120
∴ X = 70000

৪৪.

A shopkeeper sold one item at a 15% profit and another item at a 5% loss. If the cost price of both items is the same, find the overall profit percent.

ক
6.5%
খ
6%
গ
8.2%
ঘ
5%

ব্যাখ্যা

Question: A shopkeeper sold one item at a 15% profit and another item at a 5% loss. If the cost price of both items is the same, find the overall profit percent.

Solution:
ধরি,
প্রতিটি দ্রব্যের ক্রয়মূল্য = x টাকা

15% লাভে,
একটি দ্রব্যের বিক্রয়মূল্য = x + 15% of x
= x + (15x/100)
= x + (3x/20)
= 23x/20 টাকা

5% ক্ষতিতে,
অপর দ্রব্যের বিক্রয়মূল্য = x - 5% of x
= x - (5x/100)
= x - (x/20)
= 19x/20 টাকা

মোট ক্রয়মূল্য = x + x = 2x টাকা
মোট বিক্রয়মূল্য = (23x/20 + 19x/20) টাকা
= 42x/20
= 21x/10 টাকা

∴ মোট লাভ = বিক্রয়মূল্য - ক্রয়মূল্য
= (21x/10) - 2x
= x/10 টাকা

∴ শতকরা লাভ = (লাভ/ক্রয়মূল্য) × 100%
= (x/10 ÷ 2x) × 100%
= (1/20) × 100%
= 5%

৪৫.

A is 6 times greater than B then by what percent is B smaller than A?

ক
83.33%
খ
85%
গ
89.33%
ঘ
72%
ঙ
None

ব্যাখ্যা

Question: A is 6 times greater than B then by what percent is B smaller than A?

Solution:

Let B = 10

Then, A = 10 + 60 = 70

∴ A - B = 70 - 10 = 60

B is 60 less than A.

∴ B, % less than A = (60/70) × 100 = 85.71%

৪৬.

Raktim sold a book at a loss of 30%. If he has sold it for Tk. 140 more, he would have made a profit of 40%. The cost price of the book is =?

ক
Tk. 180
খ
Tk. 200
গ
Tk. 220
ঘ
Tk. 250

ব্যাখ্যা

Question: Raktim sold a book at a loss of 30%. If he has sold it for Tk. 140 more, he would have made a profit of 40%. The cost price of the book is =?

Solution:
let, cost price of the book is x taka

selling price = 0.7x taka

ATQ,
.7x + 140 = 1.4x
⇒ 0.7x = 140
⇒ x = 140/0.7
= Tk. 200

৪৭.

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

ক
ক) 40
খ
খ) 50
গ
গ) 60
ঘ
ঘ) 30

ব্যাখ্যা

Number of students (passed) = 20×30% + 30×50% + 40×60%
= 6 + 15 + 24
= 45
Percentage of passed students of the entire school = 45/90 × 100 = 50%

৪৮.

The marked price of a radio is Tk. 480. The owner allows a discount of 10% and still earns the profit of 8%. If no discount is allowed, find his gain percent?

ক
25%
খ
12%
গ
15%
ঘ
20%

ব্যাখ্যা

Question: The marked price of a radio is Tk. 480. The owner allows a discount of 10% and still earns the profit of 8%. If no discount is allowed, find his gain percent?

Solution:
Marked price= 480
The shopkeeper allows a discount of 10%, so, the Selling price will be= 480 × (90/100) = 432.

And the profit is 8%.
Apply formula:
C.P = (100/(100 + p%)) × S.P
C.P = (100/108) × 432
C.P = 400

If the discount is not allowed:
Let Profit= P%

S.P = Marked price = 480, and C.P = 400
Profit = S.P - C.P

Now, apply formula:
P% = (Profit/C.P) × 100

So, gain % = ((480 - 400)/400) × 100
= 80/4
= 20%

৪৯.

If the length of a rectangle is increased by 20% and width is decreased by 20%, what is the change in area of the rectangle?

ক
unchanged
খ
decreased by 4%
গ
increases by 4%
ঘ
increases by 5%

ব্যাখ্যা

Question: If the length of a rectangle is increased by 20% and width is decreased by 20%, what is the change in area of the rectangle?

Solution:
Let,
length of rectangle = 20 and width = 10
so, area = 20 × 10 = 200

Now new length = 20 + 20 × 20%
= 20 + 4
= 24

New Width = 10 - 10 × 20%
= 10 - 2
= 8

So, New area = 24 × 8 = 192

And area decreased by (200 - 192) = 8

In percent = (8/200) × 100 = 4%
So, 4% decreased

৫০.

According to a recent survey of students at a public university, 65% are skilled in Mathematics and 45% are skilled in Statistics. How many students are proficient in both Mathematics and Statistics?

ক
10%
খ
15%
গ
20%
ঘ
25%

ব্যাখ্যা

Question: According to a recent survey of students at a public university, 65% are skilled in Mathematics and 45% are skilled in Statistics. How many students are proficient in both Mathematics and Statistics?

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

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

৫১.

The percentage profit earned by selling an article for Tk. 1,920 is equal to the percentage loss incurred by selling the same article for Tk. 1,280. At what price should the article be sold to make 25% profit?

ক
ক) Tk. 2,000
খ
খ) Tk. 2,200
গ
গ) Tk. 2,400
ঘ
ঘ) Data inadequate

ব্যাখ্যা

Let, the cost price be Tk. x
Now, according to the question
19,20 - x = x - 1,280
⇒ x + x = 19,20 + 1,280
⇒ 2x = 3,200
⇒ x = 3,200 /2
∴ x = 1,600

The cost price of the article is Tk. 1,600.

Now at 25% profit , the selling price will be = {1600 + (1600×25)/100}
= (1600 + 400) Tk.
= 2000 Tk.

৫২.

A reduction is 25% of the price of an article enables a buyer to buy 50 kilograms more for tk 500. What is the reduced price per kilogram in Taka?

ক
2
খ
2.50
গ
3
ঘ
3.50

ব্যাখ্যা

Question: A reduction is 25% of the price of an article enables a buyer to buy 50 kilograms more for tk 500. What is the reduced price per kilogram in Taka?

Solution:
25% মূল্য হ্রাসে
পূর্বের 100 টাকা দ্রব্য পাওয়া যায় 75 টাকায়

পূর্বের 1 টাকা দ্রব্য পাওয়া যায় 75/100 টাকায়
500 টাকা দ্রব্য পাওয়া যায় (75 × 500)/100
= 375 টাকায়

500 টাকায় এখন পূর্বাপেক্ষা 50 কেজি দ্রব্য বেশি পাওয়া যায়।

50 কেজির বর্তমান মূল্য 125 টাকা

50 কেজির বর্তমান মূল্য 125/50 টাকা

= 2.5 টাকা

৫৩.

If a man estimates his loss as 20% of the selling price, then his loss percent is = ?

ক
ক) 20/3%
খ
খ) 25/3%
গ
গ) 40/3%
ঘ
ঘ) 50/3 %

ব্যাখ্যা

According to the question,
Loss = 20% Selling price
i.e.
Loss/ Selling price = 1/5
∴ Cost price = Selling price + Loss
= 5 + 1
= 6
∴Loss%=1/6 ×100=50/3%

৫৪.

The volume of a rectangular solid is to be increased by 50% without altering its base. To what extent the height of the solid must be changed.

ক
ক) 50%
খ
খ) 40%
গ
গ) 30%
ঘ
ঘ) 20%

ব্যাখ্যা

Question: The volume of a rectangular solid is to be increased by 50% without altering its base. To what extent the height of the solid must be changed?

Solution:
ধরি,
আয়তাকার বস্তুর, দৈর্ঘ্য = a
প্রস্থ = b
উচ্চতা = h
∴ আয়তন V = abh
আয়তন ৫০% বাড়ালে নতুন আয়তন = 1.5 abh

নতুন উচ্চতা যদি H হয় তাহলে = abH = 1.5abh
H = 1.5h
∴ উচ্চতার পরিবর্তন = 1.5h - h = 0.5h

শতকরা পরিবর্তন = (0.5h/h)100% = 50%

৫৫.

Passing marks in an examination are 40%. If a candidate gets 65 marks and fails by 15 marks, the maximum marks in the examination are-

ক
250
খ
220
গ
200
ঘ
180

ব্যাখ্যা

Question: Passing marks in an examination are 40%. If a candidate gets 65 marks and fails by 15 marks, the maximum marks in the examination are-

Solution:
Let,
The maximum marks be x
passing marks be 40% of x = (40/100)x = (2x)/5

ATQ,
65 + 15 = (2x)/5
⇒ 80 = (2x)/5
⇒ 2x = 400
∴ x = 200

৫৬.

A man sells two chairs at Tk. 120 each and by doing so he gains 25% on one chair and loses 25% on the other. His loss on the whole in Tk. is = ?

ক
ক) Tk. 16
খ
খ) Tk. 12
গ
গ) Tk. 14
ঘ
ঘ) Tk. 20

ব্যাখ্যা

Question: A man sells two chairs at Tk. 120 each and by doing so he gains 25% on one chair and loses 25% on the other. His loss on the whole in Tk. is = ?

Solution:
Cost price of first chair = (100/125) × 120
= Tk. 96

Cost price of second chair = (100/75) × 120
= Tk. 160

∴ Loss = (160 + 96) - 240
= 256 - 240
= Tk. 16

৫৭.

If P is 20% less than X, and Q is 10% more than Y, than PQ is what percent of XY?

ক
ক) 84%
খ
খ) 85%
গ
গ) 87%
ঘ
ঘ) 88%

ব্যাখ্যা

Question: If P is 20% less than X, and Q is 10% more than Y, than PQ is what percent of XY?

Solution:
ধরি,
X = 100
∴ P = 100 - (20% of 100)
= 80

আবার,
Y = 100
∴ Q = 100 + (10% of 100)
= 110

তাহলে,
PQ, XY এর = ((80 × 110)/(100 × 100)} × 100%
= (8800/10000) × 100%
= 88%

৫৮.

A seller 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 percentage is:

ক
5%
খ
8%
গ
10%
ঘ
14%
ঙ
20%

ব্যাখ্যা

Question: A seller 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 percentage is:

Solution:
Given, Cost of 1kg of rice = Tk. 20
∴ Cost of 26kg of rice = 20 × 26 = 520 Tk.

Again, Cost of 1kg of rice = Tk. 36
∴ Cost of 30kg of rice = 36 × 30 =1080 Tk.

∴ Total C.P = Tk. (520 + 1080)
= Tk. 1600

Total rice weight = (30 + 26) kg = 56 kg

So,
Trader sold this 56kg of rice at Tk. 30 per kg
∴ Total S.P = Tk. (56 × 30)
= Tk. 1680.

Hence,
Profit = 1680 - 1600 = Tk. 80
Profit percentage = (80/1600) × 100
= 5%

৫৯.

A book seller allowed 10% discount on printed price. He gets 30% commission from publisher. His profit in percent will be?

ক
10%
খ
20%
গ
(200/7)%
ঘ
(225/7)%

ব্যাখ্যা

Question: A book seller allowed 10% discount on printed price. He gets 30% commission from publisher. His profit in percent will be?

Solution:
let, the marked price of book is 100 taka
buying price 100 × 0.7 taka
= 70 taka

selling price of book seller = 100 × 0.9 taka
= 90 taka

Profit in percent = {(90 - 70)/70} × 100%
= (200/7)%

৬০.

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
no profit no loss
খ
1% loss
গ
1% profit
ঘ
5% profit

ব্যাখ্যা

Question: 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:

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

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

∴ Profit = 1680 - 1600
= 80 taka

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

৬১.

A person's salary has increased from tk7200 to tk.8100. What is the percentage increase in his salary?

ক
ক) 25%
খ
খ) 18%
গ
গ) 12.5%
ঘ
ঘ) 16.67%
ঙ
ঙ) 20%

ব্যাখ্যা

Salary Increased = 8100-7200 = 900
Percent increased = (900/7200) × 100 = 12.5%

৬২.

A student scores 55% marks in 8 papers, each carrying 100 marks. He obtains 15% of his total obtained marks in the Bangla paper. How many marks did he score in Bangla?

ক
62
খ
66
গ
68
ঘ
72

ব্যাখ্যা

Question: A student scores 55% marks in 8 papers, each carrying 100 marks. He obtains 15% of his total obtained marks in the Bangla paper. How many marks did he score in Bangla?

Solution:
৮ টি বিষয়ে মোট নম্বর = 8 × 100 = 800
সে নম্বর পেয়েছে = 800 এর 55%
= 800 এর 55/100
= 440

∴ সে বাংলায় নম্বর পেয়েছে = 440 এর 15%
= 440 এর 15/100
= 66

৬৩.

If x is 50% of y, then what percent of x is y?

ক
50%
খ
100%
গ
150%
ঘ
200%

ব্যাখ্যা

50% of y = x
or, x = y/2
or, y = 2x
or, y = 2 × 100% of x [ 100% = 1 ]
= 200% of x
Required percentage = 200%

৬৪.

A fruit seller buys lemons at 2 for one tk and sells then at 5 for three tk. His gain percentage is

ক
22%
খ
18%
গ
15%
ঘ
20%

ব্যাখ্যা

Question: A fruit seller buys lemons at 2 for one tk and sells then at 5 for three tk. His gain percentage is

Solution:
2 lemons cost 1 tk
So 1 lemon costs 1/2 tk
For comparing, let's calculate CP for 10 lemons
CP of 10 lemons = 10 × (1/2) = 5 tk

Now let's find selling price (SP) of lemons:
5 lemons cost 3 tk
So 10 lemons will cost = (10/5) × 3 = 6 tk

Gain = SP - CP = 6 - 5 = 1 tk
Gain percentage = (Gain/CP) × 100
= (1/5) × 100
= 20%

৬৫.

A TV set is marked at Tk. 18,000. During a sale, a customer buys it at Tk. 16,200. what is the discount percentage.

ক
5%
খ
8%
গ
10%
ঘ
18%

ব্যাখ্যা

Question: A TV set is marked at Tk. 18,000. During a sale, a customer buys it at Tk. 16,200. what is the discount percentage.

Solution:
Given,
Marked Price = Tk. 18000
Selling price = Tk. 16200

∴ Discount = (18,000 - 16,200) = Tk. 1,800

∴ Discount % = (1800/18000) × 100 = 10%

৬৬.

A company's profits have doubled for each of the last 6 years. If the total profits for the last 6 years were Tk. 126 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. 6,00,000

ব্যাখ্যা

Question: A company's profits have doubled for each of the last 6 years. If the total profits for the last 6 years were Tk. 126 lacs, what were the profits in the first year?

Solution:
মনে করি, প্রথম বছরে কোম্পানির লাভ ছিল x টাকা।
যেহেতু প্রতি বছর লাভ দ্বিগুণ হচ্ছে, তাই 6 বছরের লাভগুলো হবে যথাক্রমে: x, 2x, 4x, 8x, 16x এবং 32x

প্রশ্নমতে,
x + 2x + 4x + 8x + 16x + 32x = 1,26,00,000
⇒ 63x = 1,26,00,000
⇒ x = 1,26,00,000/63
⇒ x = 2,00,000

∴ প্রথম বছরে কোম্পানির লাভ ছিল 2,00,000 টাকা।

৬৭.

The retail price of a pen is 40 taka. Asif got a discount of 20% over the retail price and he eventually saved taka 240 on his total purchase of the pens. How many pens did he buy?

ক
ক) 20
খ
খ) 24
গ
গ) 12
ঘ
ঘ) 30

ব্যাখ্যা

According to the question,
Retail price 40 Tk. (per pen).
20% discount = 40 × (20/100)
= 8 Tk.
অর্থ্যাৎ,
প্রতি pen এ save হয় = 8 Tk.
Total savings = 240 Tk.
∴ Number of pen = 240/8
= 30 pen.

৬৮.

Sohan bought some oranges of which 10% are rotten. He gives 80% of the remaining to his neighbor. Now he is left out with 36 oranges. How many oranges he bought?

ক
188 oranges
খ
200 oranges
গ
176 oranges
ঘ
220 oranges
ঙ
None of these

ব্যাখ্যা

Question: Sohan bought some oranges of which 10% are rotten. He gives 80% of the remaining to his neighbor. Now he is left out with 36 oranges. How many oranges he bought?

Solution:
Let,
Sohanr bought = 100 oranges.
Oranges after removing rotten ones = 90.
Oranges given to neighbor = 80% of 90 = 72 Oranges.

Now,
He left with eggs = (90 - 72) Oranges
= 18 Oranges.

Now,
Comparing,
Remaining 18 when total oranges = 100
Remaining 18 when total oranges = 100/18
Remaining 36 when total oranges = (100 × 36)/18
= 200

৬৯.

A discount of 10% on one article is equal in amount to a discount of 25% on a second article. What can be the ratio of their marked prices?

ক
5 : 2
খ
2 : 5
গ
1 : 5
ঘ
2 : 1

ব্যাখ্যা

Question: A discount of 10% on one article is equal in amount to a discount of 25% on a second article. What can be the ratio of their marked prices?

Solution:
Let
the marked prices of the two articles be X and Y

ATQ,
10% of X = 25% of Y
⇒ 10X/100 = 25Y/100
⇒ 10X = 25Y
⇒ X/Y = 25/10
∴ X : Y = 5 : 2

The ratio of their marked prices is = 5 : 2

৭০.

একটি পণ্যের বিক্রয়মূল্য দ্বিগুণ হলে বিক্রেতার মুনাফা বেড়ে তিনগুণ হয়। মূল্য বৃদ্ধি না করে পণ্যটি বিক্রয় করলে শতকরা কত লাভ হবে?

ক
৫০%
খ
১০০%
গ
১৫০%
ঘ
১২৫%
ঙ
কোনোটিই নয়

ব্যাখ্যা

প্রশ্ন: একটি পণ্যের বিক্রয়মূল্য দ্বিগুণ হলে বিক্রেতার মুনাফা বেড়ে তিনগুণ হয়। মূল্য বৃদ্ধি না করে পণ্যটি বিক্রয় করলে শতকরা কত লাভ হবে?

সমাধান:
ধরি,
ক্রয়মূল্য ১০০ টাকা
বিক্রয়মূল্য = ১০০ + ক টাকা

লাভ হয় = (১০০ + ক - ১০০) = ক টাকা
বিক্রয়মূল্য দ্বিগুণ= ২(১০০ + ক)

প্রশ্নমতে
৩ক = ২(১০০ + ক) - ১০০
বা, ৩ক = ২০০ + ২ক - ১০০
বা, ৩ক - ২ক = ১০০
ক = ১০০

বিক্রয়মূল্য = ১০০ + ১০০ = ২০০ টাকা
লাভ = ১০০ টাকা
শতকরা লাভ = (১০০/১০০) × ১০০ = ১০০%

৭১.

A company makes a profit of 5% on its first TK. 1000 of sales each day, and 4% on all sales in excess of 1000 for that day. What would be the profit of the company in a day when sales are TK. 6000?

ক
Tk. 300
খ
Tk. 250
গ
Tk. 275
ঘ
Tk. 325

ব্যাখ্যা

Question: A company makes a profit of 5% on its first TK. 1000 of sales each day, and 4% on all sales in excess of 1000 for that day. What would be the profit of the company in a day when sales are TK. 6000?

Solution:
Profit for first TK. 1000 = 1000 × (5/100) = TK. 50

Total sales excess of Tk. 1000 = (6000 - 1000) = Tk. 5000

∴ Profit for excess of Tk. 1000 = 5000 × (4/100) = Tk. 200

∴ Total Profit (50+ 200) = Tk. 250

৭২.

Payel bought an item at 20% discount on its original price. he sold it with 40% increase on the price he bought it. The new sale price is by what percent more than the original price?

ক
10%
খ
12%
গ
14%
ঘ
18%

ব্যাখ্যা

Question: Payel bought an item at 20% discount on its original price. he sold it with 40% increase on the price he bought it. The new sale price is by what percent more than the original price?

Solution:
Let, the original price be 100
After 20% discount, the price is = 100 - 20
= 80 taka

Selling price = 80 + 80 × 0.4
= 80 + 32
= 112 taka

%increase = (112 - 100)%
= 12%

৭৩.

By selling an article at 1/2 of the marked price, there is a 25% loss. Find the profit percent if the article is sold at the marked price.

ক
58%
খ
70%
গ
80%
ঘ
50%
ঙ
40%

ব্যাখ্যা

Question: By selling an article at 1/2 of the marked price, there is a 25% loss. Find the profit percent if the article is sold at the marked price.

Solution:
Let the marked price be x TK

Then,
Selling price = (1/2)x , loss = 25%

∴ Cost price = TK. (100/75) × (x/2)
= TK. (2x/3)

If an article is sold at marked price.
Then profit = TK. {x - (2x/3)}
= TK. (x/3)

∴ profit%
= {(x/3) × (3/2x) × 100}%
= 50%

৭৪.

A man bought 40 shares of Tk. 50 at 5tk discount, the rate of dividend being 27%. The rate of interest obtained is-

ক
35%
খ
30%
গ
38%
ঘ
32%
ঙ
25%

ব্যাখ্যা

Question: A man bought 40 shares of Tk. 50 at 5tk discount, the rate of dividend being 27%. The rate of interest obtained is-

Solution:
Given,
Total investment = Tk. [40 × (50 - 5)] = Tk. 1800.
Face value = Tk. (50 × 40) = Tk. 2000.

∴ Dividend = (27/100) × 2000
= Tk. 540

∴ Interest obtained = (540/1800) × 100%
= 30%

৭৫.

Rasel bought accessories worth Tk. 150. Out of the amount spent for buying accessories, Tk. 10 was spent on sales tax due to taxable purchases. If the tax rate was 10%, calculate the price of the tax-free items.

ক
Tk. 50
খ
Tk. 60
গ
Tk. 40
ঘ
Tk. 45

ব্যাখ্যা

Question: Rasel bought accessories worth Tk. 150. Out of the amount spent for buying accessories, Tk. 10 was spent on sales tax due to taxable purchases. If the tax rate was 10%, calculate the price of the tax-free items.

Solution:
Total Price = 150
Tax paid = 10
Paid Price of accessories without Tax = 150 - 10 = 140
Tax = 10%

Let the taxable purchases = Tk. x

⇒ 10% of x = 10

⇒ 0.1x = 10

∴ x = 100

∴ Price of Tax free items = 140 - 100 = 40

৭৬.

A trader marks his goods at 20% above the cost price . If he allows a discount of 5% for each down payment, his profit for such a transaction is

ক
ক) 15%
খ
খ) 12%
গ
গ) 14%
ঘ
ঘ) 17%

ব্যাখ্যা

ধরি
পণ্যটির ক্রয়মূল্য ১০০ টাকা
বিক্রেতা মূল্য নির্ধারণ করলো = ১০০ + ২০ টাকা
৫% ছাড়ে
পণ্যটির বিক্রয়মূল্য = ১২০ - (১২০ × ৫০) /১০০
= ১১৪ টাকা

শতকরা লাভ হবে = ১১৪ - ১০০
= ১৪%

৭৭.

A team lost 25% of the matches it played. If it won 15 matches, find the number of matches it played.

ক
ক) 30
খ
খ) 18
গ
গ) 20
ঘ
ঘ) 25

ব্যাখ্যা

প্রশ্ন: A team lost 25% of the matches it played. If it won 15 matches, find the number of matches it played.

সমাধান:
জয়ী হয় (১০০ - ২৫)% = ৭৫% ম্যাচ

৭৫ ম্যাচ জয়ী হয় যখন মোট ম্যাচ ১০০টি
∴ ১৫ ম্যাচ জয়ী হয় যখন মোট ম্যাচ (১০০ × ১৫)/৭৫টি
= ২০টি

৭৮.

If the price of sugar rises from tk. 6 per kg to tk. 7.50 per kg, a person, to have no increase in his expenditure on sugar, will have to reduce his consumption of sugar by-

ক
ক) 15%
খ
খ) 20%
গ
গ) 25%
ঘ
ঘ) 30%
ঙ
ঙ) Insufficient Data

ব্যাখ্যা

Increase = 7.5 - 6
= 1.5
percentage of increase= (1.5/6) × 100
= 25%
so, consumption must be reduced by (r/100+r) × 10
= (25/100+25) × 100
= 20%

৭৯.

If x is 30% greater than y, what percent of y is x?

ক
ক) 70
খ
খ) 77
গ
গ) 120
ঘ
ঘ) 130

ব্যাখ্যা

If, y = 100 then x = 100 + 30 = 130
then, x is 130% of y

৮০.

12/15 is how many percent?

ক
ক) 90 percent
খ
খ) 70 percent
গ
গ) 80 percent
ঘ
ঘ) 60 percent

ব্যাখ্যা

Question: 12/15 is how many percent?

Solution:

12/15

= 4/5

= (4 × 20)/(5 × 20)

= 80/100

= 80%

৮১.

Normally a Play Station costs Tk. 5000, but you only want to pay Tk. 4500. How much discount (in percent) do you want?

ক
11.11%
খ
10%
গ
5%
ঘ
15%

ব্যাখ্যা

Question: Normally a Play Station costs Tk. 5000, but you only want to pay Tk. 4500. How much discount (in percent) do you want?

Solution:
Discount = 5000 - 4500 = 500

% Discount = (500/5000) × 100 = 10%

৮২.

If 25% of a number is 75, 80% of the number is:

ক
ক) 300
খ
খ) 180
গ
গ) 375
ঘ
ঘ) 240

ব্যাখ্যা

ধরি,
সংখ্যাটি = x

প্রশ্নমতে,
x এর 25% = 75
25x/100 = 75
x/4 = 75
x = 300

300 এর 80% = 300 × 80/100
= 240

৮৩.

A man bought oranges at the rate of 8 for Tk. 34 and sold them at the rate of 12 for Tk. 57. How many oranges should be sold to earn a net profit of Tk. 45?

ক
ক) 90
খ
খ) 99
গ
গ) 190
ঘ
ঘ) 150

ব্যাখ্যা

CP of 1 orange
= Tk.34/8
= Tk.4.25
SP of 1 orange
=Tk. 57/12
=Tk.4.75
Profit on each apple = (4.75 - 4.25) = Tk. 0.50
∴ Number of apples required
= 45/ 0.50
=90

৮৪.

If 40% of an amount is 250, what will be 60% of that amount?

ক
300
খ
320
গ
375
ঘ
400

ব্যাখ্যা

Question: If 40% of an amount is 250, what will be 60% of that amount?

Solution:
Let,
The amount be x

ATQ,
40% of x = 250
⇒ (40x)/100 = 250
⇒ 40x = 25000
∴ x = 625

60% of 625 = (60 × 625)/100 = 375

৮৫.

When a plot is sold at TK. 18700, the owner loss at 15%, at price he must sold it to get 15% profit = ?

ক
ক) 21,000
খ
খ) 22,500
গ
গ) 25,300
ঘ
ঘ) 25,800
ঙ
ঙ) 26,300

ব্যাখ্যা

Let the new S.P. be Tk . x
Then, 85 : 18700 = 115 : x
⇒ x = (18700 × 115)/85
⇒ x = 25300

৮৬.

If 2 m, 60 cm cloths is required for one shirt, then the cloth required for 7 shirts is?

ক
ক) 14 m 80 cm
খ
খ) 18 m 20 cm
গ
গ) 15 m 20 cm
ঘ
ঘ) 16 m 80 cm
ঙ
ঙ) 13 m 60 cm

ব্যাখ্যা

Cloth is required for 1 shirt
= 2 m, 60 cm or 260 cm
Cloth is required for 7 shirt
= 260 × 7
= 1820 cm or 18 m 20 cm

৮৭.

If 10% of m is the same as the 20% of n, then m : n is equal to

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

ব্যাখ্যা

10% of m = 20% of n
⇒ (10/100) × m = (20/100) × n
⇒ 10 m = 20 n
⇒ m/n = 20/10
∴ m : n = 2 : 1

৮৮.

Tanveer bought some oranges of which 10% are rotten. He gives 80% of the remaining to his neighbor. Now he is left out with 36 oranges. How many oranges he bought?

ক
200
খ
100
গ
72
ঘ
40

ব্যাখ্যা

Question: Tanveer bought some oranges of which 10% are rotten. He gives 80% of the remaining to his neighbor. Now he is left out with 36 oranges. How many oranges he bought?

Solution:
Let,
Tanveer bought 100 oranges.
Oranges after removing rotten ones = 90.
Oranges given to neighbor = 80% of 90 = 72 Oranges.
Now,
He left with eggs = 90 - 72 = 18 Oranges.

Now,
Comparing,
Remaining 18 when total oranges = 100
∴ Remaining 18 when total oranges = 100/18
∴ Remaining 36 when total oranges = (100 × 36)/18
= 200

So, he bought 200 Oranges.

৮৯.

What is the value of c, If 8 is 4% of a, and 4 is 8% of b. c equals b/a?

ক
1/2
খ
1/4
গ
0.155
ঘ
None of these

ব্যাখ্যা

Question: What is the value of c, If 8 is 4% of a, and 4 is 8% of b. c equals b/a?

Solution:
Let be the 4% of a is 4a/100.
Since this equals 8, we have,
4a/100 = 8.
⇒ a = (8 × 100)/4 = 200.

Also, 8% of b = 8b/100, and this equals 4.
Hence, we have,
8b/100 = 4.
⇒ b = (4 × 100)/8 = 50.

Now,
c = b/a = 50/200 = 1/4

৯০.

A stock is currently at Tk. 40 per share. If the price increases by 20 percent and then decreases by 25 percent, what will be the new value of the share?

ক
ক) Tk. 36
খ
খ) Tk. 40
গ
গ) Tk. 48
ঘ
ঘ) Tk. 30

ব্যাখ্যা

First increase by 20%
So, per share value is = 40 + 40×20% = 48
Then, decrease by 25%,
So new value will become = 48 - 48×25% = 36

৯১.

If the price of the commodity is increased by 50% by what fraction must its consumption be reduced so as to keep the same expenditure on its consumption?

ক
1/2
খ
1/3
গ
1/4
ঘ
1/5
ঙ
None

ব্যাখ্যা

Question: If the price of the commodity is increased by 50% by what fraction must its consumption be reduced so as to keep the same expenditure on its consumption?

Solution:
Let the initial price of the commodity be 100.

After a 50% increase in price, It will become, 100, and a 50% increase will be 150.
Now, we have to reduce the consumption to keep expenditure 100.

Increase in price= 150 - 100 = 50
We have to reduce the consumption = (50/150) × 100
= 33.33% or 1/3

৯২.

A box contains 200 pens of which 25% are red and the rest are black. You sold a certain number of pens of which 60% were black. You then found that among the remaining pens, only 20% are red. How many pens did you sell?

ক
50
খ
60
গ
75
ঘ
80

ব্যাখ্যা

Question: A box contains 200 pens of which 25% are red and the rest are black. You sold a certain number of pens of which 60% were black. You then found that among the remaining pens, only 20% are red. How many pens did you sell?

Solution:
Initial pens = 200
Red pens = 25% of 200 = 50
Black pens = 75% of 200 = 150
Let sold pens = x

∴ Black pens sold = 60% of x = 0.6x
Remaining pens = 200 - x

Remaining red = 20% of (200 - x)
∴ 50 - (0.4x) = 0.2(200 - x) [Red pens remaining]
⇒ 50 - 0.4x = 40 - 0.2x
⇒ 50 - 40 = 0.4x - 0.2x
⇒ 10 = 0.2x
∴ x = 50

৯৩.

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

ক
ক) 46%
খ
খ) 32%
গ
গ) 64%
ঘ
ঘ) 23%

ব্যাখ্যা

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

Solution:
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 = {(1600/15) × (3/500) × 100}% = 64%.

৯৪.

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

ক
5000
খ
5750
গ
6000
ঘ
6250

ব্যাখ্যা

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

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

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

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

৯৫.

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

ক
1/5
খ
20/100
গ
0.5
ঘ
0.2

ব্যাখ্যা

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

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

৯৬.

If 60% of a number is equal to three-fourths of another number, what is the ratio of the first number to the second number?

ক
3 : 5
খ
5 : 3
গ
3 : 8
ঘ
5 : 4

ব্যাখ্যা

Question: If 60% of a number is equal to three-fourths of another number, what is the ratio of the first number to the second number?

Solution:
ধরি,
প্রথম সংখ্যাটি x এবং দ্বিতীয় সংখ্যাটি y।
প্রশ্নমতে,
60% of x = (3/4) of y
⇒ (60/100) × (x) = (3/4) × y
⇒ (3/5)x = (3/4)y
⇒ x/5 = y/4
⇒ 4x = 5y
⇒ x/y = 5/4

∴x : y = 5 : 4

৯৭.

In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?

ক
7500
খ
8000
গ
8900
ঘ
Data inadequate

ব্যাখ্যা

Question: In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?

Solution:
Let, the number of candidates appeared from each State was x

0.07x - 0.06x = 80
⇒ 0.01x = 80
⇒ x = 80/0.01
= 8000

৯৮.

The price of rice has fallen by 20%. How much rice can be bought now with the money that was sufficient to buy 10 kg of rice previously?

ক
ক) 11kg
খ
খ) 12.5kg
গ
গ) 12kg
ঘ
ঘ) 10.8kg

ব্যাখ্যা

Question: The price of rice has fallen by 20%. How much rice can be bought now with the money that was sufficient to buy 10 kg of rice previously?

Solution:
Let 100Tk is spend on rice initially for 10kg
after 20% fall, the price is needed now is = 100 - (20% of 100)
= 100 - 20
= 80Tk

new price of rice per kg is = 80/10 = 8Tk

at 8Tk per kg, rice can be bought in 100Tk is = 100/8 = 12.5kg

৯৯.

What percent of 10 kg is 50 grams?

ক
0.5%
খ
0.25%
গ
5%
ঘ
1%

ব্যাখ্যা

Question: What percent of 10 kg is 50 grams?

Solution:
Required Percentage = {(50gm/10kg) × 100}%
= {(50/10000) × 100}% [1kg = 1000gm]
= (5000/10000)%
= 0.5%

১০০.

Bananas are bought at Tk. 36 per dozen and sold at a profit of 25%. How much is the selling price of twenty bananas?

ক
ক) Tk. 70
খ
খ) Tk. 72
গ
গ) Tk. 75
ঘ
ঘ) Tk. 65

ব্যাখ্যা

Question: Bananas are bought at Tk. 36 per dozen and sold at a profit of 25%. How much is the selling price of twenty bananas?

Solution:
৩৬ টাকায় ক্রয় করে ১২ টি কলা
∴ ১ টাকায় ক্রয় করে ১২/৩৬ টি কলা
∴ ১০০ টাকায় ক্রয় করে (১২ × ১০০)/৩৬ টি কলা
= ১০০/৩ টি কলা

২৫% লাভে বিক্রয়মূল্য = (১০০ + ২৫) টাকা = ১২৫ টাকা

২৫% লাভ করতে হলে,
১০০/৩ টি কলার বিক্রয়মূল্য ১২৫ টাকা
∴ ১ টি কলার বিক্রয়মূল্য (১২৫ × ৩)/১০০ টাকা
∴ ২০ টি কলার বিক্রয়মূল্য (১২৫ × ৩ × ২০)/১০০ টাকা
= ৭৫ টাকা