Percentage and Profit & Loss

PrepBank · পাতা ১৬ / ১৭ · ১,৫০১–১,৬০০ / ১,৬৯৬

১,৫০১.

What is the profit percentage if a dozen bananas are bought for Tk 37.50 and sold for Tk 39.75?

ক
2.25%
খ
3%
গ
4.25%
ঘ
6%

ব্যাখ্যা

Question: What is the profit percentage if a dozen bananas are bought for Tk 37.50 and sold for Tk 39.75?

Solution:
লাভ = ৩৯.৭৫ - ৩৭.৫০ = ২.২৫ টাকা

৩৭.৫০ টাকায় লাভ হয় = ২.২৫ টাকা
১ টাকায় লাভ হয় = ২.২৫/৩৭.৫০ টাকা
∴ ১০০ টাকায় লাভ হয় = (২.২৫ × ১০০)/৩৭.৫০ টাকা
= (২২৫ × ১০০)/৩৭৫০ টাকা
= ৬ টাকা বা ৬%

১,৫০২.

The price of a pen is 25% more than the price of a book. The price of a pen holder is 50% more than the price of the book. How much is the price of the pen holder more than the price of the pen?

ক
ক) 50%
খ
খ) 25%
গ
গ) 20%
ঘ
ঘ) 37.5%

ব্যাখ্যা

Let the price of book = 100 tk
Price of pen = 100 + 100×25% = 125 tk
Price of penholder = 100 + 100×50% = 150 tk
Difference of penholder and pen's price = 150 -125 = 25 tk

∴ Price of the pen holder more than the price of the pen (in percentage) = {(25×100)/125}% = 20%

১,৫০৩.

A man purchased a shirt at Taka 300 after availing a discount of 25%. What is the catalog price of the shirt?

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

ব্যাখ্যা

Question: A man purchased a shirt at Taka 300 after availing a discount of 25%. What is the catalog price of the shirt?

Solution:
25% ডিসকাউন্টে,
তালিকা মূল্য 100 টাকা হলে ক্রয়মূল্য = 100 - 25 = 75 টাকা

75 টাকা ক্রয়মূল্য হলে তালিকামূল্য = 100 টাকা
1 টাকা ক্রয়মূল্য হলে তালিকামূল্য = 100/75 টাকা
300 টাকা ক্রয়মূল্য হলে তালিকামূল্য = (100 × 300)/75 টাকা
= 400 টাকা

১,৫০৪.

Ahmed sold a t-shirt for Tk. 810, and gain 8%. How much did he purchase it for?

ক
Tk. 750
খ
Tk. 875
গ
Tk. 745
ঘ
Tk. 756

ব্যাখ্যা

Question: Ahmed sold a t-shirt for Tk. 810, and gain 8%. How much did he purchase it for?

Solution:
8% লাভে
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য = (100 + 8) টাকা বা 108 টাকা

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

১,৫০৫.

In ABC College, 65% of students are less than 20 years of age. The number of students more than 20 years of age is 2/3 of number of students of 20 years of age which is 42. What is the total number of students in the ABC College?

ক
75
খ
90
গ
130
ঘ
200

ব্যাখ্যা

Question: In ABC College, 65% of students are less than 20 years of age. The number of students more than 20 years of age is 2/3 of number of students of 20 years of age which is 42. What is the total number of students in the ABC College?

Solution:
Let total number of students is x.
Then, number of students more than or equal to 20 years of age = (100 - 65)% of x = 35% of x.
As per the question,
35% of x = 42 + (2/3 of 42)
⇒ 35x/100 = 70.
⇒ x = (70 × 100)/35
∴ x = 200

১,৫০৬.

If a product is sold at 250% profit, then what is the ratio of buying and selling price?

ক
ক) 1 : 2.5
খ
খ) 1 : 3.5
গ
গ) 3.5 : 1
ঘ
ঘ) 2.5 : 1

ব্যাখ্যা

Question: If a product is sold at 250% profit, then what is the ratio of buying and selling price?

Solution:
ধরি,
ক্রয়মূল্য = ১০০
২৫০% লাভে বিক্রয়মূল্য = ১০০ + ১০০ এর ২৫০%
= ৩৫০

∴ ক্রয়মুল্য : বিক্রয়মুল্য = ১০০ : ৩৫০
= ১ : ৩.৫

১,৫০৭.

By selling 16 toffees for a taka, a man loses 10%. How many toffees for a taka should be sell to get a gain of 20%?

ক
ক) 8
খ
খ) 10
গ
গ) 12
ঘ
ঘ) 15

ব্যাখ্যা

Question: By selling 16 toffees for a taka, a man loses 10%. How many toffees for a taka should be sell to get a gain of 20%?

Solution:
At 10% loss, 90% = Tk. 1
So, at 20% profit 120% = 120/90 = Tk. 4/3
For Tk. 4/3, toffees sold = 16
For Tk. 1, toffees sold = (16 × 3)/4 = 12

১,৫০৮.

A person sold a book at 20% profit and another at 12% loss, both at Tk. 330 each. Find his overall profit or loss percent.

ক
1.54% profit
খ
1.54% loss
গ
3.08% profit
ঘ
3.08% loss

ব্যাখ্যা

Question: A person sold a book at 20% profit and another at 12% loss, both at Tk. 330 each. Find his overall profit or loss percent.

Solution:
Let the cost price of the first book = C1
Let the cost price of the second book = C2

First book:
Sold at 20% profit, Selling Price = 330
C1 × 1.2 = 330
⇒ C1 = 330 / 1.2 = 275

Second book: Sold at 12% loss,
Selling Price = 330
C2 × 0.88 = 330
⇒ C2 = 330 / 0.88 = 375

Total cost price = 275 + 375 = 650
Total selling price = 330 + 330 = 660

Profit/Loss = SP - CP
= 660 - 650
= 10

Profit% = (10/650) × 100%
= 1.538%
= 1.54%

∴ His overall profit = 1.54%

১,৫০৯.

Ashik buys a calculator for Tk. 600 and sells it to Neaz at 10% profit. Neaz sells it to Mahfuj for 5 % profit. Mahfuz after using it for certain time, sells it to Faysal at a loss of 20%. For how much Mahfuz sell the calculator to Faysal.

ক
Tk. 550.50
খ
Tk. 564.40
গ
Tk. 554.40
ঘ
None of these

ব্যাখ্যা

Question: Ashik buys a calculator for Tk. 600 and sells it to Neaz at 10% profit. Neaz sells it to Mahfuj for 5 % profit. Mahfuz after using it for certain time, sells it to Faysal at a loss of 20%. For how much Mahfuz sell the calculator to Faysal.

Solution:
SP for Mahfuz = 600 × (110/100) × (105/100) × (80/100)
= 600 × (924/1000)
= Tk. 554.40

১,৫১০.

Two numbers are respectively 20% and 50% of the third number. What percent is the first number of the second ?

ক
ক) 10%
খ
খ) 20%
গ
গ) 30%
ঘ
ঘ) 40%

ব্যাখ্যা

Let the 3rd number is 100
According to the question,
1st :2nd: 3rd= 20:50:100
Required % = (20/50) × 100 = 40%

১,৫১১.

Mr. Khan's salary is Tk. 5000.00 and he gets 10% commission of his salary. If his salary increased by 10%, by what percent his commission will increase?

ক
ক) 5%
খ
খ) 10%
গ
গ) 20%
ঘ
ঘ) 25%

ব্যাখ্যা

Question: Mr. Khan's salary is Tk. 5000.00 and he gets 10% commission of his salary. If his salary increased by 10%, by what percent his commission will increase?

Solution:
পূর্বের কমিশন:
= 5000 এর 10% টাকা
= 5000 এর 10/100
= 500 টাকা

১০% বৃদ্ধিতে
বর্তমান বেতন = 5000 + 5000 এর 10%
= 5000 + 5000 এর 10/100
= 5000 + 500
= 5500 টাকা

নতুন কমিশন = 5500 এর 10%
5500 এর 10/100
= 550 টাকা

কমিশন বৃদ্ধি পায় = 550 - 500 = 50 টাকা

শতকরা কমিশন বৃদ্ধি পায় = {(50/500) × 100}%
= 10%

১,৫১২.

P sells a product to Q and makes a profit of 25%. Q sells it to R at a loss of 20%. If R buys it for Tk. 140, what price did P pay for it?

ক
ক) 211
খ
খ) 169
গ
গ) 140
ঘ
ঘ) 139

ব্যাখ্যা

Let the cost price of P be Tk. x
selling price of P = (x + 25% of x) = Tk. 5x/4
So, cost price of Q = Tk. 5x/4
selling price of Q = 80% of Tk. 5x/4 = Tk. x
So, cost price of R = Tk. x = Tk. 140
Therefore, the cost price of P is Tk. x = Tk. 140

১,৫১৩.

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

ব্যাখ্যা

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

১,৫১৪.

What is the profit percentage if the price for 120 bananas equals the selling price of 100 bananas?

ক
20%
খ
30%
গ
35%
ঘ
40%

ব্যাখ্যা

Question: What is the profit percentage if the price for 120 bananas equals the selling price of 100 bananas?

Solution:
Let the C.P. of 120 bananas be Tk. 120
As per question,
S.P. of 100 bananas = Tk. 120

C.P. of 100 bananas would be = Tk. 100
∴ Profit = (S.P. - C.P.) = 120 - 100 = 20

Profit percent = (20/100) × 100%
= 20%

১,৫১৫.

All of the students of Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 119 students in the band. If 50 percent of the students are in the band only, how many students are in the orchestra only?

ক
30
খ
51
গ
60
ঘ
100

ব্যাখ্যা

Question: All of the students of Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 119 students in the band. If 50 percent of the students are in the band only, how many students are in the orchestra only?

Solution:
only in orchestra = 80% - 50% = 30%
students in both band and orchestra = 100 - 80 = 20%

total students in band = 50% + 20% = 70%

70% of total students = 119
total students = 119/0.7
= 170

students in orchestra = 30% of 170 = 170 × 0.3 = 51

১,৫১৬.

A girl bought a book for Tk. 450 and sold it at 20% profit. By using that amount she bought another book and sold it at 5% loss. Then the overall profit amount is -

ক
Tk. 102
খ
Tk. 132
গ
Tk. 58
ঘ
Tk. 63

ব্যাখ্যা

Cost Price of 1st book = Tk. 450.
Profit % of 1st book = 20% profit
Selling price of 1st book = Cost Price of 1st book + Profit % of 1st book
= Tk. 450 + 20% of 450
= Tk. 540
Cost price of 2nd book = Tk. 540
Loss % of 2nd book = 5%
Selling price of 2nd book = Cost Price of 1st book + Profit % of 1st book
= Tk. 540 - 5% of 540 = Tk. 513
Overall profit = Tk. 513 - Tk. 450
= Tk. 63.

১,৫১৭.

In a metro train there are 600 passengers out of which 34% are females. Fare of each male is Tk. 20 and each female's fare is 25% less than each male. What is the total revenue generated by all the passengers together?

ক
Tk. 10772
খ
Tk. 10850
গ
Tk. 10891
ঘ
Tk. 10980

ব্যাখ্যা

Question: In a metro train there are 600 passengers out of which 34% are females. Fare of each male is Tk. 20 and each female's fare is 25% less than each male. What is the total revenue generated by all the passengers together?

Solution:
Total Passengers = 600
No. of females = (600 × 34)/100
= 204
No. of male passengers = (600 - 204)
= 396
Fare of each male = Tk. 20
Fare of female, 15% less,
= (20 × 75)/100
= Tk. 15 each

∴ Total revenue generated by male = Tk. (396 × 20)
= Tk. 7920

∴ Total revenue generated by female = (204 × 15)
= 3060

So, Total Revenue = (7920 + 3060)
= Tk. 10980

১,৫১৮.

A fruit seller buys lemons at 2 for Tk. 1 and sells them at 5 for Tk. 3. What is his gain percent?

ক
25%
খ
26.67%
গ
33.33%
ঘ
20%

ব্যাখ্যা

Question: A fruit seller buys lemons at 2 for Tk. 1 and sells them at 5 for Tk. 3. What is his gain percent?

Solution:
Cost price,
2 lemons = Tk. 1
So, cost price of 1 lemon = 1/2

Selling price,
5 lemons = Tk. 3
So, selling price of 1 lemon = 3/5

Profit per lemon = SP - CP
= (3/5) - (1/2)
= (6 - 5)/10
= 1/10

Gain percent = (Profit/CP) × 100%
= (1/10)/(1/2) × 100%
= (1/10) × (2/1) × 100%
= (2/10) × 100%
= 100/5%
= 20%

So his gain percent is 20%.

১,৫১৯.

A shopkeeper buys 100 pencils for 500 taka. How many pencils should he sell for 400 taka to make a 25% profit?

ক
68
খ
56
গ
64
ঘ
58

ব্যাখ্যা

Question: A shopkeeper buys 100 pencils for 500 taka. How many pencils should he sell for 400 taka to make a 25% profit?

Solution:
Cost price of 100 pencils = Tk. 500
Cost price per pencil = 500/100 = Tk. 5

Since the seller wants 25% profit,
The selling price per pencil will be = 5 × (1 + 25/100) = (5 × 1.25) = 6.25 tk

Now, the number of pencils the seller can sell = 400/6.25 = 64

So the shopkeeper should sell 64 pencils for 400 taka to make a 25% profit.

১,৫২০.

A man sells a watch for 960 Taka and loses 20%. What was the cost price?

ক
1100
খ
1000
গ
1200
ঘ
1150

ব্যাখ্যা

Question: A man sells a watch for 960 Taka and loses 20%. What was the cost price?

Answer: Here, Given Selling Price = 960 Taka
- With Loss 20 % If,
The Selling Price is 80 Taka then Cost Price is =100 Taka
The Selling Price is 1 Taka then Cost Price is =100/80 Taka
The Selling Price is 960 Taka then Cost Price is = (100×960)/80 Taka = 1200 Taka

১,৫২১.

In the cost price of 12 pens is equal to the selling price of 16 pens, find the loss per cent.

ক
ক) 25%
খ
খ) 40%
গ
গ) 33.33%
ঘ
ঘ) 15%

ব্যাখ্যা

Question: In the cost price of 12 pens is equal to the selling price of 16 pens, find the loss per cent.

Solution:
Let the C.P. of 1 pen =Tk. 1
∴ C.P of 12 pens=Tk. 12×1 =Tk. 12

C.P. of 12 pens = S.P of 16 pens
∴ S.P of 16 pens= Tk. 12
∴ C.P of 16 pens= Tk. 16

∴ Loss = C.P - S.P
=16- 12
=4 Tk.

Loss = {(4/16) × 100}%
= 25%.

১,৫২২.

A house worth Tk. 150000 is sold by X at a 5% profit to Y, Y sells the house back to X at a 2% loss. Then find profit and loss in the entire transaction = ?

ক
X gains Tk. 4250
খ
X loses Tk. 2750
গ
X loses Tk. 3740
ঘ
X gains Tk. 3150
ঙ
None

ব্যাখ্যা

Question: A house worth Tk. 150000 is sold by X at a 5% profit to Y, Y sells the house back to X at a 2% loss. Then find profit and loss in the entire transaction = ?

Solution:
Here,

Money spent by X = Tk. 150000

Money received by X = 105% of Tk. 150000 = Tk. 157500

Cost Price to X = 98% of Tk. 157500 = Tk. 154350

∴ X gains = Tk. (157500 - 154350) = Tk. 3150

১,৫২৩.

The difference of the two numbers is 20% of the large number, if the smaller number is 20, then the larger number is-

ক
22
খ
25
গ
30
ঘ
45

ব্যাখ্যা

Question: The difference of the two numbers is 20% of the large number, if the smaller number is 20, then the larger number is-

Solution:
Let the large number be x.
Then,
x - 20 = 20% of x = 20x/100 = x/5
⇒ x - x/5 = 20
⇒ 5x - x = 100
⇒ 4x = 100
∴ x = 25

১,৫২৪.

Radha’s salary is 50% more than Seeta’s salary. Radha got a raise of 40% on her salary while Seeta got a raise of 30% on her salary. By what percent is Radha’s salary more than Seeta’s?

ক
65.5%
খ
63.33%
গ
61.53%
ঘ
60.53%

ব্যাখ্যা

Question: Radha’s salary is 50% more than Seeta’s salary. Radha got a raise of 40% on her salary while Seeta got a raise of 30% on her salary. By what percent is Radha’s salary more than Seeta’s?

Solution:
Let Seeta’s salary = Tk. 100
Then Radha’s salary = 100 × 50% + 100 = 150

Radha got a raise of 40% then 150 × 40% + 150 = 210
Seeta got a raise of 30% then 100 × 30% + 100 = 130

Now Radha salary more than Seeta salary by 210 - 130 = 80
Percent = (80/130) × 100 = 61.53%

১,৫২৫.

How much would I have to pay for a book which cost Tk. 70 to produce, if the printing company sold it to a book seller at 20% profit and the book seller sold it to me at a profit of 25%?

ক
ক) Tk. 90
খ
খ) Tk. 95
গ
গ) Tk. 105
ঘ
ঘ) Tk. 110

ব্যাখ্যা

Question: How much would I have to pay for a book which cost Tk. 70 to produce, if the printing company sold it to a book seller at 20% profit and the book seller sold it to me at a profit of 25%?

Solution:
উৎপাদন খরচ = 70 টাকা

20% লাভে
উৎপাদন খরচ 100 টাকা হলে বিক্রয়মূল্য = 100 + 20 বা 120 টাকা
উৎপাদন খরচ 1 টাকা হলে বিক্রয়মূল্য = 120/100 টাকা
উৎপাদন খরচ 70 টাকা হলে বিক্রয়মূল্য = (120 × 70)/100 টাকা
= 84 টাকা

company এর বিক্রয়মূল্য = খুচরা বিক্রেতার ক্রয়মূল্য

খুচরা বিক্রেতার 25% লাভে
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য = 100 + 25 বা 125 টাকা
ক্রয়মূল্য 1 টাকা হলে বিক্রয়মূল্য = 125/100 টাকা
ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য = (125 × 84)/100 টাকা
= 105 টাকা

১,৫২৬.

If 65% of x = 13% of y, then find the value of x if y = 2,000.

ক
ক) 200
খ
খ) 300
গ
গ) 400
ঘ
ঘ) 500
ঙ
ঙ) None of these

ব্যাখ্যা

Question: If 65% of x = 13% of y, then find the value of x if y = 2,000.

Solution:
65% of x = 13% of y
⇒ 65x/100 = 13y/100
⇒ 65x = 13y
⇒ x = 13y/65
⇒ x = (13 × 2000)/65
x = 400

১,৫২৭.

In a market survey 20% respondents opted for product A whereas 60% opted for product B, the remaining individuals were not certain. If the difference in number between those who opted for product B and those who were uncertain was 720, how many individuals were covered in the survey ?

ক
ক) 1,440
খ
খ) 1,800
গ
গ) 3,600
ঘ
ঘ) None

ব্যাখ্যা

Question: In a market survey 20% respondents opted for product A whereas 60% opted for product B, the remaining individuals were not certain. If the difference in number between those who opted for product B and those who were uncertain was 720, how many individuals were covered in the survey?

Solution:
Percentage of uncertain individuals
=[100 - (20 + 60)]%
= 20%

Now
60% of x - 20% of x = 720
40% of x = 720
40x/100 = 720
40x = 720 × 100
x = (720 × 100)/40
x = 1800

১,৫২৮.

By selling an article for Tk 2800, a seller gains 12%. If the profit is reduced to 10% then the selling price will be -

ক
ক) 2600
খ
খ) 2650
গ
গ) 2700
ঘ
ঘ) 2750

ব্যাখ্যা

Question: By selling an article for Tk 2800, a seller gains 12%. If the profit is reduced to 10% then the selling price will be -

Solution:
let, the cost price = x

now,
112% of x = Tk 2800
∴ 1% of x = Tk 2800/112
∴ 110% of x = Tk (2800 × 110)/112
= Tk 2750

১,৫২৯.

If A's income is 25% less than that of B, then how much percent is B's income more than that of A?

ক
33.33%
খ
35%
গ
25%
ঘ
30.33%

ব্যাখ্যা

Question: If A's income is 25% less than that of B, then how much percent is B's income more than that of A?

Solution:
Let B's income 100
So, A’s income = 75
So, B’s income more than A in % = (25×100)/75
= 100/3
= 33.33%

১,৫৩০.

Sawpon buys a car at 20% discount of the price and sells it at 20% higher price. His percentage gain is-

ক
ক) 40%
খ
খ) 20%
গ
গ) 30%
ঘ
ঘ) 50%

ব্যাখ্যা

Question: Sawpon buys a car at 20% discount of the price and sells it at 20% higher price. His percentage gain is-

Solution:
Let
The value of the car (M.P.) = Tk. 100
Then, C.P. = 80% of 100= Tk. 80
S.P. =120% of 100= Tk. 120
Profit = (120 - 80) Tk.

∴ Profit % = (40/80) × 100 = 50%

The profit percentage is 50%.

১,৫৩১.

If w is 20% less than m, and n is 20% less than z, than wn is what percent less than mz ?

ক
ক) 37%
খ
খ) 36%
গ
গ) 20%
ঘ
ঘ) 40%

ব্যাখ্যা

ধরি,
m = 100
w = 100 - 100 এর 20% = 100 - 20 = 80
আবার,
z = 100
n = 100 - 100 এর 30% = 100 - 20 = 80

wn = 80 × 80 = 6400
mz = 100 × 100 = 10000

wn , mz এর চেয়ে কম = 10000 - 6400 = 3600
wn , mz এর চেয়ে শতকরা কম ={(3600/10000) × 100}% = 36%

১,৫৩২.

30% of 50% of 4/7 of a number is 420. What is 20% of 3/7 of that number?

ক
360
খ
420
গ
480
ঘ
490

ব্যাখ্যা

Question: 30% of 50% of 4/7 of a number is 420. What is 20% of 3/7 of that number?

Solution:
Let the number be x.

Then,
30% of 50% of 4/7 of x = 420
⇒ (30/100) × (50/100) × (4/7) × x = 420
⇒ 3/10 × 1/2 × 4/7 × x = 420
⇒ 12x/140 = 420
⇒ 3x/35 = 420
⇒ x = (420 × 35)/3
∴ x = 4900

Now,
20% of 3/7 of x
= (20/100) × (3/7) × 4900
= (1/5) × (3/7) × 4900
= (3/35) × 4900
= 420

১,৫৩৩.

What is 35% of (11 × 160)/56 ?

ক
9
খ
10
গ
11
ঘ
12

ব্যাখ্যা

35% of (11 × 160)/56
= (35 × 11 × 160) ÷ (56 × 100)
= 11

১,৫৩৪.

A merchant selling 44 meters of cloth obtains a profit equal to the selling price of 11 meters of cloth, the profit is = ?

ক
55%
খ
50%
গ
33.33%
ঘ
None of the above

ব্যাখ্যা

Question: A merchant selling 44 meters of cloth obtains a profit equal to the selling price of 11 meters of cloth, the profit is = ?

Solution:
Profit = selling price of 11 m of cloth = 1/4 selling price of 44 m of cloth

Let the selling price of 44 meters of cloth = 4x
∴ profit = (1/4) × (4x) = x

So, cost price = selling price - profit = 4x - x = 3x

% Profit = (x/3x) × 100% = 33.33%

১,৫৩৫.

If 30% of C = 25% of A and 2d% of C = A, find the value of d?

ক
ক) 40
খ
খ) 50
গ
গ) 60
ঘ
ঘ) 80

ব্যাখ্যা

Given that
30% of C = 25% of A
2d% of C = A

According to the questions,
⇒ (30/100) × C = (25/100) × A
⇒ (30/25) = A/C
⇒ 6/5 = A/C

From the above question,
⇒ 2d% of C = A
⇒ 2d/100 = A/C
⇒ 2d/100 = 6/5
⇒ 2d = (6/5) × 100
⇒2d = 120
⇒ d = 60

∴ The value of d is 60

১,৫৩৬.

A bag costs 20% more than a purse. A wallet costs 30% less than the bag. If the price of the purse is 200 Tk, then by what percentage is the wallet cheaper than the purse?

ক
15%
খ
16%
গ
24%
ঘ
28%

ব্যাখ্যা

Question: A bag costs 20% more than a purse. A wallet costs 30% less than the bag. If the price of the purse is 200 Tk, then by what percentage is the wallet cheaper than the purse?

Solution:
Given,
the price of the purse = 200 tk

∴ Price of the bag = 200 + (200 × 20%)
= 240 tk

Price of the wallet = 240 − (240 × 30%)
= 240 − 72
= 168 Tk

Difference is = (200 - 168) = 32 tk

∴ Percentage = (32 × 100)/200 = 16%

১,৫৩৭.

5% loss is incurred when Rahim sells a watch for Tk. 1,140. At what price should the watch be sold to earn 5% profit?

ক
Tk. 1,260
খ
Tk. 1,200
গ
Tk. 1,300
ঘ
Tk. 1,450

ব্যাখ্যা

Question: 5% loss is incurred when Rahim sells a watch for Tk. 1,140. At what price should the watch be sold to earn 5% profit?

Solution:
৫% ক্ষতিতে বিক্রয়মূল্য = ১০০ - ৫ = ৯৫ টাকা

বিক্রয়মূল্য ৯৫ টাকা হলে ক্রয়মূল্য ১০০ টাকা
বিক্রয়মূল্য ১ টাকা হলে ক্রয়মূল্য ১০০/৯৫ টাকা
বিক্রয়মূল্য ১১৪০ টাকা হলে ক্রয়মূল্য (১০০/৯৫) × ১১৪০ = ১২০০ টাকা

আবার,
৫% লাভে বিক্রয়মূল্য = ১০০ + ৫ = ১০৫ টাকা
ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য ১০৫ টাকা
ক্রয়মূল্য ১ টাকা হলে বিক্রয়মূল্য ১০৫/১০০ টাকা
ক্রয়মূল্য ১২০০ টাকা হলে বিক্রয়মূল্য (১০৫/১০০) × ১২০০ = ১২৬০ টাকা

১,৫৩৮.

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

ক
100%
খ
54%
গ
30%
ঘ
200%

ব্যাখ্যা

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

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

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

∴ শতকরা লাভ 200%

১,৫৩৯.

In college Rahim scored 80 marks out of 150 in History and 95 marks out of 120 in English. If he wants to score 70% marks in 3 subjects, find the minimum marks he should score in Geography out of 100.

ক
ক) 70
খ
খ) 55
গ
গ) 76
ঘ
ঘ) None of these

ব্যাখ্যা

Total marks = 150 + 120 + 100 = 370
Marks obtained in 2 subjects = 80+95 = 175
Total marks to be obtained = 370 × 70% = 259
∴ Minimum marks needed to be scored in Geography = 259 – 175 = 84

১,৫৪০.

What is the original price of a T- shirt, if the sale price after 16% discount is Tk. 264?

ক
Tk. 300
খ
Tk. 310
গ
Tk. 314
ঘ
Tk. 318

ব্যাখ্যা

Let the cost price of the T-shirt be Tk. y
or, y - 16% of y = 264
or, y - 16y/100 = 264
or, (1 - 16/100)y = 264
or, 84y/100 = 264
or, y = 314.28

১,৫৪১.

The cost price of 15 articles is same as the selling price of 25 articles. What is loss percentage?

ক
ক) 20%
খ
খ) 10%
গ
গ) 40%
ঘ
ঘ) None of the above

ব্যাখ্যা

Question: The cost price of 15 articles is same as the selling price of 25 articles. What is loss percentage?

Solution:
Let CP of each article be Tk. 25 and SP of each article be Tk. 15
Loss Percentage
={(25x - 15x) × 100}/25x
= (10x × 100 )/25x
= 40%

১,৫৪২.

A trader sells his goods at a discount of 10%. He still makes a profit of 20%. If he sells the goods at the marked price only, his profit will be -

ক
ক) 33.33%
খ
খ) 30%
গ
গ) 28.35%
ঘ
ঘ) 22.35%

ব্যাখ্যা

Question: A trader sells his goods at a discount of 10%. He still makes a profit of 20%. If he sells the goods at the marked price only, his profit will be -

Solution:
ডিসকাউন্ট এর পর বিক্রয়মূল্য = ১০০ - (১০০ এর ১০%) = ৯০ টাকা
২০% লাভে ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য ১২০ টাকা

∴ ৮০ টাকা বিক্রয়মূল্য হলে ক্রয়মূল্য = (১০০ × ৯০)/১২০ টাকা
= ৭৫ টাকা

প্রকৃত দামে বিক্রি করলে লাভ হত = ১০০ - ৭৫ = ২৫ টাকা

∴ শতকরা লাভ = (২৫ × ১০০)/৭৫ = ৩৩.৩৩%

১,৫৪৩.

The price of a pen is 25% more than the price of a book. The price of a pen holder is 50% more than the price of the book. How much is the price of the pen holder more than the price of the pen?

ক
20%
খ
25%
গ
50%
ঘ
37.5%

ব্যাখ্যা

Question: The price of a pen is 25% more than the price of a book. The price of a pen holder is 50% more than the price of the book. How much is the price of the pen holder more than the price of the pen?

Solution:
Let price of book = 100tk
Price of pen = 100 + 100 × 25%
= 125 tk
Price of pen-holder = 100 + 100 × 50%
= 150 tk

Difference is = 150 - 125 = 25 tk

∴ Percentage = (25 × 100)/125
= 20%

১,৫৪৪.

If Profit = 25 Taka and Cost Price = 150 Taka, what is the profit percentage?

ক
10.6 %
খ
15 %
গ
16.6 %
ঘ
12 %

ব্যাখ্যা

Question: If Profit = 25 Taka and Cost Price = 150 Taka, what is the profit percentage?

Solution:
Here,
Cost Price = 150 Tk
Profit = 25 Tk

Now,
Cost Price is 150 and Profit is 25 Taka.
∴ When cost Price is 1 Taka then the Profit is = 25/150 Taka
∴ When cost Price is 100 Taka then the Profit is = (25× 100)/150 Taka
= 16.6 %

১,৫৪৫.

A shopkeeper purchased two varieties of rice, 80 KG at Tk. 13.50 per KG and 120 KG at Tk. 16 per KG. The shopkeeper being greedy, mixed the two varieties of rice and sold the mixture at a gain of 16%. Find the per KG selling price of the mixture.

ক
Tk. 17.00
খ
Tk. 17.35
গ
Tk. 17.50
ঘ
Tk. 17.40
ঙ
Tk. 17.75

ব্যাখ্যা

Question: A shopkeeper purchased two varieties of rice, 80 KG at Tk. 13.50 per KG and 120 KG at Tk. 16 per KG. The shopkeeper being greedy, mixed the two varieties of rice and sold the mixture at a gain of 16%. Find the per KG selling price of the mixture.

Solution:
We are given that the shopkeeper bought 80 Kg at Tk. 13.50 per KG and 120 KG at Tk. 16 per KG.
Total cost price = (80 × 13.50) + (120 × 16) = 1080 + 1920 = Tk. 3000
and total rice = 80 + 120 = 200 KG
Now,
total selling price = Total cost price + 16 % of total cost price
⇒ Total selling price = 3000 + (0.16 × 3000) = Tk. 3480

Thus, selling price per KG = 3480/200 = Tk. 17.40

Alternative:

⇒ (m - 13.50)/(16 - m) = 120/80 [where ‘m’ is the per KG cost price of the mixture]
⇒ 80m - 1080 = 1920 - 120m
⇒ 200m = 3000
⇒ m = 15,

Therefore, per KG selling price of the mixture = Tk. 15 + 16% of 15 = Tk. 17.40

১,৫৪৬.

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

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

ব্যাখ্যা

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

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

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

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

১,৫৪৭.

30% of apples out of 450 are rotten. How many apples are in good condition?

ক
ক) 125
খ
খ) 315
গ
গ) 240
ঘ
ঘ) 180

ব্যাখ্যা

Question: 30% of apples out of 450 are rotten. How many apples are in good condition?

Solution:
30% of 450 = (450 × 30/100) = 135
So, 450 - 135 = 315 apples are in good condition.

১,৫৪৮.

After paying 10 % tax on all income over 3000 Kawser had a net income of Tk 12000. Kawser's income before tax was.

ক
ক) Tk. 13300
খ
খ) Tk. 12000
গ
গ) Tk. 13000
ঘ
ঘ) Tk. 12300

ব্যাখ্যা

Question: After paying 10 % tax on all income over 3000 Kawser had a net income of Tk 12000. Kawser's income before tax was.

Solution:
Let Kawser income was x.
Taxable income = x - 3000
∴ Tax paid = 10%(x - 3000)

ATQ,
x - 10%(x - 3000) = 12000
⇒ x - {10(x - 3000)/100} = 12000
⇒ (10x - x + 3000)10 = 12000
⇒ 9x + 3000 = 120000
⇒ 9x = 120000 - 3000
⇒ 9x = 117000
⇒ x = 117000/9
∴ x = 13000

Kawser income was Tk.13000

১,৫৪৯.

A person saves Tk. 5,000 in his bank account. If the bank gives 10% annual profit, how will be his balance after 6 years ?

ক
ক) Tk. 3,000
খ
খ) Tk. 5,000
গ
গ) Tk. 7000
ঘ
ঘ) Tk. 8,000

ব্যাখ্যা

Question: A person saves Tk. 5,000 in his bank account. If the bank gives 10% annual profit, how will be his balance after 6 years ?

Solution:
আসল P = 5,000 টাকা
মুনাফার হার r = 10% = 1/100 = 1/10
সময় n = 6 বছর

সরল মুনাফার ক্ষেত্রে,
I = Pnr
= ( 5000 × 6 × 1/10)
= 3000 টাকা

মুনাফা আসল = ( 5000 + 3000) টাকা = 8000 টাকা

১,৫৫০.

A dishonest merchant sells his grocery using weights 15% less than the true weights and shows that he makes profit of 20%. Find his actual gain percentage.

ক
ক) 41%
খ
খ) 41.17%
গ
গ) 40%
ঘ
ঘ) None of these

ব্যাখ্যা

প্রশ্ন: A dishonest merchant sells his grocery using weights 15% less than the true weights and shows that he makes profit of 20%. Find his actual gain percentage.

সমাধান:
Let us consider 1 kg of grocery bag.
Its actual weight is 85% of 1000 gm = 850 gm.

Let the cost price of each gram be Tk. 1
Then the CP of each bag = Tk. 850

SP of 1 kg of bag = 120% of the true CP
Therefore, SP = (120/100) × 1000 = Tk. 1200

Gain = 1200 - 850 = Tk. 350

Hence Gain % = (350/850) × 100% = 41.17%

১,৫৫১.

Two successive discounts of 25% and 15% are equal to a single discount of ___

ক
30%
খ
33.33%
গ
36.25%
ঘ
40%

ব্যাখ্যা

Question: Two successive discounts of 25% and 15% are equal to a single discount of___

Solution:
Formula for successive discounts
Single equivalent discount = d₁ + d₂ - (d₁ × d₂)/100
⇒ d = (25 + 15) - (25 × 15)/100
⇒ d = 40 - (375/100)
⇒ d = 40 - 3.75
d = 36.25

∴ Single discount = 36.25%

১,৫৫২.

In a certain store, the profit is 80% of the cost. If the cost increases by 20% but the selling price remains constant, how much is the decrease in profit percentage?

ক
30%
খ
70%
গ
100%
ঘ
250%
ঙ
None of these

ব্যাখ্যা

Question: In a certain store, the profit is 80% of the cost. If the cost increases by 20% but the selling price remains constant, how much is the decrease in profit percentage?

Solution:
Let us assume CP = Tk. 100.
Then Profit = Tk. 80 and selling price = Tk. 180

The cost increases by 20%
∴ New CP = Tk. 120,
SP = Tk. 180.

∴ Profit = 180 - 120 = Tk. 60
Profit % = (60/120) × 100% = 50%.

Therefore, Profit decreases by (80 - 50)% = 30%.

১,৫৫৩.

Some students (only boys and girls) from different schools appeared for an Olympiad exam. 20% of the boys and 15% of the girls failed the exam. The number of boys who passed the exam was 70 more than that of the girls who passed the exam. A total of 90 students failed. Find the number of students that appeared for the exam.

ক
350
খ
420
গ
400
ঘ
500

ব্যাখ্যা

Question: Some students (only boys and girls) from different schools appeared for an Olympiad exam. 20% of the boys and 15% of the girls failed the exam. The number of boys who passed the exam was 70 more than that of the girls who passed the exam. A total of 90 students failed. Find the number of students that appeared for the exam.

Solution:
20% of the boys and 15% of the girls failed the exam.
Total number of students who failed = 90
The percentage of boys who passed = (100 - 20)% = 80%
The percentage of girls who passed = (100 - 15)% = 85%
Let, the number of appeared boys = x The number of appeared girls = y

80x/100 - 85y/100 = 70
⇒ 5(16x - 17y) = 7000
⇒ 16x - 17y = 1400 ..........(1)

20x/100 + 15y/100 = 90
⇒ 5(4x + 3y) = 9000
⇒ 4x + 3y = 1800 .............(2)
Multiplying 4 to equation (2),
16x + 12y = 7200 ................(3)

(3) - (1) ⇒
16x + 12y - 16x + 17y = 7200 - 1400
⇒ 29y = 5800
⇒ y = 5800/29 = 200
∴ The number of girls appeared = 200

Putting y = 200 in equation (2),
4x + 3 × 200 = 1800
⇒ 4x = 1800 - 600 = 1200
⇒ x = 1200/4 = 300
∴ The number of boys who appeared = 300

The total number of students who appeared = 300 + 200 = 500
∴ The number of students that appeared for the exam is 500

১,৫৫৪.

Sakib buys an old bicycle for Tk 4700 and spends Tk 800 on its repairs. If he sells the bicycle for Tk 5800, his gain percent is:

ক
13%
খ
(60/11) %
গ
(50/9)%
ঘ
15%

ব্যাখ্যা

Question: Sakib buys an old bicycle for Tk 4700 and spends Tk 800 on its repairs. If he sells the bicycle for Tk 5800, his gain percent is:

Solution:

Cost Price = 4700 + 800 = 5500 Tk

Selling Price = 5800 Tk

Gain = 5800 - 5500 = 300 Tk

Gain % = (300/5500) × 100
= 60/11 %

১,৫৫৫.

Due to a reduction in books price by 10%, the number of books sold increased by 35%. What was the percentage increase in revenue?

ক
17
খ
18
গ
19
ঘ
20
ঙ
None of these

ব্যাখ্যা

প্রশ্ন: Due to a reduction in books price by 10%, the number of books sold increased by 35%. What was the percentage increase in revenue?

সমাধান:
Let,
x = price of product,
y = number of products sold

New price = 0.9x
New number of products sold =1.35y

Total increase in revenue = Final revenue - initial revenue = (0.9x × 1.35y) - xy
= 1.215xy - xy
= .215xy

Increase in percentage= {(0.215/xy) × 100}%
= 21.5%

বিকল্প সমাধান:
ধরি,
বইয়ের মূল্য = 100 টাকা
10% কমে বইয়ের মূল্য = 90 টাকা
35% বৃদ্ধিতে বিক্রয়মূল্য = 90 × (135/100) = 121.5 টাকা

∴ শতকরা রেভিনিউ = (121.5 - 100)/100 × 100%
= 21.5%

১,৫৫৬.

If two values are 25% and 75% of a third value, what percentage is the first value of the second value?

ক
33.33%
খ
50%
গ
66.67%
ঘ
45.67%

ব্যাখ্যা

Question: If two values are 25% and 75% of a third value, what percentage is the first value of the second value?

Solution:
Let
The third value x
∴ First value = (25x)/100 = x/4
∴ Second value = (75x)/100 = 3x/4

Now,
(First Value/Second value) × 100
= (x/4) × (4/3x) × 100
= 33.33%

১,৫৫৭.

On selling 13 pens at Tk. 540, there is a loss equal to the cost price of 3 pens. The cost price of a pen is-

ক
Tk. 80
খ
Tk. 72
গ
Tk. 54
ঘ
Tk. 48

ব্যাখ্যা

Question: On selling 13 pens at Tk. 540, there is a loss equal to the cost price of 3 pens. The cost price of a pen is-

Solution:
Let,
cost price of 1 pen is = Tk. x
∴ cost price of 13 pens is = Tk. 13x
∴ cost price of 3 pens is = Tk. 3x

We know,
Loss = Cost price - Selling price
3x = 13x - 540
⇒ 10x = 540
⇒ x = 540/10
∴ x = 54

∴ Cost price of 1 pen is Tk. 54

১,৫৫৮.

Mr. Anis marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price. What is his profit or loss percent?

ক
2% profit
খ
1% loss
গ
2.33% loss
ঘ
3.50% profit

ব্যাখ্যা

Question: Mr. Anis marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price. What is his profit or loss percent?

Solution:
Let the cost price of goods = Tk. 100
The market price of goods = 110% of 100
= (110/100)×100
= Tk. 110

After the discount, the selling price of the goods
= 90% of 110
= (90/100) × 110
= Tk. 99

Loss = 100 - 99 = Tk. 1

∴ Loss % = (1/100) × 100 = 1%

১,৫৫৯.

(88% of 370) + (24% of 210) - ? = 118

ক
196
খ
225
গ
258
ঘ
300

ব্যাখ্যা

Question: 88% of 370 + 24% of 210 - ? = 118

Solution:
88% of 370 + 24% of 210 - x = 118
⇒ 88 × 370/100 + 24 × 210/100 - x = 118
⇒ 325.6 + 50.4 - x = 118
⇒ x = 325.6 + 50.4 - 118 = 258

১,৫৬০.

A shopkeeper marks up his goods by 40% above the cost price. He then offers a discount of 15% on the marked price. What is the overall percentage profit?

ক
19%
খ
25%
গ
20%
ঘ
23%

ব্যাখ্যা

Question: A shopkeeper marks up his goods by 40% above the cost price. He then offers a discount of 15% on the marked price. What is the overall percentage profit?

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

Marked Price = 40% more than cost price
= 100 + 40
= Tk. 140

Discount = 15% of 140
= (15/100) × 140
= Tk. 21

Selling Price (SP)= 140 - 21 = Tk. 119

∴ Profit = SP - CP = 119 - 100 = Tk. 19

∴ overall percentage profit = (profit/cost price) × 100%
= (19/100) × 100%
= 19%

১,৫৬১.

A man buys an article for 25% more than its value and sells it for 20% less than its value. His gain or loss percentage is –

ক
23% gain
খ
33.33% loss
গ
28.25% gain
ঘ
36% loss

ব্যাখ্যা

Question: A man buys an article for 25% 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
∴ Cost Price (CP) = 100 + 25% of 100
= 100 + 25 = 125

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

Since SP 80 is less than CP 125, there is a Loss.

∴ Loss = CP - SP = 125 - 80 = 45 টাকা
∴ Loss percentage = (Loss/CP) × 100%
= (45/125) × 100%
= 36% loss

১,৫৬২.

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

ক
583.33 gallons
খ
1000 gallons
গ
1250 gallons
ঘ
1625 gallons

ব্যাখ্যা

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

Solution:
let, the capacity of pool is x gallons

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

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

১,৫৬৩.

A man wanted to sell an article with 20% profit: but he actually sold at 20% loss for Tk. 480, at what price he wanted to sell it to earn the profit = ?

ক
ক) Tk 720
খ
খ) Tk. 840
গ
গ) Tk. 600
ঘ
ঘ) Tk. 750

ব্যাখ্যা

According to the question,
Loss 20%
Selling price
=100%−20=80%
80%=480
1=480/80
∴(Profit 20%) = 480/ 80 ×120
=Tk. 720

১,৫৬৪.

When heated an iron bar expands 0.2%. If the increased length is 1 cm. What is the original length of the bar?

ক
ক) 5 cm
খ
খ) 0.98 cm
গ
গ) 500 cm
ঘ
ঘ) 50 cm

ব্যাখ্যা

Question: When heated an iron bar expands 0.2%. If the increased length is 1 cm. What is the original length of the bar?

Solution:
দেওয়া আছে,
প্রসারিত দৈর্ঘ্য = 1 সে.মি.

প্রশ্নমতে,
0.2% প্রসারণ = 1 সে.মি.
∴ 100% প্রসারণ = (100 × 10)/2 সে.মি.
= 500 সে.মি.

১,৫৬৫.

A merchant has 1000 kg of sugar, part of which he sells at 8% and the remaining at 18% profit. He gains 14% on the whole. Find the quantity of sugar that he sold at 18% profit.

ক
400 kg
খ
560 kg
গ
600 kg
ঘ
640 kg

ব্যাখ্যা

Question: A merchant has 1000 kg of sugar, part of which he sells at 8% and the remaining at 18% profit. He gains 14% on the whole. Find the quantity of sugar that he sold at 18% profit.

Solution:
Let
The cost price of sugar be tk. x per kg
∴ Total cost price = Tk. 1000x
The sugar sold at 8% gain by y kg
The sugar sold at 18% gain by (1000 - y) kg

Now
{(108xy)/100} + [{118x(1000 - y)}/100] = (114/100) × (1000x)
⇒ (108y)/100 + [{118(1000 - y)}/100] = (114 × 1000)/100
⇒ 108y + {118(1000 - y)} = 114 × 1000
⇒ 108y + 118000 - 118y = 114000
⇒ 118000 - 114000 = 10y
⇒ 4000 = 10y
∴ y = 400

∴ The sugar sold at 18% gain by (1000 - 400) kg
= 600 kg

১,৫৬৬.

If the cost price of 15 books is equal to the selling price of 20 books, what is the loss percentage?

ক
10%
খ
20%
গ
15%
ঘ
25%

ব্যাখ্যা

Question: If the cost price of 15 books is equal to the selling price of 20 books, what is the loss percentage?

Solution:
Let C.P. of each books Tk. 1
Cost Price of 20 books Tk. 20
Selling Price of 20 books Tk. 15

∴ Loss = TK. (20 - 15)
= Tk.5

∴ Percentage of loss = {(5/20) × 100}%
= 25%

১,৫৬৭.

500 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child receive?

ক
9
খ
10
গ
11
ঘ
12

ব্যাখ্যা

Question: 500 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child receive?

Solution:
Let Children = X
A/Q,
500/X = 20% of X
⇒ 500/X = X/5
⇒ X² =5 × 500
⇒ X² = 2500
X = 50

So each children receive = 500/50
= 10

১,৫৬৮.

If a watch is sold for Tk. 560, there is a loss 20%. What is the cost price of the watch?

ক
ক) Tk. 500
খ
খ) Tk. 700
গ
গ) Tk. 650
ঘ
ঘ) Tk. 600

ব্যাখ্যা

Question: If a watch is sold for Tk. 560, there is a loss 20%. What is the cost price of the watch?

Solution:
দেওয়া আছে,
বিক্রয়মূল্য ৫৬০ টাকা
২০% ক্ষতিতে বিক্রয়মূল্য = (১০০ - ২০) = ৮০ টাকা

বিক্রয়মূল্য ৮০ টাকা হলে ক্রয়মূল্য ১০০ টাকা
বিক্রয়মূল্য ৫৬০ টাকা হলে ক্রয়মূল্য (১০০ × ৫৬০)/৮০ টাকা
= ৭০০ টাকা

১,৫৬৯.

A retailer buys a TV from a wholesaler at a 25% discount. He then marks up the price by 50% on the discounted price and offers a 20% discount to the customer. What is the retailer’s profit percentage?

ক
30%
খ
25%
গ
20%
ঘ
40%

ব্যাখ্যা

Question: A retailer buys a TV from a wholesaler at a 25% discount. He then marks up the price by 50% on the discounted price and offers a 20% discount to the customer. What is the retailer’s profit percentage?

Solution:
Let the original price of the TV be 1000 Taka.

Wholesaler’s discount = 25%
Retailer’s purchase price:
1000 − 25% of 1000 = 1000−250 = 750 Taka

Retailer’s markup = 50% on Taka 750
New marked price:
750 + 50% of 750 = 750 + 375 = 1125 Taka

Customer’s discount = 20% on Taka 1125
Selling price:
1125 − 20% of 1125 = 1125 − 225 = 900 Taka

So, Profit = {(900 - 750)/750} × 100%
= 20%

১,৫৭০.

In an examination it is required to get 40% of the aggregate marks to pass. A student get 261 marks and is declared failed by 4% marks. What are the maximum aggregate marks a student can get ?

ক
ক) 700
খ
খ) 730
গ
গ) 745
ঘ
ঘ) None of these

ব্যাখ্যা

Let the maximum marks be x.
Then,
(40−4)% of x =261
⇒ 36% of x =261
⇒ 36x/100 =261
⇒ x = (261×100/36)
⇒ x = 725

১,৫৭১.

30% of 10 is 10% of which?

ক
ক) 30
খ
খ) 60
গ
গ) 40
ঘ
ঘ) 600

ব্যাখ্যা

30% of 10 = 10% of x
⇒ (30/100) × 10 = (10/100) × x
⇒ 3 = x/10
So, x = 30

১,৫৭২.

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

ক
No profit, no loss
খ
20% profit
গ
Less than 20% profit
ঘ
More than 20% profit

ব্যাখ্যা

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

Solution:
Let, value of article is x taka

Buying price = x - 0.1x
= 0.9x taka

Selling price = x + 0.1x
= 1.1x taka

Profit = 1.1x - 0.9x = 0.2x taka

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

১,৫৭৩.

In 1982 and 1983, Company B’s operating expenses were 12.0 million and 14.0 million, respectively, and its revenues were 15.6 million and 18.8 million, respectively. What was the percent increase in Company B’s profit (revenues minus operating expenses) from 1982 to 1983?

ক
3%
খ
16.67%
গ
33.3%
ঘ
25%

ব্যাখ্যা

Question: In 1982 and 1983, Company B’s operating expenses were 12.0 million and 14.0 million, respectively, and its revenues were 15.6 million and 18.8 million, respectively. What was the percent increase in Company B’s profit (revenues minus operating expenses) from 1982 to 1983?

Solution:
Profit = Revenue - operating expenses
Profit in 1982 = Revenue in 1982 - operating expenses in 1982
= 15.6 million - 12 million
= 3.6 million

Profit in 1983 = Revenue in 1983 - operating expenses in 1983
= 18.8 million - 14 million
= 4.8 million

Percentage increase in company B's profit from 1982 to 1983 = {(4.8 - 3.6)/3.6} × 100
= (1.2/3.6) × 100
= 33.33%

১,৫৭৪.

The price of a pen is 25% more than the price of a book. The price of a pen holder is 50% more than the price of the book. How much is the price of the pen holder more than the price of the pen?

ক
25%
খ
20%
গ
15%
ঘ
10%

ব্যাখ্যা

Question: The price of a pen is 25% more than the price of a book. The price of a pen holder is 50% more than the price of the book. How much is the price of the pen holder more than the price of the pen?

Solution:
Let, the price of the book = 100 tk
Price of pen = 100 + 100 × 25%
= 125 tk
Price of pen-holder = 100 + 100 × 50%
= 150 tk

Difference is = 150 - 125 = 25 tk

∴ Percentage = (25 × 100)/125
= 20%

১,৫৭৫.

It costs Tk. 1 to photocopy a sheet of paper. However, 2% discount is allowed on all photocopies done after the first 1000 sheets. How much will it cost to copy 5000 sheets of paper?

ক
5000
খ
5200
গ
4900
ঘ
4920

ব্যাখ্যা

Question: It costs Tk. 1 to photocopy a sheet of paper. However, 2% discount is allowed on all photocopies done after the first 1000 sheets. How much will it cost to copy 5000 sheets of paper?

Solution:
For the first 1000 sheets, cost = 1000 × 1 = Tk. 1000

Cost for rest (5000 - 1000) or 4000 sheets = 4000 × (1 - 0.02)
= 4000 × 0.98
= Tk. 3920

Total cost = 3920 + 1000
= Tk. 4920

১,৫৭৬.

A car is sold at a profit of 25%. Had it been sold for Tk. 15,000 less, there would have been a loss of 15%. What was the cost price?

ক
Tk. 34000
খ
Tk. 37500
গ
Tk. 39520
ঘ
Tk. 42800

ব্যাখ্যা

Question: A car is sold at a profit of 25%. Had it been sold for Tk. 15,000 less, there would have been a loss of 15%. What was the cost price?

Solution:
ধরি, গাড়িটির ক্রয়মূল্য = x টাকা

25% লাভে বিক্রয়মূল্য = x + x এর 25%
= x + 25x/100
= x + x/4
= 5x/4

15% ক্ষতিতে বিক্রয়মূল্য = x - x এর 15%
= x - 15x/100
= x - 3x/20
= 17x/20

প্রশ্নমতে,
(5x/4) - (17x/20) = 15000
⇒ (25x/20) - (17x/20) = 15000
⇒ 8x/20 = 15000
⇒ 2x/5 = 15000
⇒ 2x = 15000 × 5
⇒ 2x = 75000
⇒ x = 75000/2
∴ x = 37500

∴ গাড়িটির ক্রয়মূল্য = 37,500 টাকা

১,৫৭৭.

Bus fares were recently increased from Taka 1.50 to Taka 2.00. What was the approximate percentage of the increase?

ক
20%
খ
22%
গ
25%
ঘ
33.33%

ব্যাখ্যা

Question: Bus fares were recently increased from Taka 1.50 to Taka 2.00. What was the approximate percentage of the increase?

Solution:
the approximate percentage of the increase = (2 - 1.5)/1.5 × 100%
= (0.5/1.5) × 100%
= 33.33%

১,৫৭৮.

In an aeroplane of 65 passengers and 4 crew, each passenger got chocolates that are 20% of the total number of passengers and each crew got chocolates that are 40% of the total number of passengers. How many chocolates are there?

ক
845
খ
949
গ
897
ঘ
104

ব্যাখ্যা

Question: In an aeroplane of 65 passengers and 4 crews, each passenger got chocolates that are 20% of the total number of passengers and each crew got chocolates that are 40% of the total number of passengers. How many chocolates are there?

Solution:
There are 65 passengers and 4 crews
Each passenger got chocolates that are 20% of the total number of passengers.
So each passenger got chocolates = 65 × 20%
= 13 chocolates.

∴ Total chocolates for passengers is = 65 × 13 = 845

each crew got chocolates that are 40% of the total number of passengers.
So each crew got chocolates = 65 × 40% = 26 chocolates

There are 4 crews
∴ Total chocolates for crews is = 26 × 4 = 104

∴ Total chocolates = chocolates for passengers + chocolates for crews
= 845 + 104
= 949

Therefore, the total number of chocolates is 949.

১,৫৭৯.

Two-third of one-fifth of one-fourth of a number is 10. What is 30% of that number?

ক
60
খ
100
গ
270
ঘ
90

ব্যাখ্যা

Question: Two-third of one-fifth of one-fourth of a number is 10. What is 30% of that number?

Solution:
Let,
The number be x.

ATQ,
(2/3) × (1/5) × (1/4) × x = 10
⇒ (1/30) × x = 10
⇒ x = 10 × 30
∴ x = 300

30% of 300 = (30 × 300)/100 = 90

১,৫৮০.

In New jersey 90% of the population own a car, 15% own a motorcycle, and everybody owns one or the other or both. What is the percentage of motorcycle owners who own cars?

ক
ক) 46/7%
খ
খ) 47/3%
গ
গ) 100/3%
ঘ
ঘ) 91/2%

ব্যাখ্যা

গাড়ি বা মোটরসাইকেল এর মালিক = ১০০%
গাড়ির মালিক = ৯০%
মোটরসাইকেলের মালিক = ১৫%

গাড়ি ও মোটরসাইকেল এর মালিক =(৯০ + ১৫)% - ১০০% = ১০৫% - ১০০% = ৫%
গাড়ির মালিকের মোটর সাইকেল রয়েছে = {(৫/১৫) × ১০০}% = ১০০/৩%

১,৫৮১.

Kabir sold his wallet at a loss of 4% . Had he sold it for Tk 84 more, he would have gained 10%. What was the cost of the wallet?

ক
300Tk
খ
400Tk
গ
500Tk
ঘ
600Tk
ঙ
700Tk

ব্যাখ্যা

Question: Kabir sold his wallet at a loss of 4% . Had he sold it for TK 84 more, he would have gained 10%. What was the cost of the wallet?

Solution:
Let the original price of the wallet is x TK

∴ [x × (100% - 4%)] + 84 = x × (100% + 10%)
⇒ (x × 96%) + 84 = x × 110%
⇒ (96x + 8400)/100 = 110x/100
⇒ 110x - 96x = 8400
⇒ 14x = 8400
⇒ x = 600

১,৫৮২.

A clock 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. 80
গ
Tk. 100
ঘ
Tk. 120

ব্যাখ্যা

Question: A clock 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

১,৫৮৩.

A tradesman marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price. What is his profit or loss percent?

ক
1% loss
খ
2% loss
গ
1% profit
ঘ
2% profit

ব্যাখ্যা

Question: A tradesman marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price. What is his profit or loss percent?

Solution:
Let cost price of goods = Tk. 100
The market price of goods = 110% of 100
= (110/100)×100
= Tk. 110

After discount selling price of goods
= 90% of 110
= (90/100) × 110
= Tk. 99

Loss = 100 - 99 = Tk. 1

∴ Loss % = (1/100) × 100 = 1%

১,৫৮৪.

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

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

১,৫৮৫.

A student bought a bag for Tk. 3500 and later sold it for Tk. 4000. Find the profit percentage he earned.

ক
14%
খ
14.29%
গ
15.29%
ঘ
10%

ব্যাখ্যা

Question: A student bought a bag for Tk. 3500 and later sold it for Tk. 4000. Find the profit percentage he earned.

Solution:
Here,
CP = 3500, and SP = 4000
As SP > CP,
∴ Profit = SP - CP = 4000 - 3500 = 500

Profit% = (500/3500) ×100%
=100/7 %
= 14.29%

১,৫৮৬.

A lamp is manufactured to sell for $35.00, which yields a profit of 25% of cost. If the profit is to be reduced to 15% of cost, what will be the new retail price of the lamp?

ক
ক) $31.50
খ
খ) $28.00
গ
গ) $21.00
ঘ
ঘ) $32.20

ব্যাখ্যা

In 25% profit,
If selling price is $125 then cost is $100
So, when selling price is $35 then cost = (100×35)/125 = $28
In 15% profit,
If cost is $100 then selling price = $115
So, when cost is $28, then selling price = (115×28)/100 = $32.20

১,৫৮৭.

Alom invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is

ক
62.5%
খ
37.5%
গ
24.8%
ঘ
None of these

ব্যাখ্যা

Question: Alom invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is

Solution:
let, Alom invest x taka at 15% per annum for 4 years and y taka at 12% per annum for 3 years

ATQ,
x × 0.15 × 4 = y × 0.12 × 3
⇒ x/y = 0.36/.6 = 3/5
⇒ x : y = 3 : 5

%percentage = (3/8) × 100%
= 37.5%

১,৫৮৮.

A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25% . The percentage of water in the mixer is:

ক
ক) 8%
খ
খ) 10%
গ
গ) 20%
ঘ
ঘ) 15%

ব্যাখ্যা

25% লাভ হওয়ায়,
100 টাকার দুধ বিক্রয় করে = 100 + 25 = 125 টাকা
অর্থাৎ 125 টাকার পানি মিশ্রিত দুধ বিক্রয় করে = 100 টাকায়
100 টাকার পানি মিশ্রিত করে = (100 ×100)/125 = 80 টাকায়

দুধে পানির শতকরা পরিমাণ = (100 - 80)% = 20%

১,৫৮৯.

In an election, 4% of the total votes cast are invalid. Of the valid votes, one candidate secures 55% and wins the election by a margin of 4,800 votes. Find the total number of votes cast.

ক
50000
খ
45000
গ
42000
ঘ
60000

ব্যাখ্যা

Question: In an election, 4% of the total votes cast are invalid. Of the valid votes, one candidate secures 55% and wins the election by a margin of 4,800 votes. Find the total number of votes cast.

Solution:
বিজয়ী প্রার্থী ভোট পায়= 55%
বৈধ ভোট = (100 - 4)% = 96%

বিজয়ী প্রার্থী বৈধ ভোটের শতকরা পায় = (55 × 96)/100
= 52.8%

পরাজিত প্রার্থী ভোট পায় = (96 - 52.8)%
= 43.2%

বিজয়ী প্রার্থী ও পরাজিত প্রার্থীর ভোটের পার্থক্য = (52.8 - 43.2)%
= 9.6%

প্রশ্নমতে
9.6% = 4800
1% = 4800/9.6
100% = (4800 × 100)/9.6
= 50000

১,৫৯০.

By selling an article for Tk. 100, a man gains Tk. 15. Then, his gain % is

ক
ক) 15%
খ
খ) (38/3)%
গ
গ) (69/4)%
ঘ
ঘ) (300/17)%

ব্যাখ্যা

Question: By selling an article for Tk. 100, a man gains Tk. 15. Then, his gain % is

Solution:
Selling price = Tk. 100
profit =Tk. 15
Cost price = S.P. - Profit
= 100 -15
= 85
Gain % = (Profit/C.P.) × 100
= (15/85) ×100
= (300/17)%

১,৫৯১.

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

ক
28
খ
30
গ
36
ঘ
38

ব্যাখ্যা

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

Solution:
S.P of 90 chocolets = Tk. 160
C.P of 90 chocolets = Tk. {160×(100/80)}
= Tk. 200

Desired S.P of 90 chocolets = Tk. (120/100) × 200
= Tk. 240

For Tk. 240 chocolets sold = 90
For Tk. 96 chocolets sold = (90/240) × 96
= 36

১,৫৯২.

Anik invested 25,200 taka in two accounts, which pay 5 % and 10% interest annually. The amount invested at 10% rate is 110% of the amount invested at 5% rate. After three years, he earns 5760 taka in interest. How much did he invest at the 10% rate?

ক
Tk. 10000
খ
Tk. 11500
গ
Tk. 13200
ঘ
Tk. 14800

ব্যাখ্যা

Question: Anik invested 25,200 taka in two accounts, which pay 5 % and 10% interest annually. The amount invested at 10% rate is 110% of the amount invested at 5% rate. After three years, he earns 5760 taka in interest. How much did he invest at the 10% rate?

Solution:
5% সুদের জন্য আসল x টাকা
10% সুদের জন্য আসল 110%x = 1.1x টাকা

5% হারে সুদ = x × 3 × 5/100 = 3x/20 টাকা
10% হারে সুদ = 1.1x × 3 × 10/100 = 3.3x/10 টাকা

(3x/20) + (3.3x/10) = 5760
⇒ (3x + 6.6x)/20 = 5760
⇒ 9.6x = 5760 × 20
⇒ x = (5760 × 20)/9.6
= 12000 tk.

10% সুদের হারের জন্য আসল = 1.1 × 12000
= 13200 tk.

১,৫৯৩.

In an election with three candidates, Candidate A received 30% of the valid votes, and Candidate B received 45%. If 15% of the total votes were invalid and 8,000 votes were cast in total, how many valid votes did Candidate C receive?

ক
1780
খ
1520
গ
1700
ঘ
1850

ব্যাখ্যা

Question: In an election with three candidates, Candidate A received 30% of the valid votes, and Candidate B received 45%. If 15% of the total votes were invalid and 8,000 votes were cast in total, how many valid votes did Candidate C receive?

Solution:
Invalid votes = 15% of 8000 = (15/100) × 8000 = 1200

∴ Valid votes = 8000 - 1200 = 6800
Now,
Votes for A and B = 30% + 45% = 75% of 6800 = (75/100) × 6800 = 5100

∴ Votes for C = 6800 - 5100 = 1700

∴ So Candidate C received 1700 valid votes.

১,৫৯৪.

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

ক
20%
খ
15%
গ
17.33%
ঘ
25%
ঙ
None

ব্যাখ্যা

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

Solution:

Let the cost price be Tk. 5x

The selling price is Tk. 4x

Hence, the loss percent = [(5x - 4x)/5x] × 100%

= (1/5) × 100%

= 20%

১,৫৯৫.

A television and a washing machine were sold for Tk. 12500 each. If the television was sold at a gain of 30% and the washing machine at a loss of 30%. Find the overall profit% or loss% on the entire transaction?

ক
9% profit
খ
9% loss
গ
12% profit
ঘ
12% loss

ব্যাখ্যা

Question: A television and a washing machine were sold for Tk. 12500 each. If the television was sold at a gain of 30% and the washing machine at a loss of 30%. Find the overall profit% or loss% on the entire transaction?

Solution:

Total SP = 2 × 12500 = 25000

CP of TV = [100/(100 + 30)] × 12500 = 12500 × 100/130

CP of Washing machine = [100/ (100 - 30)] × 12500 = 12500 × 100/70

∴ Total CP = 12500 [(100/130) + (100/70)] = 12500 × 200/91 = 2500000/91 = 27472.53

Clearly SP < CP, that is, there is a loss.

Reqiured loss percentage = [{(2500000/91) - 25000}/(2500000/91)] × 100%
= {(2500000 - 2275000)/2500000} × 100%
= (225000/2500000) × 100%
= 9%
Therefore, there is loss of 9%

১,৫৯৬.

The percentage profit earned by selling an article for Tk. 1920 is equal to the percentage loss by selling the same article for Tk. 1280. At what price should the article be sold to make 25% profit?

ক
Tk. 1800
খ
Tk. 2000
গ
Tk. 2250
ঘ
Tk. 2500

ব্যাখ্যা

Question: The percentage profit earned by selling an article for Tk. 1920 is equal to the percentage loss by selling the same article for Tk. 1280. At what price should the article be sold to make 25% profit?

Solution:
Let the cost price of the article be C.
From the given problem, the percentage profit made by selling the article for Tk. 1920 is equal to the percentage loss incurred by selling the article for Tk. 1280. This can be expressed as:
{(1920 - C)/C} × 100 = {(C - 1280)/C} ×100
⇒ 1920 - C = C - 1280
⇒ 1920 + 1280 = 2C
⇒ 3200 = 2C
∴ C = 1600

Now, to make a 25% profit, the selling price should be:
Selling Price = C + (25/100) × C = 1600 + (25/100) ×1600 = 1600 + 400 = 2000

১,৫৯৭.

If a man were to sell his table for Tk 800, he would lose 20%. To gain 25% he should sell it for -

ক
ক) 1250 Tk
খ
খ) 1000 Tk
গ
গ) 1200 Tk
ঘ
ঘ) 950 Tk

ব্যাখ্যা

Question: If a man were to sell his table for Tk 800, he would lose 20%. To gain 25% he should sell it for -

Solution:
Let, the cost price is 100 Tk
At 20% loss, Selling price = 100 - 20 = 80 Tk

Original cost price = (100 × 800) / 80 = 1000 Tk

to gain 25%, selling price be = 1000 × 125% = 1250 Tk

১,৫৯৮.

An article costs TK 500 and the marked price is mentioned as Tk. 800. What is the profit % for the seller if he sells and offers a discount of 10% on the marked price?

ক
ক) 30%
খ
খ) 44%
গ
গ) 56%
ঘ
ঘ) 64%

ব্যাখ্যা

10% of 800 = 800 × 10/100 = 80
So, the selling price is = 800 - 80 = 720
Profit = 720 - 500 = 220
So, profit percentage = (220 × 100)/500 = 44%

১,৫৯৯.

The price of a jewellery, passing through three hands. rises on the whole by 65%. If the first and the second sellers earned 20% and 25% profit respectively, the profit earned by the third seller is-

ক
20%
খ
15%
গ
10%
ঘ
5%
ঙ
None of above

ব্যাখ্যা

Let,
Cost price = 100
Selling price of third seller = 100 + 65 = 135
Selling price of 1st seller = 100 × 120% = 120
Selling price of 2nd seller = 120 × 125% = 150
So profit of third seller = 165 - 150 = 15
So profit percent = (15/150) × 100 = 10%

১,৬০০.

A grocer buys some eggs at Tk. 3 each. He finds that 12 of them are broken, but he sells the others at Tk. 4 each and makes a profit of Tk. 96. How many eggs did he buy?

ক
ক) 140
খ
খ) 142
গ
গ) 144
ঘ
ঘ) 150

ব্যাখ্যা

Let, The grocer buys = x eggs
ATQ,
4(x - 12) - 3x = 96
Or, 4x - 48 - 3x = 96
∴ x = 96 + 48 = 144