Percentage and Profit & Loss

PrepBank · পাতা ৫ / ১৭ · ৪০১–৫০০ / ১,৬৯৬

৪০১.

A retail fruit vendor buys pineapples at a score for Tk. 200, and retails them at a dozen for Tk 156. Did he gain or lose in the transaction and what % was his gain or loss?

ক
30% loss
খ
22% loss
গ
22% gain
ঘ
30% gain

ব্যাখ্যা

Question: A retail fruit vendor buys pineapples at a score for Tk. 200, and retails them at a dozen for Tk 156. Did he gain or lose in the transaction and what % was his gain or loss?

Solution:
C.P of 1 Pineapple = Tk. 200/score = 200/20 = 10 (Note: 1 score = 20)

S.P of 1 Pineapple = Tk.156/dozen = 156/12 = 13 (Note: 1 dozen = 12)

∴ Profit of 1 Pineapple = 13 - 10 = 3

∴ % Profit = (3/10) × 100 % = 30%

৪০২.

One dozen eggs and ten pounds of apples are currently the same price. If the price of a dozen eggs rises by 10% and that of apples rises by 2%, how much more will it cost to buy a dozen of eggs and ten pounds of apples?

ক
ক) 2%
খ
খ) 10%
গ
গ) 6%
ঘ
ঘ) 12%

ব্যাখ্যা

Say both egg and apple cost $10 each per unit
An increase of 10% for the eggs would bring the new total to $11
And an increase of 2% for the apples would bring the new total to $10.2
The original total was $20 and the new total is $21.2.
Change in price = 21.2 - 20 = 1.2
∴ Percentage increased in price = 1.2/20 × 100 = 6%.

৪০৩.

If the price of petrol is increased by 20%, by what percentage should the consumption be decreased by the consumer, if the expenditure on petrol remains unchanged?

ক
16.67%
খ
6.67%
গ
8%
ঘ
15%
ঙ
None of above

ব্যাখ্যা

Here,
(r × 100)/(100 + r)
= (20 × 100)/(100 + 20)
= 16.67

৪০৪.

A television is priced at Tk. 15,600. A customer pays Tk. 12,150 for it after getting two successive discounts. If the rate of first discount is 10%, the rate of 2nd discount is:

ক
9.46%
খ
15.23%
গ
10.19%
ঘ
11. 43%
ঙ
None

ব্যাখ্যা

Question: A television is priced at Tk. 15,600. A customer pays Tk. 12,150 for it after getting two successive discounts. If the rate of first discount is 10%, the rate of 2nd discount is:

Solution:
MP = 15,600
After first discount Marked Price (MP) becomes,
= 15,600 - 10% of 15,600
= 15,600 - 1,560
= 14,040

The Selling Price (SP) = 12,150
Let second discount be x% on 14,040
14,040 - x% of 14,040 = 12,150
14,040 - 14,040x/100 = 12,150
14,040 - 140.4x = 12,150
-140.4x = 12,150 - 14,040
-140.4x = -1,890
x = 1,890/140.4
x = 13.46%

৪০৫.

If the cost price of 18 pens is equal to the selling price of 12 pens, the gain percent is?

ক
12%
খ
30%
গ
50%
ঘ
60%
ঙ
150%

ব্যাখ্যা

Question: If the cost price of 18 pens is equal to the selling price of 12 pens, the gain percent is?

Solution:
Let the cost price of 1 pen is Tk. 1
Cost of 12 pens = Tk. 12

Selling price of 12 pens = Tk. 18
Gain = 18 - 12 = 6

Gain% = (gain/cost × 100)%
= (6/12 × 100)%
= 50%

৪০৬.

A shopkeeper marks an article 40% above the cost price and allows a discount of 10%. What is his profit percentage?

ক
20%
খ
36%
গ
26%
ঘ
25%

ব্যাখ্যা

Question: A shopkeeper marks an article 40% above the cost price and allows a discount of 10%. What is his profit percentage?

Answer:
Cost Price 100 Taka
Then Mark Price = 140, (40% above the cost price)

10% discount
If marked price is 100, then discount is 10 taka
If marked price is 1, then discount is 10/100 taka
If marked price is 140, then discount is 140/10 = 14 taka

Selling Price = 140 - 14 = 126,
As the Cost Price = 100
Then, the Profit percentage is = 26%

৪০৭.

Rahman spends 50% of his monthly income on household items, 20% of his monthly income on buying clothes, 5% of his monthly income on medicines and saves remaining Tk. 11,250. What is Rahman’s monthly income?

ক
Tk. 48560
খ
Tk. 45325
গ
Tk. 45000
ঘ
Tk. 35000

ব্যাখ্যা

Question: Rahman spends 50% of his monthly income on household items, 20% of his monthly income on buying clothes, 5% of his monthly income on medicines and saves remaining Tk. 11,250. What is Rahman’s monthly income?

Solution:
Total spends = (50 + 20 + 5) = 75%

∴ Saves = (100 - 75) = 25%

Let total income of Rahman be x. Then,
⇒ x × 25% = 11250
⇒ 25x/100 = 11250
⇒ x/4 = 11250
⇒ x = 11250 × 4
∴ x = 45000

∴ Rahman’s monthly income is Tk. 45000

৪০৮.

The salaries A and B together amount to Tk. 3000. A spends 95% of his salary and, B spends 85% of his salary. If now, their savings are the same, What is A's salary?

ক
Tk. 1850
খ
Tk. 2250
গ
Tk. 2480
ঘ
Tk. 2190
ঙ
None of these

ব্যাখ্যা

Question: The salaries A and B together amount to Tk. 3000. A spends 95% of his salary and, B spends 85% of his salary. If now, their savings are the same, What is A's salary?

Solution:
Let, A's salary x and B's salary = (3000 - x)

ATQ,
⇒ (100 - 95)% of A = (100 - 85)% of B
⇒ (5/100)x = (15/100)(3000 - x)
⇒ x = 3(3000 - x)
⇒ x = 9000 - 3x
⇒ 4x = 9000
⇒ x = 9000/4
⇒ x = 2250

So, A's salary is Tk. 2250

৪০৯.

Which of the following is the 350% of 1?

ক
0.0035
খ
3.5
গ
0.35
ঘ
35

ব্যাখ্যা

Question: Which of the following is the 350% of 1?

Solution:
Let,
350% of 1 = x
or, (350/100) × 1 = x
∴ x = 3.5
So, 350% of 1 is 3.5

৪১০.

Moyna and Noyna respectively got 20% more and 10% less marks than Jolin in exam. What is the ratio of Noyna and Moyna's exam scores?

ক
2 : 1
খ
11 : 12
গ
3 : 4
ঘ
4 : 3
ঙ
None

ব্যাখ্যা

Question: Moyna and Noyna respectively got 20% more and 10% less marks than Jolin in exam. What is the ratio of Noyna and Moyna's exam scores?

Solution:
Let,
Jolin got 100
∴ Moyna got 120
∴ Noyna got 90

Noyna : Moyna = 90 : 120 = 9 : 12 = 3 : 4

৪১১.

If the cost price of 5 oranges is equal to the selling price of 4 oranges, then find a profit percentage.

ক
15%
খ
30%
গ
20%
ঘ
25%

ব্যাখ্যা

Question: If the cost price of 5 oranges is equal to the selling price of 4 oranges, then find a profit percentage.

Solution:
ধরি,
৫টি কমলার ক্রয়মূল্য ক টাকা
∴ ১টি কমলার ক্রয়মূল্য ক/৫ টাকা

৪ টি কমলার বিক্রয়মূল্য ক টাকা
∴ ১ টি কমলার বিক্রয়মূল্য ক/৪ টাকা

∴ লাভ = ক/৪ - ক/৫ = (৫ক - ৪ক)/২০ = ক/২০

শতকরা লাভ = (ক/২০)/(ক/৫) × ১০০% = ২৫%

৪১২.

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

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

ব্যাখ্যা

মোট খরচ = (80 × 40 + 40 × 50) টাকা
= (3200 + 2000) = 5200 টাকা
10% লাভে বিক্রয়মূল্য (5200 + 5200×10/100) = 5720 টাকা
∴ প্রতি কেজির বিক্রয়মূল্য (5720 ÷ 120) টাকা = 47.7 টাকা

৪১৩.

Ashim bought 5 apples at taka 10 and sold 4 apples at taka 10. What will be the rate of profit?

ক
20%
খ
25%
গ
30%
ঘ
40%

ব্যাখ্যা

Question: Ashim bought 5 apples at taka 10 and sold 4 apples at taka 10. What will be the rate of profit?

Solution:
5টি আপেলের ক্রয়মূল্য 10 টাকা
1টি আপেলের ক্রয়মূল্য 10/5 টাকা
= 2 টাকা

4টি আপেলের বিক্রয়মূল্য 10 টাকা
1টি আপেলের বিক্রয়মূল্য 10/4 টাকা
= 2.5 টাকা
লাভ = (2.5 - 2)টাকা = 0.5 টাকা

শতকরা লাভ = {(0.5/2) × 100}%
= 25%

৪১৪.

30% of 80% of 5/2 is -

ক
ক) 6/11
খ
খ) 2/5
গ
গ) 5/3
ঘ
ঘ) 3/5

ব্যাখ্যা

Question: 30% of 80% of 5/2 is -

Solution:
80% of 5/2 is = 5/2 × 80%
= 5/2 × 8/10
= 2

30% of 2 is = 2 × 30%
= 2 × 3/10
= 3/5

৪১৫.

In an examination, 32% is the pass mark. If an examinee gets 14 marks and fails by 10 marks, what is the maximum mark?

ক
60
খ
65
গ
70
ঘ
75

ব্যাখ্যা

Question: In an examination, 32% is the pass mark. If an examinee gets 14 marks and fails by 10 marks, what is the maximum mark?

Solution:
If the candidate fails by 10 marks, it means the pass marks = 14 + 10
= 24

Let the maximum marks be x

ATQ,
32% of x = 24
⇒ x × (32/100) = 24
⇒ 32x = 2400
⇒ x = 2400/32
⇒ x = 75

৪১৬.

X buys a product for Tk. 400 and sells it to Y at a profit of 30%. Y then sells it to Z at a profit of 15%. How much does Z pay to Y?

ক
Tk. 698
খ
Tk. 588
গ
Tk. 620
ঘ
Tk. 598

ব্যাখ্যা

Question: X buys a product for Tk. 400 and sells it to Y at a profit of 30%. Y then sells it to Z at a profit of 15%. How much does Z pay to Y?

সমাধান:
X এর 30% লাভে বিক্রয়মূল্য = 400 + 400 এর 30%
= 400 + (400 × 30/100)
= 400 + 120
= 520

X এর বিক্রয়মূল্য = Y এর ক্রয়মূল্য

Y এর 15% লাভে বিক্রয়মূল্য = 520 + 520 এর 15%
= 520 + (520 × 15/100)
= 520 + 78
= 598

সুতরাং, Y এর বিক্রয়মূল্য = Z এর ক্রয়মূল্য = Tk. 598

৪১৭.

A Hudi is sold for Tk. 2400 at a profit of 25%. What would have been the actual profit or loss if it had been sold at Tk. 1800?

ক
loss 5.25%
খ
profit 5.25%
গ
profit 6.25%
ঘ
loss 6.25%

ব্যাখ্যা

Question: A Hudi is sold for Tk. 2400 at a profit of 25%. What would have been the actual profit or loss if it had been sold at Tk. 1800?

Solution:
Firstly let us find the cost price of the same. C.P. = 2400 × (100/125) = 1920.
New selling price = 1800
Loss = 1920 - 1800 = 120

∴ Loss percentage = 100 × (120/1920)
= 6.25%.

৪১৮.

Three varieties of rice costing Tk. 30, Tk, 50. and Tk. 20 are mixed in the ratio 3 : 2 : 4 in terms of weight. A retailer sells the mixture at Tk. 33 per kg. What percentage of profit does he make?

ক
ক) 5%
খ
খ) 10%
গ
গ) 9%
ঘ
ঘ) None

ব্যাখ্যা

Question: Three varieties of rice costing Tk. 30, Tk, 50. and Tk. 20 are mixed in the ratio 3 : 2 : 4 in terms of weight. A retailer sells the mixture at Tk. 33 per kg. What percentage of profit does he make?

Solution:
Assume the trader bought 3 kg, 2 kg and 4 kg of the three varieties.
Total weight = (3 + 2 + 4) kg = 9 kg
C.P. of 9 kg = Tk. (3 × 30 + 2 × 50 + 4 × 20) = Tk.270.
S.P. of 9 kg = Tk.(9 × 33) = TK. 297.

∴ Profit = {(297−270)/270} × 100) %
= 10%

৪১৯.

A merchant purchases a wrist watch for tk 450 and fixes its list price in such a way that after allowing a discount of 10%, he earns a profit of 20%. Then the list price of the watch is

ক
500 tk
খ
550 tk
গ
600 tk
ঘ
650 tk

ব্যাখ্যা

Question: A merchant purchases a wrist watch for tk 450 and fixes its list price in such a way that after allowing a discount of 10%, he earns a profit of 20%. Then the list price of the watch is

Solution:
Here ,
Cost Price = tk 450 and discount on marked price = 10%
If the marked price of watch be y, then
y × (90/100) = (450 × 120)/100
⇒ y = (450 × 120)/90
∴ y = 600

৪২০.

Aman, Belal, and Dipto are partners in a business. Their shares are in the proposition of (1/3) : (1/4) : (1/5). Aman withdraws half of his capital after 15 months and after another 15 months, a profit of Tk. 4340 is divided. The share of Belal is -

ক
Tk. 1240
খ
Tk. 1420
গ
Tk. 1550
ঘ
Tk. 1600

ব্যাখ্যা

Question: Aman, Belal, and Dipto are partners in a business. Their shares are in the proposition of (1/3) : (1/4) : (1/5). Aman withdraws half of his capital after 15 months and after another 15 months, a profit of Tk. 4340 is divided. The share of Belal is -

Solution:
প্রাথমিক বিনিয়োগের অনুপাত = (1/3) : (1/4) : (1/5)
= 20 : 15 : 12

বিনিয়োগ যথাক্রমে 20x, 15x, 12x

A : B : C = (20x × 15) + (10x × 15) : (15x × 30) : (12x × 30)
= 450x : 450x : 360x
= 5 : 5 : 4

বেলালের শেয়ার = (5/14) × 4340
= 1550 টাকা

৪২১.

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

ক
5%
খ
6%
গ
8%
ঘ
9%

ব্যাখ্যা

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

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

Selling price of 56 kg rice = 56 × 30 tk
= 1680 tk

Profit = 1680 - 1600 tk = 80 tk
∴ Gain = (80/1600) ×100
= 5%

৪২২.

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

ক
3300
খ
2300
গ
2700
ঘ
2400

ব্যাখ্যা

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

Solution:
Number of valid votes = 80% of 7500
= 6000

Valid votes polled by other candidate = 45% of 6000
= (45/100) x 6000
= 2700

৪২৩.

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

ক
ক) 200
খ
খ) 250
গ
গ) 320
ঘ
ঘ) 400

ব্যাখ্যা

ধরি,
পণ্যটির ক্রয়মূল্য x টাকা

20% লাভে,
বিক্রয়মূল্য = (120 × x)/100 টাকা
=6x/5 টাকা

10% খরচ বৃদ্ধিতে,
নতুন ক্রয়মূল্য = (110 × x)/100
= 11x/10 টাকা

নতুন বিক্রয়মূল্য = (6x/5) + 26 টাকা
= (6x+130)/5

নতুন লাভ= {(6x+130)/5} -(11x/10)
= (2(6x+130) -11x)/10
= (12x-11x+260)/10
= (x+260)/10
প্রশ্নমতে,
15 =[{(x+260)/10} × 100]/(11x/10)
15 =(x + 260)×10 × 10/11x
11x × 15 = 100(x+260)
165x = 100x + 26000
165x - 100x = 26000
65x = 26000
x = 26000/65 = 2000/5= 400 TK

পণ্যটির ক্রয়মূল্য 400 টাকা

৪২৪.

What percent of 50 is 15?

ক
30%
খ
35%
গ
70%
ঘ
300%

ব্যাখ্যা

Question: What percent of 50 is 15?

Solution:
15 = x% of 50
⇒ 15 = (x/100) × 50
⇒ x = 1500/50 = 30%

৪২৫.

If 75% of the students in a school are boys and the number of girls is 520, the number of boys is:

ক
1450
খ
1560
গ
1230
ঘ
1280

ব্যাখ্যা

Question: If 75% of the students in a school are boys and the number of girls is 520, the number of boys is:

Solution:
No. of boys = 75%
No. Girls = 25% = 520

Now
25% = 520
1% = 520/25
75% = (520 × 75)/25
= 1560

৪২৬.

Mr. Kamal bought 20 mangoes for Tk. 55. He found that 10% of the mangoes were damaged and sold the rest at the rate of Taka 54 per dozen. How much profit in Taka did he make?

ক
ক) 28
খ
খ) 26
গ
গ) 24
ঘ
ঘ) 20

ব্যাখ্যা

According to the question,
10% of 20 = 2 mangoes were damaged
∴ বিক্রি করলো 20 - 2
=18
= 1(1/2) dozen.
বিক্রয় মূল্য = 54 × 1(1/2)
= 81
∴ Profit = 81 - 55
= 26.

৪২৭.

A person spends 80% of his income. If he earns $5000, what is his savings?

ক
$400
খ
$1000
গ
$4000
ঘ
$500

ব্যাখ্যা

Question: A person spends 80% of his income. If he earns $5000, what is his savings?

Solution:
মোট আয় করে = $5000
ব্যয় করে = $5000 এর 80%
= $5000 এর 80/100
= $4000

সে জমা করে = ($5000 - $4000)
= $1000

৪২৮.

What will be the difference in taka between simple and compound interest at 10% on a sum of Tk. 1,000 after 4 years?

ক
ক) 31.90
খ
খ) 32.10
গ
গ) 44.90
ঘ
ঘ) 64.10

ব্যাখ্যা

প্রশ্ন: What will be the difference in taka between simple and compound interest at 10% on a sum of Tk. 1,000 after 4 years?

সমাধান:
দেওয়া আছে,
মূলধন, P = 1000 টাকা
সময়, n = 4 বছর
সুদের হার, r = 10/100
আমরা জানি
সরল মুনাফা,
I = Pnr
= 1000 × 4 × 10/100 = 400 এবং
চক্রবৃদ্ধি মুনাফায় সবৃদ্ধিমূল,
C = P(1+r)ⁿ
= 1000(1 + 10/100)⁴
= 1000 × (110/100)⁴
= 1464.1
চক্রবৃদ্ধি মুনাফা = 1464.1 - 1000
= 464.1

চক্রবৃদ্ধি মুনাফা ও সরল মুনাফার পার্থক্য = (464.1 - 400) টাকা
=64.10 টাকা।

৪২৯.

A football team has won 40 games out of 60 played. It has 32 more games to play. How many of these must the team win to make it a record 75% win for the season?

ক
ক) 20
খ
খ) 25
গ
গ) 29
ঘ
ঘ) 32

ব্যাখ্যা

Team won 40 games out of 60 and the remaining games were 32.
Total games = 60 + 32
= 92
75% of 92 = 69
Team has to win 69 games in total.
Team has already won 40.
∴ Games to win = 69 - 40
= 29

৪৩০.

Three-fourths of a number is equal to 60% of another number and the difference between these two number is 10. What is the sum of these two numbers?

ক
40
খ
50
গ
70
ঘ
90

ব্যাখ্যা

Question: Three-fourths of a number is equal to 60% of another number and the difference between these two number is 10. What is the sum of these two numbers?

Solution:
Let the numbers be x and x + 10

Then,
3x/4 = 60% of (x + 10)
⇒ 3x/4 = 60(x + 10)/100
⇒ 3x/4 = 3(x + 10)/5
⇒ x/4 = (x + 10)/5
⇒ 5x = 4x + 40
⇒ 5x - 4x = 40
⇒ x = 40

The sum of these two numbers = x + x + 10
= 2x + 10
= 2 × 40 + 10
= 80 + 10
= 90

৪৩১.

If Anil’s income is 50% less than that of Borhan, then Borhan’s income is what percent more than that of Anil?

ক
80%
খ
90%
গ
100%
ঘ
120%

ব্যাখ্যা

Question: If Anil’s income is 50% less than that of Borhan, then Borhan’s income is what percent more than that of Anil?

Solution:
Borhan's income:
= {50/(100 - 50) × 100 }%
= 100%
Borhan's income is 100% more than that of Anil's

৪৩২.

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

ক
18%
খ
20%
গ
30%
ঘ
40%

ব্যাখ্যা

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

Solution:
একক এর ঘরে ১ আছে এমন সংখ্যা = ৭ টি
একক এর ঘরে ৯ আছে এমন সংখ্যা = ৭ টি

মোট = ১৪ টি

শতকরা পরিমাণ = (১৪/৭০) × ১০০%
= ২০%

৪৩৩.

A hawker buys every 4 oranges at Tk. 25 and then sells every 8 oranges at Tk. 56. What is the percentage of the profit?

ক
ক) 12%
খ
খ) 9%
গ
গ) 7.5%
ঘ
ঘ) 5.25%

ব্যাখ্যা

৪ টি কমলার ক্রয়মুল্য ২৫ টাকা হলে ৮ টি কমলা কিনে ৫০ টাকায়।
৫০ টাকায় ৮ টি কমলা কিনে ৫৬ টাকায় বিক্রয় করলে লাভ হয় ৬ টাকা।
সুতরাং, ১০০ টাকায় লাভ হবে (৬/৫০)×১০০ = ১২ টাকা।

৪৩৪.

In an examination A got 25% marks more than B, B got 10% less than C and C got 25% more than D. If D got 320 marks out of 500, the marks obtained by A were :

ক
490
খ
780
গ
570
ঘ
450
ঙ
680

ব্যাখ্যা

Question: In an examination A got 25% marks more than B, B got 10% less than C and C got 25% more than D. If D got 320 marks out of 500, the marks obtained by A were :

Solution:
Marks obtained by D = 320

Marks obtained by C = 320 × (125/100)
= 400

Marks obtained by B
= 400 × (100 - 10)/100
= 360

Marks obtained by A
= 360 × (125/100)
= 450

∴ Hence, required marks obtained by A = 450

৪৩৫.

In a business, Belal invests half the amount invested by Aman. After 6 months from the start of the business, Nazma joins the business with an amount equal to twice of Belal's investment. After 8 months from the start of the business Belal withdraws completely from the business. If at the end of the year, Nazma's share in the profit was Tk. 2460, what was the total profit received that year?

ক
9600 taka
খ
9020 taka
গ
8050 taka
ঘ
11000 taka

ব্যাখ্যা

Question: In a business, Belal invests half the amount invested by Aman. After 6 months from the start of the business, Nazma joins the business with an amount equal to twice of Belal's investment. After 8 months from the start of the business Belal withdraws completely from the business. If at the end of the year, Nazma's share in the profit was Tk. 2460, what was the total profit received that year?

Solution:
let, Aman invested 2x taka
Belal invests x taka
Nazma invests 2x taka

ratio of profit = (2x ×12) : (x × 8) : (2x × 6)
= 24x : 8x : 12x
= 6 : 2 : 3

3 × total profit/(6 + 2 + 3) = 2460
⇒ total profit = 2460 × 11/3
= 9020 taka

৪৩৬.

64% of a number is 1920. What is 88% of that number?

ক
2160
খ
2420
গ
2240
ঘ
2640

ব্যাখ্যা

Question: 64% of a number is 1920. What is 88% of that number?

Solution:

Let the number be x

Then,
64% of x = 1920
64x/100 = 1920
x = (1920 × 100)/64
x = 3000

88% of 3000 = 3000 × (88/100)
= 2640

৪৩৭.

A and B are two fixed points 10 cm apart and C is a point on AB such that AC is 6cm. if the length of AC is increased by 10%, by what percentage is CB decreased?

ক
5%
খ
10%
গ
15%
ঘ
9%
ঙ
None

ব্যাখ্যা

Question: A and B are two fixed points 10 cm apart and C is a point on AB such that AC is 6cm. if the length of AC is increased by 10%, by what percentage is CB decreased?

Solution:
দেওয়া আছে
AB = 10 cm
AC = 6 cm
CB = (10 - 6) = 4

AC 10% বৃদ্ধিতে = 6 + 6 এর 10%
= 6 + 6 এর 10/100
= 6 + .6
= 6.6

CB এর নতুন দৈর্ঘ্য = 4 - . 6
= 3.4

CB এর দৈর্ঘ্য হ্রাস পায় = 4 - 3.4
= .6

শতকরা হ্রাস পায় = (.6/4) × 100%
= 15%

৪৩৮.

A man spends 75% of his income. His income has increased by 20% and he has increased his expenses by 10%. His saving is increased by -

ক
57%
খ
60%
গ
65%
ঘ
75%
ঙ
50%

ব্যাখ্যা

Let his initial income is 100 taka
He spends = 75 taka
So, his savings is = 100 - 75 = 25 taka
Income increases by 20%
So new income is 120 taka
At 10% increase, the expense is = 75 + 10% of 75 = 83.5
So, now the savings is = 120 - 83.5 = 37.5
His savings increases = 37.5 - 25 = 12.5 taka
In percent = (12.5×100) / 25 = 50%

৪৩৯.

In a certain organization, 40% of employees are matriculated, 50% of the remaining are graduates and the remaining 180 are post-graduates. What is the number of graduate employees?

ক
120
খ
320
গ
180
ঘ
410
ঙ
None

ব্যাখ্যা

Question: In a certain organisation, 40% of employees are matriculated, 50% of the remaining are graduates and the remaining 180 are post-graduates. What is the number of graduate employees?

Solution:

Let the total number of employees be p

Then,

(100 - 50)% of (100 - 40)% of p = 180
⇒ 50% of 60% of p = 180
⇒ (50/100) × (60/100) of p = 180
⇒ 3p/10 = 180
⇒ p = (180 × 10)/3
⇒ p =600

∴ Number of graduate employees :

= 50% of 60% of p
= 50% of 60% of 600
= (50/100) × (60/100) × 600
= 180

৪৪০.

65% of a number is more than 25% of the number by 160. What is 20% of that number?

ক
ক) 60
খ
খ) 80
গ
গ) 40
ঘ
ঘ) 120

ব্যাখ্যা

Question: 65% of a number is more than 25% of the number by 160. What is 20% of that number?

Solution:
Let the number be x
According to question,
(65x/100) - (25x/100) = 160
⇒ (65x - 25x)/100 = 160
⇒ 40x/100 = 160
⇒ x = (160 × 100)/40
⇒ x = 400

But we have to find 20%, so (20/100) × 400 = 80

৪৪১.

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

ক
15%
খ
20%
গ
25%
ঘ
30%

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%

৪৪২.

If Kamal's salary is 25% more than Jamal's salary, then Jamal's salary is how much lower than Kamal's salary?

ক
20%
খ
15%
গ
25%
ঘ
10%

ব্যাখ্যা

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

Solution:
Let Jamal's Salary is Tk. 100. Then,
Kamal's Salary = (100 + 25% of 100)
= 100 + (25× 100)/100
= 125

Difference between Kamal's Salary and Jamal's Salary = 125 - 100 = 25

∴ lower = (25/125) × 100 = 20%

∴ Jamal's salary is 20% lower than Kamal's salary.

৪৪৩.

P scored 30% marks and failed by 15 marks. Q scored 45% marks and obtained 30 marks more than the pass marks. What is the pass percentage?

ক
27%
খ
33%
গ
35%
ঘ
40%

ব্যাখ্যা

Question: P scored 30% marks and failed by 15 marks. Q scored 45% marks and obtained 30 marks more than the pass marks. What is the pass percentage?

Solution:
Let the total marks be x.

Given,
P scored 30% marks and failed by 15 marks:
0.30x + 15 = Pass marks
Q scored 45% marks and obtained 30 marks more than the pass marks:
0.45x - 30 = Pass marks

Now,
0.30x + 15 = 0.45x - 30
⇒ 0.45x - 0.30x = 15 + 30
⇒ 0.15x = 45
⇒ x = 45/0.15
∴ x = 300

Pass marks = 0.30 × 300 + 15
= 90 + 15 = 105

∴ Pass percentage = (105/300) × 100% = 35%

৪৪৪.

In an election, 30% of the voters voted for candidate A whereas 60% of the remaining voted for candidate B. The remaining voters did not vote. If the difference between those who voted for candidate A and those who did not vote was 1200, how many individuals were eligible for casting vote in that election?

ক
70000
খ
60000
গ
77000
ঘ
68000

ব্যাখ্যা

Question: In an election, 30% of the voters voted for candidate A whereas 60% of the remaining voted for candidate B. The remaining voters did not vote. If the difference between those who voted for candidate A and those who did not vote was 1200, how many individuals were eligible for casting vote in that election?

Solution:
Let, the number of persons eligible to vote be = x

Then,
votes who voted for A = 30% of x
Votes who voted for B = 60% of (70% of x)
= {(60/100) × (70/100) × 100} % of x
= 42% of x

Now,
Voters who did not vote = [100 - (30 + 42)]% of x
= 28% of x

∴ 30% of x - 28% of x = 1200
⇒ 2% of x = 1200
⇒ x = (1200 × 100)/2
⇒ x = 60000

৪৪৫.

The price of a mobile set is Tk 8,000 and that of a tab is 50% more than the price of a mobile set. If a total of 18 mobiles and tabs were sold for a total of Tk 188,000, how many tabs were sold?

ক
9
খ
11
গ
13
ঘ
14
ঙ
None

ব্যাখ্যা

Question: The price of a mobile set is Tk 8,000 and that of a tab is 50% more than the price of a mobile set. If a total of 18 mobiles and tabs were sold for a total of Tk 188,000, how many tabs were sold?

Solution:
Given that,
Price of mobile = Tk. 8,000
Price of tab = 50% more than mobile
= 8,000 + (50/100) × 8,000
= 8,000 + 4000 = Tk. 12,000
Total items sold = 18 (mobiles + tabs)
Total sales = Tk 188,000

Now, Let, Number of mobiles = m,Number of tabs = t
Then we get,
m + t = 18
∴ m = 18 - t .......(1)

And,
8000m + 12000t = 188,000
⇒ 2m + 3t = 47 ; [Dividing by 4,000]
⇒ 2(18 - t) + 3t = 47 ; [From (1)]
⇒ 36 - 2t + 3t = 47
⇒ t = 47 - 36
∴ t = 11

∴ The number of tabs sold is 11.

৪৪৬.

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

ক
10%
খ
15%
গ
20%
ঘ
25%

ব্যাখ্যা

৪৪৭.

The price of a flower is 25% more than the price of a book. The price of a flower-vase is 75% more than the price of the book. How much is the price of the flower-vase more than the price of the flower?

ক
ক) 20%
খ
খ) 25%
গ
গ) 30%
ঘ
ঘ) 40%

ব্যাখ্যা

Let the price of book
= Tk. 100

Price of flower
= Tk. (100 + 100 × 25%)
= Tk. 125

Price of flower-vase
= Tk. (100 + 100 × 75%)
= Tk. 175

Difference of flower-vase and flower's price
= Tk. (175 -125)
= Tk. 50

∴ Price of the flower-vase more than the price of the flower (in percentage)
= {(50×100)/125}%
= 40%

৪৪৮.

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

ক
33.33% loss
খ
40% loss
গ
36% gain
ঘ
28% gain

ব্যাখ্যা

Question: A man buys an article for 20% more than its value and sells it for 20% less than its value. His gain or loss percentage is –

Solution:
Let the original value of the article = 100 টাকা
∴ Cost Price (CP) = 100 + 20% of 100 টাকা
= 100 + 20 = 120 টাকা

∴ Selling Price (SP) = 100 - 20% of 100 টাকা
= 100 - 20 = 80 টাকা

Since SP (80 টাকা) is less than CP (120 টাকা), there is a Loss.

∴ Loss = CP - SP = 120 - 80 = 40 টাকা
∴ Loss percentage = (Loss/CP) × 100%
= (40/120) × 100%
= (1/3) × 100%
= 33.33% loss

৪৪৯.

35% of Nabila's income is equal to 25% of Sakira's income. The ratio of their income is

ক
5 : 7
খ
4 : 7
গ
7 : 3
ঘ
4 : 3

ব্যাখ্যা

35% of Nabila's income = 25% of Sakira's income
Nabila's income/Sakira's income = 25/35 = 5/7

৪৫০.

A shopkeeper marks the price of an article at TK. 80. What will be the selling price, if he allows two successive discounts of 5% each?

ক
ক) Tk. 72
খ
খ) Tk. 85
গ
গ) Tk. 72.2
ঘ
ঘ) Tk. 7.2

ব্যাখ্যা

At 5% discount for the first time = 80 × 95/100 = Tk. 76
At 5% discount for second time = 76 × 95/100 = Tk. 72.20

৪৫১.

A wholesaler buys a television for Tk. 18,000 and sells it to a retailer at a profit of 30%. The retailer then sells it to a customer at a profit of 25%. How much does the customer pay to the retailer?

ক
Tk. 29250
খ
Tk. 31520
গ
Tk. 33500
ঘ
Tk. 28570

ব্যাখ্যা

Question: A wholesaler buys a television for Tk. 18,000 and sells it to a retailer at a profit of 30%. The retailer then sells it to a customer at a profit of 25%. How much does the customer pay to the retailer?

সমাধান:
পাইকারের 30% লাভে বিক্রয়মূল্য = 18,000 + 18,000 এর 30%
= 18,000 + (18,000 × 30/100)
= 18,000 + 5,400 = 23,400 টাকা

পাইকারের বিক্রয়মূল্য = খুচরা বিক্রেতার ক্রয়মূল্য = 23,400 টাকা

খুচরা বিক্রেতার 25% লাভে বিক্রয়মূল্য = 23,400 + 23,400 এর 25%
= 23,400 + (23,400 × 25/100)
= 23,400 + 5,850 = 29,250 টাকা

সুতরাং, খুচরা বিক্রেতার বিক্রয়মূল্য = ক্রেতার ক্রয়মূল্য = Tk. 29,250

৪৫২.

Which phrase is the most similar in meaning to "pass the buck"?

ক
Face the consequences
খ
Accept responsibility
গ
Offer assistance
ঘ
Passing judgment
ঙ
None of the above

ব্যাখ্যা

• The most similar in meaning to "pass the buck" - Shift the blame.
- অপশনে "pass the buck" এর সামঞ্জস্যপূর্ণ অর্থ না থাকায় "None of the above" উত্তর হবে।

• Pass the buck
English Meaning: to blame someone or make them responsible for a problem that others should deal with.
Bangla Meaning: অন্যায়ভাবে দোষারোপ করা / এক জনের দোষ অন্যের ঘাড়ে চাপানো।

Ex. Sentence: She's always trying to pass the buck and I'm sick of it!
Bangla Meaning: সে সময়ই অন্যায়ভাবে দোষারোপ করার চেষ্টা করে এবং আমি এটা নিয়ে বিরক্ত।

Source: Live MCQ Lecture.

৪৫৩.

The difference between the selling price and cost price of an article is Tk. 210. If the profit percent is 25, then the selling price of the article is =?

ক
Tk. 950
খ
Tk. 1050
গ
Tk. 2000
ঘ
Tk. 2250

ব্যাখ্যা

Question: The difference between the selling price and cost price of an article is Tk. 210. If the profit percent is 25, then the selling price of the article is =?

Solution:
Let, selling price of the article is x taka
cost price x - 210

ATQ,
210/(x - 210) = 25/100
⇒ 210/(x - 210) = 1/4
⇒ x - 210 = 840
∴ x = 1050 taka

৪৫৪.

A sold a watch to B at a gain of 20% and B sold it to C at loss of 10%. If C bought the watch for TK.216 at what price did A purchase it?

ক
Tk. 180
খ
Tk. 200
গ
Tk. 210
ঘ
Tk. 220

ব্যাখ্যা

Question: A sold a watch to B at a gain of 20% and B sold it to C at loss of 10%. If C bought the watch for TK.216 at what price did A purchase it?

Solution:
A purchase at x taka
selling price of A = purchasing price of B = x + 20% of x = 1.2x
buying price of C = 1.2x - 10% of 1.2x = 1.2x - 0.12x = 1.08x

1.08x = 216
⇒ x = 216/1.08 = Tk. 200

৪৫৫.

From a container, full of pure milk, 20% is replaced by water and this process is repeated two times. At the end of second operation, the quantity of pure milk reduces to-

ক
38%
খ
45%
গ
55%
ঘ
64%

ব্যাখ্যা

Question: From a container, full of pure milk, 20% is replaced by water and this process is repeated two times. At the end of second operation, the quantity of pure milk reduces to-

Solution:
ধরি, শুরুতে দুধের পরিমাণ ১০০ লিটার

২০% পানি দ্বারা প্রতিস্থাপন করলে, বিশুদ্ধ দুধের পরিমাণ = ১০০ - ২০ লিটার
= ৮০ লিটার

দ্বিতীয়বার পুনরায় ২০% দ্বারা পানি প্রতিস্থাপন করলে, বিশুদ্ধ দুধের পরিমাণ = ৮০ - ৮০ এর ২০%
= ৮০ - ১৬
= ৬৪ লিটার

অতএব, ৬৪% বিশুদ্ধ দুধ থাকে।

৪৫৬.

During a certain season, a team won 80 percent of its first 100 games and 50 percent of its remaining games. If the team won 70 percent of its games for the entire season, what was the total number of games that the team played?

ক
ক) 180
খ
খ) 170
গ
গ) 156
ঘ
ঘ) 150

ব্যাখ্যা

Let the number of the remaining games be x
then,
0.8×100 + 0.5×x = 0.7×(100+x)
⇒ 80 - 70 = 0.7x - 0.5x = 0.2x
⇒ x = 50
∴ total number of games thus equal to = 100+x
= 100+50
= 150

৪৫৭.

A dealer buys an article marked at Tk. 25000 with 20% and 5% off. He spends Tk. 1000 for its repairs and sells it for Tk. 25000. What is his profit or loss percent?

ক
ক) loss of 20%
খ
খ) loss of 25%
গ
গ) profit of 25%
ঘ
ঘ) profit of 15%

ব্যাখ্যা

Question: A dealer buys an article marked at Tk. 25000 with 20% and 5% off. He spends Tk. 1000 for its repairs and sells it for Tk. 25000. What is his proft or loss percent?

Solution:
Given,
Marked Price = 25000.

After first discount it become,
= 25000 - 20% of 25000
= Tk. 20000.

After second discount, it becomes
= 20000 - 5% of 20000
= Tk. 19000.

So, Selling price = Tk. 19000.

Cost price for the man who bought it, as he spends tk. 1000 on repair.

∴ Cost price = (19000 + 1000) = Tk. 20000

∴ Profit = 25000 - 20000 = Tk. 5000.
% Profit = (5000 × 100)/20000
= 25%

৪৫৮.

Rafiq bought 120 storybooks at Tk. 250 each and sold them at a profit of 15%. Find the total profit he made.

ক
4500 Tk.
খ
500 Tk.
গ
5500 Tk.
ঘ
45000 Tk.

ব্যাখ্যা

Question: Rafiq bought 120 storybooks at Tk. 250 each and sold them at a profit of 15%. Find the total profit he made.

Solution:
Cost Price of 120 storybooks = 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

৪৫৯.

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

ক
ক) 10%
খ
খ) 20%
গ
গ) 15%
ঘ
ঘ) 25%

ব্যাখ্যা

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

Solution:
Numbers from 1 to 50 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%

৪৬০.

Atul sells a bicycle to Bijoy at a profit of 20%. Bijoy sells it to Jalal at a profit of 25%. If Jalal pays Tk. 225 for it, the cost price of the bicycle for Atul is =?

ক
Tk. 150
খ
Tk. 130
গ
Tk. 125
ঘ
Tk. 120

ব্যাখ্যা

Question: Atul sells a bicycle to Bijoy at a profit of 20%. Bijoy sells it to Jalal at a profit of 25%. If Jalal pays Tk. 225 for it, the cost price of the bicycle for Atul is =?

Solution:
cost price of the bicycle for Bijoy = 225/1.25
= (225 × 100)/125
= 180 taka

cost price of the bicycle for Atul = 180/1.2
= (180 × 10)/12
= 150 taka

৪৬১.

Nabil's monthly income is reduced by 15%. By what percentage his monthly income must be increased so that it is again equal to his original monthly income?

ক
16.6%
খ
15.6%
গ
14.6%
ঘ
17.6%

ব্যাখ্যা

Question: Nabil's monthly income is reduced by 15%. By what percentage his monthly income must be increased so that it is again equal to his original monthly income?

Solution:
Let,
Nabil's monthly income is Tk. 100.
After reduced 15%,
Nabil's monthly income after reduced (100 - 15) = 85

Nabil's monthly income must be increased Tk. 15 so that it is again equal to his original monthly income.

∴ Percentage his monthly income must be increased = (15/85) × 100%
= 17.6%

৪৬২.

If a rectangle's length and width are both doubled, by what percent is the rectangle's area increased?

ক
ক) 50%
খ
খ) 100%
গ
গ) 200%
ঘ
ঘ) 300%

ব্যাখ্যা

Question: If a rectangle's length and width are both doubled, by what percent is the rectangle's area increased?

Solution:
ধরি,
আয়তক্ষেত্রের দৈর্ঘ্য ক একক
আয়তক্ষেত্রের প্রস্থ খ একক
∴ আয়তক্ষেত্রের ক্ষেত্রফল কখ বর্গএকক

দৈর্ঘ্য ও প্রস্থ দ্বিগুণ হলে ক্ষেত্রফল হবে = ২ক × ২খ বর্গএকক
= ৪কখ বর্গএকক

ক্ষেত্রফল বৃদ্ধি পায় = (৪কখ - কখ) বর্গএকক
= ৩কখ

কখ বর্গএকক এ বৃদ্ধি পায় ৩কখ বর্গএকক
∴ ১ বর্গএকক এ বৃদ্ধি পায় (৩কখ)/(কখ) = ৩ বর্গএকক
∴ ১০০ বর্গএকক এ বৃদ্ধি পায় ৩ × ১০০ বর্গএকক
= ৩০০ বর্গএকক

∴ আয়তক্ষেত্রের ক্ষেত্রফল ৩০০% বৃদ্ধি পাবে।

৪৬৩.

A merchant marks up his goods by 25% above the cost price. He then offers a discount of 10% on the marked price. What is the overall percentage profit?

ক
10%
খ
12.5%
গ
15%
ঘ
20%

ব্যাখ্যা

Question: A merchant marks up his goods by 25% 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 = 25% more than the cost price
= 100 + 25
= Tk. 125

Discount = 10% of 125
= (10/100) × 125
= Tk. 12.5

Selling Price (SP) = 125 - 12.5 = Tk. 112.5

∴ Profit = SP - CP = 112.5 - 100 = Tk. 12.5

∴ Overall percentage profit = (profit/cost price) × 100%
= (12.5/100) × 100%
= 12.5%

৪৬৪.

A shopkeeper incurs a loss by selling an article for Tk 600. If he had sold it for Tk 900, he would have made a profit which is three times the initial loss. At what price should he sell the article to make 20% profit?

ক
Tk. 790
খ
Tk. 810
গ
Tk. 850
ঘ
Tk. 920

ব্যাখ্যা

Question: A shopkeeper incurs a loss by selling an article for Tk 600. If he had sold it for Tk 900, he would have made a profit which is three times the initial loss. At what price should he sell the article to make 20% profit?

Solution:
ধরি, পণ্যের ক্রয়মূল্য = x টাকা
600 টাকায় বিক্রি করলে ক্ষতি = x - 600 টাকা
900 টাকায় বিক্রি করলে লাভ = 900 - x টাকা

প্রশ্নমতে,
900 - x = 3(x - 600)
⇒ 900 - x = 3x - 1800
⇒ 900 + 1800 = 3x + x
⇒ 2700 = 4x
∴ x = 675 টাকা

এখন, 20% লাভে,
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য 120 টাকা
ক্রয়মূল্য 1 টাকা হলে বিক্রয়মূল্য 120/100 টাকা
∴ ক্রয়মূল্য 675 টাকা হলে বিক্রয়মূল্য = (120 × 675)/100 টাকা
= 810 টাকা

∴ বিক্রয়মূল্য: Tk. 810

৪৬৫.

The numerical value of the profit % is equal to the cost price of a book on selling it at Tk. 96. So, how much profit (in Tk.) is there on selling it?

ক
ক) 24
খ
খ) 52
গ
গ) 36
ঘ
ঘ) None of above

ব্যাখ্যা

Question: The numerical value of the profit % is equal to the cost price of a book on selling it at Tk. 96. So, how much profit (in Tk.) is there on selling it?

Solution:

Let the CP of the book be = Tk. x
So, the profit will be x%.
SP of the book = Tk. 96

Hence,
⇒ x = {(96 - x)/x} × 100
⇒ x² + 100x - 9600 = 0
⇒ x² + 160x - 60x - 9600 = 0
⇒ x(x + 160) - 60(x + 160) = 0
⇒ x = 60, -160

So, CP of a book = Tk. 60
⇒ Profit = Tk. 96 - Tk. 60
⇒ Profit = Tk.36

Hence, the correct answer is "36".

৪৬৬.

Prateek sold a music system to Karthik at 20% gain and karthik sold it to Swastik at 40% gain. If Swastik paid Tk. 10500 for the music system, What amount did Prateek pay for the same?

ক
ক) Tk. 6250
খ
খ) Tk. 7200
গ
গ) Tk. 8240
ঘ
ঘ) Cannot be determined

ব্যাখ্যা

Let the price paid by Prateek be Tk. x
Then,
140% of 120% of x=10500
⇒(140/100)×(120/100)×x=10500
⇒ x=(10500×25/42)=6250

৪৬৭.

If two numbers are respectively 30% and 40% more than a third number, what percent is the first of the second?

ক
87.52%
খ
94.88%
গ
99.85%
ঘ
92.86%
ঙ
None of these

ব্যাখ্যা

Question: If two numbers are respectively 30% and 40% more than a third number, what percent is the first of the second?

Solution:
Let the third number be 100
Then,
1st number = 100 + 30 = 130
2nd number = 100 + 40 = 140

To find what percent the first number is of the second number is,
=(130 × 100)/140
= 650/7
=92.86%

∴ The first number is 92.86% of the second number.

৪৬৮.

Rimi bought a mobile phone at a discount of 20%. Had the discount received was 25%, she would have saved Tk 2,000 more. How much did she pay (in Tk) for the mobile phone?

ক
ক) 32,000
খ
খ) 24,000
গ
গ) 18,000
ঘ
ঘ) 36,000

ব্যাখ্যা

Question : Rimi bought a mobile phone at a discount of 20%. Had the discount received was 25%, she would have saved Tk 2,000 more. How much did she pay (in Tk) for the mobile phone?

Solution:

Let the actual price of the phone be 100x

Cost price of Rimi = 100x × (100 - 20)%
⇒ 100x × 80%
⇒ 80x

If 25% discount is given then,
Cost price of Rimi = 100x × (100 - 25)%
⇒ 75x

According to the question,
80x - 75x = 2000
⇒ 5x = 2000
⇒ x = 400

So, actual cost price of Rimi = 80 × 400
⇒ 32000

∴ She paid 32000 (in Tk) for the mobile phone.

৪৬৯.

A dishonest dealer marks up the price of his goods by 20% and gives a discount of 10% to the customer. He also uses a 900 gram weight instead of a 1 kilogram weight. Find his percentage profit due to these maneuvers?

ক
11%
খ
14%
গ
20%
ঘ
18%

ব্যাখ্যা

Question: A dishonest dealer marks up the price of his goods by 20% and gives a discount of 10% to the customer. He also uses a 900 gram weight instead of a 1 kilogram weight. Find his percentage profit due to these maneuvers?

Solution:
Let Cost Price, CP = Tk. 1 per gram

Dealer marks up by 20%,
Then the Marked Price of 1000 gram is = 1000 + 20% of 1000
= 1000 + 200 =Tk. 1200

Now Dealer gives 10% discount,
So, Selling price after discount = 1200 - 10% of 1200
= 1200 - 120 = Tk. 1080

Then, Dealer is dishonest and sells 900 grams for the price of 1080 Tk.
The Cost Price of 900 grams is Tk. 900 (since the cost price per gram is Tk. 1).

Profit = 1080 - 900 = 180
so, Percentage profit = (Profit/Cost Price) × 100%
= (180/900) × 100%
= 20%

৪৭০.

Rasel started a business investing Tk. 9000. After five months, Sohel joined with a capital of Tk. 8000. If at the end of the year, they earn a profit of Tk. 6970, then what will be the share of Sohel in the profit ?

ক
ক) Tk. 2380
খ
খ) Tk. 2480
গ
গ) Tk. 2580
ঘ
ঘ) Tk. 2680

ব্যাখ্যা

Question: Rasel started a business investing Tk.. 9000. After five months, Sohel joined with a capital of Tk. 8000. If at the end of the year, they earn a profit of Tk.. 6970, then what will be the share of Sohel in the profit ?

Solution:
লভ্যাংশের অনুপাত = ৯০০০ × ১২ : ৮০০০ × (১২ - ৫)
= ১০৮০০০ : ৫৬০০০
= ১০৮ : ৫৬
= ২৭ : ১৪

সোহেলের লাভ = (১৪ × ৬৯৭০)/(২৭ + ১৪)
= (১৪ × ৬৯৭০)/৪১
= ২৩৮০ টাকা

৪৭১.

By selling a TV for Tk.29,500 instead of Tk.30,000,the profit decreases by 10%. What is the cost of the TV in Taka?

ক
ক) 24000
খ
খ) 25000
গ
গ) 26000
ঘ
ঘ) None

ব্যাখ্যা

Suppose, Cost Price = x & Profit = y
So, x + y = 30,000.......... (i)
x + 0.9y = 29,500....... (ii)
(i) - (ii), we get
y = 5000
So, Cost Price = 30,000 - 5000 = 25,000 Taka
বিকল্প পদ্ধতিঃ
লাভ কমলো = ৩০,০০০ - ২৯,৫০০ = ৫০০ টাকা।
প্রশ্নমতে,
১০ % = ৫০০
∴ ১০০ % = (৫০০ × ১০০)/১০ = ৫০০০ টাকা।
অর্থাৎ,
বিক্রয়মূল্য = ৩০, ০০০ টাকা।
মোট লাভ = ৫,০০০ টাকা।
∴ ক্রয়মূল্য = (৩০,০০০ - ৫,০০০) টাকা।
= ২৫,০০০ টাকা।

৪৭২.

A man sells 2 commodities for Tk. 3500 each, neither losing nor gaining in the deal. If he sold one commodity at a gain of 25%, then what is the cost price of another commodity?

ক
TK. 3600
খ
TK. 3800
গ
TK. 4200
ঘ
TK. 4500

ব্যাখ্যা

Question: A man sells 2 commodities for Tk. 3500 each, neither losing nor gaining in the deal. If he sold one commodity at a gain of 25%, then what is the cost price of another commodity?

Solution:
Total S.P. = Tk. 7000 and
Total C.P. = Tk. 7000
Let,
S.P. of 1st commodity = Tk. 3500
Gain on it = 25%

∴ C.P. of 1st commodity
= Tk. {(100/125)×3500}
= Tk. 2800

C.P. of 2nd commodity = Tk. (7000 - 2800) = TK. 4200

৪৭৩.

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

ক
Tk. 83
খ
Tk. 79
গ
Tk. 80
ঘ
Tk. 81

ব্যাখ্যা

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

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

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

৪৭৪.

There is an 80% increase in an amount in 8 years at simple interest. What will be the compound interest of Tk. 14,000 after 3 years at the same rate?

ক
ক) Tk. 3794
খ
খ) Tk. 4612
গ
গ) Tk. 4634
ঘ
ঘ) Tk. 3714

ব্যাখ্যা

80% increase in 8 years at simple interest. That is 10% each year.
Therefore,
Rate of interest is 10%
10% (14000) = 1400
10% (1400) = 140
10% (140) = 14
Required compound interest = 3(1400 + 140) + 14
= Tk. 4634.

৪৭৫.

The percentage profit earned by selling an article for TK 1730 is equal to the percentage loss incurred by selling the same article for TK 1270. At what price should the article be sold to make 20% profit?

ক
1800 TK
খ
2000 TK
গ
2400 TK
ঘ
2800 TK
ঙ
3000 TK

ব্যাখ্যা

Question: The percentage profit earned by selling an article for TK 1730 is equal to the percentage loss incurred by selling the same article for TK 1270. At what price should the article be sold to make 20% profit?

Solution:
Let C.P. = x TK
Profit = (1730 - x) TK
Loss = (x - 1270) TK

ATQ,
{(1730 - x)/x}100 = {(x - 1270)/x}100
⇒ 1730 - x = x - 1270
⇒ 2x = 3000
⇒ x = 1500

Required selling price for 20% profit = (1500 × 120%) TK
= 1500 × (120/100)
= 1500 × (6/5)
= 1800 TK

৪৭৬.

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

ক
ক) 50%
খ
খ) 100%
গ
গ) 200%
ঘ
ঘ) 300%

ব্যাখ্যা

প্রশ্ন: Novera bought a ticket to a cricket match for Tk. 25 and later sold the ticket to Nahid for Tk 75. What was the percent increase in the price of the ticket?

সমাধান:
নভেরা একটি টিকিট ২৫ টাকায় কিনে। সে ৭৫ টাকায় টিকিটটি নাহিদের কাছে বিক্রি করে।

টিকিটের মূল্য শতকরা বৃদ্ধি পায় = (৭৫ - ২৫)/২৫ × ১০০%
= (৫০/২৫) × ১০০%
= ২০০%

৪৭৭.

Rahim purchased items worth Tk. 40, including a sales tax of 60 paisa on taxable purchases. If the tax rate was 8%, what was the cost of the tax-free items?

ক
Tk. 29.3
খ
Tk. 31.9
গ
Tk. 29.1
ঘ
Tk. 33.1

ব্যাখ্যা

Question: Rahim purchased items worth Tk. 40, including a sales tax of 60 paisa on taxable purchases. If the tax rate was 8%, what was the cost of the tax-free items?

Solution:
Let the cost of taxable purchases be x taka.

According to the question,
0.08x = 60/100
⇒ x = 60/(100 × 0.08)
= 7.5 taka

∴ The cost of the tax-free items was = 40 - 7.5 - 0.6
= Tk. 31.9

৪৭৮.

What is the discount rate percentage on a gift whose selling price is Tk. 420 after a reduction of Tk. 60 on its marked price?

ক
ক) 7.2%
খ
খ) 10%
গ
গ) 8.9%
ঘ
ঘ) 12.5%

ব্যাখ্যা

Question: What is the discount rate percentage on a gift whose selling price is Tk. 420 after a reduction of Tk. 60 on its marked price?

Solution:

SP of the gift = Tk. 420
Discount = Tk. 60

MP of the gift = Tk. 420 + Tk. 60 = Tk. 480
Discount percentage = (60/480) × 100 = 12.5%

৪৭৯.

The population of a city 3 years ago was 1,28,000. If it decreased by 5% every year, then the present population of the city is -

ক
89750
খ
119035
গ
99744
ঘ
109744

ব্যাখ্যা

Population of the city 3 years ago = P = 128000 and n = 3
And,
The decreasing percentage = R = 5%
The present population = P × (1 - R/100)ⁿ [Population after n years = P × (1 - R/100)ⁿ]
128000 x (1 - 5/100)³
= 128000 × (19/20) × (19/20) × (19/20)
= 16 × 6859 = 109744.
Hence the answer is 109744.

৪৮০.

How much is 80% of 40 greater than 4/5 of 25?

ক
ক) 4
খ
খ) 6
গ
গ) 9
ঘ
ঘ) 12

ব্যাখ্যা

Question: How much is 80% of 40 greater than 4/5 of 25?

Solution:
80% of 40 = 0.8 × 40
= 32

4/5 of 25 = 20

∴ difference = 32 - 20
= 12

৪৮১.

If a man was to sell his table for Tk. 600, he would lose 20%. To gain 20% he should sell it for:

ক
Tk. 900
খ
Tk. 1000
গ
Tk. 1040
ঘ
Tk. 1200

ব্যাখ্যা

Question: If a man was to sell his table for Tk. 600, he would lose 20%. To gain 20% he should sell it for:

Solution:
Let the Cost price of the table be = x.

∴ Selling price = x - 20% of x
⇒ 600 = x - (20x/100)
⇒ 600 = 80x/100
⇒ 80x = 60000
⇒ x = 60000/80
∴ x = 750

Now, To gain 20% = 750 + 20% of 750
= 750 + 150
= Tk. 900

৪৮২.

In a town, 64 percent of the population is employed, and 48 percent of the population is employed males. What percentage of the employed people in that town is female?

ক
ক) 16%
খ
খ) 25%
গ
গ) 32%
ঘ
ঘ) 40%

ব্যাখ্যা

Given that, Total employed people are 64% of the population, out of that population 48% are employed males, hence 16% are employed females.

So, (employed females)/(total employed people)
= 16/64
= (1/4)
= 25%

৪৮৩.

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

ক
ক) 25%
খ
খ) 20%
গ
গ) 80%
ঘ
ঘ) 75%

ব্যাখ্যা

Let the initial expenses on Sugar was Tk. 100.
Now, Price of Sugar rises 25%. So, to buy same amount of Sugar, they need to expense,
= (100 + 25% of 100) = Tk. 125.
But, They want to keep expenses on Sugar, so they have to cut Tk. 25 in the expenses to keep it to Tk. 100.
Now, % decrease in Consumption,
(25/125)×100=20%

৪৮৪.

The tax on a commodity is diminished by 10% and its consumption increases by 10%. Find the effects on revenue.

ক
Increases by 2%
খ
Decreases by 1%
গ
Increases by 1%
ঘ
Decreases by 2%

ব্যাখ্যা

Question: The tax on a commodity is diminished by 10% and its consumption increases by 10%. Find the effects on revenue.

Solution:
Revenue is directly proportional to consumption (C) and tax (T).
Initial revenue = C × T

When tax decrease by 10% and consumption increases by 10%
New revenue =(C + 10C/100) × (T - 10T/100)
New revenue = (110C/100) × (90T/100)
New revenue = 0.99 × C × T
Thus, % decrease in revenue = [{(C × T) − (0.90 × C × T)}/(C × T)] ×100 = 1%

৪৮৫.

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

ক
Tk. 10,000
খ
Tk. 20,000
গ
Tk. 20,800
ঘ
Tk. 24,000

ব্যাখ্যা

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

৪৮৬.

A number is divided into two parts in such a way that 60% of 1st part is 2 more than the 40% of 2nd part and 60% of the 2nd part is 1 more than the 40% of 1st part. Find the number.

ক
12
খ
15
গ
16
ঘ
18

ব্যাখ্যা

Question: A number is divided into two parts in such a way that 60% of 1st part is 2 more than the 40% of 2nd part and 60% of the 2nd part is 1 more than the 40% of 1st part. Find the number.

Solution:
Let,
Two part of the number be a, b respectively
∴ The number = a + b

ATQ,
60% of a - 40% of b = 2
⇒ (60/100)a - (40/100)b = 2
∴ 6a - 4b = 20…………(1)

and
60% of b - 40% of a = 1
⇒ (60/100)b - (40/100)a = 1
∴ 6b - 4a = 10………….(2)

From (1) × 2 + (2) × 3 we get,
12a - 8b + 18b - 12a = 40 + 30
⇒ 10b = 70
∴ b = 7

Put b in 1, we get
6a - 28 = 20
⇒ 6a = 48
∴ a = 8

Hence, the number is (7 + 8) = 15

৪৮৭.

By what percentage should the cost price of an article be increased, so as to earn a profit of 20% even after allowing a discount of 40% on the price marked on the article?

ক
33.33%
খ
50%
গ
66.67%
ঘ
100%

ব্যাখ্যা

Discount = 40%
S.P. = (100-40)% of M.P. = 60% of M.P.
Profit = 20%

∴ S.P. = (100+20)% of C.P.
∴ 60% x MP = 120% of C.P.
∴ C.P. = (1/2) M.P.
∴ MP = 2CP

Since MP should be twice of C.P. to fit into the criteria, we need to increase C.P. by 100% to make it MP.

৪৮৮.

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

ক
500
খ
450
গ
350
ঘ
400

ব্যাখ্যা

Question: In an examination, 85% of examinees passed in Mathematics. If total 75 examinees failed in Mathematics, 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

৪৮৯.

A man spends 75% of his income, His income increases by 20% & his expenditure increases by 15%. His savings are then increased by -

ক
ক) 5%
খ
খ) 10%
গ
গ) 23%
ঘ
ঘ) 35%

ব্যাখ্যা

ধরি,
লোকটির আয় ১০০ টাকা

লোকটির ব্যয় = ৭৫ টাকা
লোকটির সঞ্চয় = ২৫ টাকা

২০% বৃদ্ধিতে নতুন আয় = (১০০ + ২০) টাকা = ১২০ টাকা
১৫% বৃদ্ধিতে নতুন ব্যয় = ৭৫ + ৭৫ এর ১৫%
= ৭৫ + ৭৫ এর ১৫/১০০
= ৮৬.২৫ টাকা

নতুন সঞ্চয় = (১২০ - ৮৬.২৫) টাকা
= ৩৩.৭৫ টাকা

সঞ্চয় বাড়ে = (৩৩.৭৫ - ২৫) টাকা = ৮.৭৫ টাকা

শতকরা বাড়ে = {(৮.৭৫/২৫) × ১০০}% = ৩৫%

৪৯০.

If the price of petrol is increased by 10% to keep the expenditure value constant, then how much percentage must be reduced in its consumption?

ক
9.09%
খ
15%
গ
16.67%
ঘ
17.765
ঙ
12%

ব্যাখ্যা

Let before increasing the price of petrol we are purchasing 1-litre petrol in 100 tk. So total quantity 100×1=100.

After increasing the price of petrol by 10% let we are receiving x litre petrol. Then final quantity 110×x=100x

After equating the initial and final quantity we will get the value of x.

100×1=110×x
Then x=10÷11

Initially, we are getting 1 litre and after increment, we are getting 10÷11
Reduction in the amount of petrol = 1-(10÷11) = 1÷11
Reduction in the amount of petrol in percentage = 1÷11×100 = 100÷11 = 9.09%

৪৯১.

A shopkeeper sells a pair of sunglasses at a profit of 25%. If he had bought it at 25% less and sold it for Tk. 10 less, he would have gained 40%. Determine the cost price of the pair of sunglasses.

ক
ক) Tk. 25
খ
খ) Tk. 30
গ
গ) Tk. 50
ঘ
ঘ) Tk. 75

ব্যাখ্যা

Question: A shopkeeper sells a pair of sunglasses at a profit of 25%. If he had bought it at 25% less and sold it for Tk. 10 less, he would have gained 40%. Determine the cost price of the pair of sunglasses.

Solution:
ধরি,
ক্রয়মূল্য = 100 টাকা
25% লাভে বিক্রয়মূল্য = 100 + 25 = 125 টাকা
25% কমে ক্রয়মূল্য = 100 - 25 = 75 টাকা

আবার,
40% লাভে বিক্রয়মূল্য = {75 + 75 × (40/100)}
= 105 টাকা
বিক্রয়মূল্য কম হয় = (125 - 105) টাকা
= 20 টাকা

এখন,
২০ টাকা বিক্রয়মূল্য কম হয় ক্রয়মূল্য = 100 টাকায়
∴ 10 টাকা বিক্রয়মূল্য কম হয় ক্রয়মূল্য = (100 × 10)/20 টাকায়
= 50 টাকা

৪৯২.

In an examination 80% candidates passed in English and 85% candidates passed in Mathematics. If 73% candidates passed in both these subjects, then what per cent of candidates failed in both the subjects?

ক
8
খ
15
গ
27
ঘ
35
ঙ
None of these

ব্যাখ্যা

Question: In an examination 80% candidates passed in English and 85% candidates passed in Mathematics. If 73% candidates passed in both these subjects, then what per cent of candidates failed in both the subjects?

Solution:
Students passed in English = 80%
Students passed in Math's = 85%
Students passed in both subjects = 73%
Then, number of students passed in at least one subject
= (80 + 85) - 73
= 92%.

Thus, students failed in both subjects = 100 - 92 = 8%.

৪৯৩.

The price of sugar increases by 25%. How much sugar can now be bought with the same amount of money that was earlier sufficient to buy 25 kg of sugar?

ক
22kg
খ
20kg
গ
18kg
ঘ
15kg

ব্যাখ্যা

Question: The price of sugar increases by 25%. How much sugar can now be bought with the same amount of money that was earlier sufficient to buy 25 kg of sugar?

Solution:
Let
Tk. 100 be spent on sugar initially for 25 kg.

As the price increases by 25%, new price for 25 kg sugar = Tk. (100 + 25% of 100)
= Tk. (100 + 25)
= Tk. 125

New price of sugar = Tk. (125/25) = Tk. 5

Sugar can be bought now = 100/5 = 20 kg

৪৯৪.

The price of diesel increases by 50%. Find by how much percent a truck owner must reduce his consumption in order to maintain the same budget?

ক
11.11%
খ
22.22%
গ
33.33%
ঘ
44.44%

ব্যাখ্যা

Question: The price of diesel increases by 50%. Find by how much percent a truck owner must reduce his consumption in order to maintain the same budget?

Solution:
Let,
the initial price of the diesel be Tk. x
Then, after 50% increase in price, it will become Tk. x + (x × 50)/100 = Tk. 1.5x
Now,
we have to reduce the consumption to keep expenditure Tk. x.

Increase in price =1.5x - x = 0.5x
We have to reduce the consumption by (0.5x × 100)/(1.5x) = 33.33%

৪৯৫.

In a store, pens are sold for 25% less than the tag price. If a pen costs Tk. 48, what will be the tag price of the pen to make a 25% profit on its cost?

ক
ক) 64
খ
খ) 72
গ
গ) 80
ঘ
ঘ) None

ব্যাখ্যা

Question: In a store, pens are sold for 25% less than the tag price. If a pen costs Tk. 48, what will be the tag price of the pen to make a 25% profit on its cost?

Solution:
25% লাভে
বিক্রয়মূল্য = (48 × 125/100) = 60 টাকা

25% কমে
ট্যাগ মূল্য = (60 × 100/75) টাকা
= 80 টাকা

৪৯৬.

What percent is 3% of 5%?

ক
15%
খ
30%
গ
50%
ঘ
60%

ব্যাখ্যা

Question: What percent is 3% of 5%?

Solution:
3% = 3/100
5% = 5/100 = 1/20

percentage = {(3/100)/(1/20)} × 100%
= 60%

৪৯৭.

Every 3 minutes, 4 litres of water are poured into a 2,000 litre tank. After 2 hours, what percent of the tank is full?

ক
ক) 0.4%
খ
খ) 4%
গ
গ) 8%
ঘ
ঘ) 12%

ব্যাখ্যা

In 3 minutes, 4 liters is poured
In, 120 minutes = (120×4)/3 = 160 liters
So, percentage filled = (160×100)/2000 = 8%

৪৯৮.

If an inspector rejects 0.08% of a product as defective, how many units of the product will he examine in order to reject 2?

ক
ক) 500
খ
খ) 1500
গ
গ) 2000
ঘ
ঘ) 2500

ব্যাখ্যা

Question: If an inspector rejects 0.08% of a product as defective, how many units of the product will he examine in order to reject 2?

Solution:
ধরি,
ক পরিমান পণ্য পরীক্ষা করতে হবে।

তাহলে,
ক এর ০.০৮% = ২
ক = (২ × ১০০)/০.০৮
= ১০০/০.০৪
= ১০০০০/৪
= ২৫০০

৪৯৯.

Last year Jaman bought two lamps. This year he sold them for BDT 2000 each. On one lamp, he made 25% profit and on the other lamp he had 25% loss. What was his net loss or profit?

ক
ক) Loss BDT 1000
খ
খ) Profit BDT 100
গ
গ) LOSS BDT 100
ঘ
ঘ) No profit loss
ঙ
ঙ) None

ব্যাখ্যা

প্রথম ল্যাম্পের ক্রয়মূল্য ১২৫ক/১০০=২০০০ টাকা
বা, ক = ১৬০০ টাকা।
অর্থাৎ, প্রথম ল্যাম্প থেকে তার লাভ হয় ৪০০ টাকা।
দ্বিতীয় ল্যাম্পের ক্রয়মূল্য ৭৫ক/১০০=২০০০
বা, ক= ২৬৬৬.৬৭ টাকা।
অর্থাৎ, দ্বিতীয় ল্যাম্প থেকে তার ক্ষতি হয় ৬৬৬.৬৭ টাকা।
তাহলে তার সর্বমোট ক্ষতি হয় ৬৬৬.৬৭ - ৪০০ = ২৬৭.৬৭ টাকা যা প্রশ্নের অপশনে নেই।

৫০০.

A shopkeeper sells two articles for Tk. 900 each. On one, he gains 20% and on the other, he loses 20%. What is his overall gain or loss percentage?

ক
2% gain
খ
4% loss
গ
No gain, no loss
ঘ
5% loss

ব্যাখ্যা

Question: A shopkeeper sells two articles for Tk. 900 each. On one, he gains 20% and on the other, he loses 20%. What is his overall gain or loss percentage?

Solution:
Sells price of two books = (900 × 2) = Tk. 1800

Cost price of first book = (100/120) × 900
= Tk. 750

Cost price of second book = (100/80) × 900
= Tk. 1125

∴ Loss = (1125 + 750) - 1800
= 1875 - 1800
= Tk. 75

∴ loss percentage = (75/1875) × 100%
= 4%