Percentage and Profit & Loss

PrepBank · পাতা ১৪ / ১৭ · ১,৩০১–১,৪০০ / ১,৬৯৬

১,৩০১.

Alal sold an article at 6% loss. Had he sold it for Tk. 64 more, he would have made a profit of 10%. Then the cost of the article is =?

ক
Tk. 320
খ
Tk. 400
গ
Tk. 450
ঘ
Tk. 480

ব্যাখ্যা

Question: Alal sold an article at 6% loss. Had he sold it for Tk. 64 more, he would have made a profit of 10%. Then the cost of the article is =?

Solution:
Let, the cost of the article is x taka

Selling price = 0.94x

ATQ,
0.94x + 64 = 1.1x
⇒ 1.1x - 0.94x = 64
⇒ 0.16x = 64
⇒ x = 64/0.16 = 400 taka

১,৩০২.

If the price of sugar increases by 10%, by what percentage a housewife should reduce the consumption of sugar so that expense is not increased?

ক
1%
খ
7%
গ
11%
ঘ
None of the above

ব্যাখ্যা

Question: If the price of sugar increases by 10%, by what percentage a housewife should reduce the consumption of sugar so that expense is not increased?

Solution:
Let the price be Tk. x per kg
Consumption be y kg

Expenditure = price × consumption
⇒ Expenditure = x × y

Price of sugar is increased by 10%
New price of sugar = Tk. 1.1x per kg

Let new consumption be z kg
New Expenditure = (1.1x) × z

New Expenditure = old Expenditure
⇒ (1.1x) × z = x × y
⇒ z = y/1.1

Reduction in consumption = (y - z) = y - y/1.1 = y/11

Percentage reduction in consumption = (reduction in consumption/original consumption)× 100
Percentage reduction in consumption = [(y/11)/y] × 100 = 100/11 = 9.09% ≈ 9.1%

১,৩০৩.

220% of a number X is 44. What is 44% of X.

ক
8.8
খ
8.9
গ
6.6
ঘ
7.7
ঙ
None of these

ব্যাখ্যা

Question: 220% of a number X is 44. What is 44% of X.

Solution:
Given,
220% of X = 44
⇒ (220X)/100 = 44
⇒ X = (44 × 100)/220
Or, X = 20

Thus,
44% of 20
= (44 × 20)/100
= 8.8

১,৩০৪.

Which of the numbers below is not equivalent to 2%?

ক
ক) 1/50
খ
খ) 1/10
গ
গ) 0.02
ঘ
ঘ) 2/100

ব্যাখ্যা

2% = 2/100 = 1/50 = 0.02

১,৩০৫.

25% of Rasel's yearly income is equal to 75% of Aman's monthly income. If Aman's yearly income is 240000 taka. What is Rasel's monthly income?

ক
Tk. 4500
খ
Tk. 6000
গ
Tk. 5000
ঘ
Tk.2300

ব্যাখ্যা

Question: 25% of Rasel's yearly income is equal to 75% of Aman's monthly income. If Aman's yearly income is 240000 taka. What is Rasel's monthly income?

Solution:
Aman's yearly income is 240000 taka
Aman's monthly income is 240000/12 taka
= 20000 taka

75% of Aman's monthly income = 0.75 × 20000 = 15000 taka

25% of Rasel's yearly income = 15000
Rasel's yearly income = 15000 × 4 = 60000 taka

∴ Rasel's monthly income = 60000/12 = Tk. 5000

১,৩০৬.

A man spent 1/2 of his money and then lost 1/4 of the remainder. He was left with Tk. 4.236. How much did he start with?

ক
ক) 9600
খ
খ) 10400
গ
গ) 11,296
ঘ
ঘ) 12800

ব্যাখ্যা

Let,
He has TK. x
ATQ, x - x/2 - x/2×1/4 = 4236
or, x/2 - x/8 = 4236
or, (4x - x)/8 = 4236
∴ x = (4236×8)/3 = 11,296

১,৩০৭.

A fruit seller had some bananas. He sells 40% bananas and still has 420 bananas. Originally, he had how many bananas?

ক
200
খ
500
গ
650
ঘ
700

ব্যাখ্যা

Question: A fruit seller had some bananas. He sells 40% bananas and still has 420 bananas. Originally, he had how many bananas?

Solution:
Suppose originally he had x bananas.

ATQ,
(100 - 40)% of x = 420
⇒ 60% of x = 420
⇒ 60x/100 = 420
⇒ 60x = 42000
⇒ x = 42000/60
∴ x = 700

Originally he had 700 pcs bananas.

১,৩০৮.

An investor earns 3% return on (1/4)^thof his capital, 5% on (2/3)^rdand 11% on the reminder. What is the average rate of return he earns on his total capital?

ক
5%
খ
5.5%
গ
10%
ঘ
10.5%

ব্যাখ্যা

Question: An investor earns 3% return on (1/4)^thof his capital, 5% on (2/3)^rdand 11% on the reminder. What is the average rate of return he earns on his total capital?

Solution:
Let, the capital be x taka

Earns on 3% rate = (x/4) × 3/100 = 3x/400
Earns on 5% interest = (2x/3) × 5/100 = x/30

Remainder = x - (x/4) - (2x/3)
= x{1 - (11/12)}
= x/12

Earns on 11% interest = (x/12) × (11/100)
= 11x/1200

Total return = (3x/400) + (x/30) + (11x/1200)
= (9x + 40x + 11x)/1200
= 60x/1200
= x/20

The average rate of return he earns on his total capital = {(x/20)/x} × 100%
= 5%

১,৩০৯.

How much water must be added to a bucket which contains 40 liters of milk at the cost price of Tk 3.50 per liter so that the cost of milk reduces to Tk 2 per liter?

ক
ক) 25 liters
খ
খ) 28 litres
গ
গ) 30 liters
ঘ
ঘ) 35 liters

ব্যাখ্যা

Total cost price = Tk (40 x 7/2) = Tk 140
Cost per litre = Tk n2,
Total quantity = 140/2 = 70 Litres.
Water to be added =(70-40) =30 Litres.

১,৩১০.

A radio sold a loss of 2.5%. Had he sold it for Tk. 100 more, he would have gained 7.5%. In order to gain 12.5%, he should sell it for:

ক
ক) 850
খ
খ) 925
গ
গ) 1080
ঘ
ঘ) 1125
ঙ
ঙ) 1200

ব্যাখ্যা

Cost Price = 100
Selling price = 100 - 2.5 = 97.5
New selling price at 7.5% = 107.5
difference between two selling price = 107.5 - 97.5 = 10
10% price is equal to Tk. 100
1% price is equal to Tk. 100/10%
100% price is equal to Tk. (100/10%) × 100
= 1000
so Cost price = 1000
SP at 12.5% = (100+12.5/100) × 1000
= 1125

১,৩১১.

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:
Percentage of boys = 75%
Percentage of girls = 25%

ATQ,
∴ Number of Girls = 25% = 520
⇒ 25% = 520
⇒ 1% = 520/25
∴ 75% = (520 × 75)/25
= 1560

১,৩১২.

Due to a 25% reduction in sugar price, a housewife can buy 5 extra kilograms for 600 Taka. Find the sugar’s original price per kg.

ক
Tk. 32
খ
Tk. 40
গ
Tk. 28
ঘ
Tk. 48

ব্যাখ্যা

Question: Due to a 25% reduction in sugar price, a housewife can buy 5 extra kilograms for 600 Taka. Find the sugar’s original price per kg.

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

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

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

∴ Original price per kg = Tk. 40

১,৩১৩.

An investor earns 3% return on 1/4 of his capital, 5% on 2/3 and 11% on the remainder. What is the average rate of return he earns on his total capital?

ক
ক) 4%
খ
খ) 3%
গ
গ) 5%
ঘ
ঘ) 6%

ব্যাখ্যা

Let
The investor total capital is x

Total return = 3% of (x/4) + 5% of (2x/3) + 11% of {x - (x/4) - (2x/3)}
= (3x/400) + (10x/300) + (11/100) of {(12x - 3x - 8x)/12}
= (3x/400) + (10x/300) + (11x/1200)
= (9x + 40x + 11x)/1200
= 60x/1200
= x/20

the average rate of return =[{(x/20)/x} × 100]%
= 5%

১,৩১৪.

A man sells a watch for Tk. 960 at a loss of 20%. What was the original cost price of the watch?

ক
1500 Tk.
খ
1220 Tk.
গ
100 Tk.
ঘ
1200 Tk.

ব্যাখ্যা

Question: A man sells a watch for Tk. 960 at a loss of 20%. What was the original cost price of the watch?

Answer:
Here,
Selling Price = 960 Tk.
and Loss 20 %,
Now we can write,
The Selling Price is 80 Tk. and the cost price is = 100 Tk.
∴ The Selling Price is 1 Tk. then the cost price is = 100/80 Tk.
∴ The Selling Price is 960 Tk. then the cost price is = (100×960)/80 Tk.
= 1200 Tk.

১,৩১৫.

In a Bank, 30% of the applicants are from Rajshahi district and 20% of them from Rajshahi city. What percent of the total applicants are from Rajshahi city?

ক
ক) 4%
খ
খ) 6%
গ
গ) 8%
ঘ
ঘ) 10%

ব্যাখ্যা

Question: In a Bank, 30% of the applicants are from Rajshahi district and 20% of them from Rajshahi city. What percent of the total applicants are from Rajshahi city?

Solution:
ধরি,
মোট আবেদনকারী = ১০০ জন
রাজশাহী থেকে আছে = ১০০ এর ৩০% = ৩০ জন

রাজশাহী শহর থেকে আছে = ৩০ এর ২০% = ৬%

১,৩১৬.

50% of a number is 1200. What is 6% of that number?

ক
216
খ
242
গ
224
ঘ
144

ব্যাখ্যা

Question: 50% of a number is 1200. What is 6% of that number?

Solution:
Let the number be x

Then,
50% of x = 1200
⇒ 50x/100 = 1200
⇒ x = (1200 × 100)/50
⇒ x = 2400

∴ 6% of 2400
= 2400 × (6/100)
= 144

১,৩১৭.

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

ক
10%
খ
9%
গ
8%
ঘ
5%

ব্যাখ্যা

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

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

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

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

১,৩১৮.

An error 2% in excess in made while measuring the side of a square. The percentage of error in the calculated area of the square is:

ক
ক) 2.00%
খ
খ) 4.04%
গ
গ) 2.02%
ঘ
ঘ) 4.00%

ব্যাখ্যা

Let the correct side of the square be x cm

Then, incorrect side =x + 2x/100 =1.02x

Correct area =x²
Incorrect area =(1.02x)²=1.0404x²

% Error ={(1.0404x² - x²/x²) × 100}%
=(0.0404×100)%
= 4.04%

১,৩১৯.

What is the purchase price of an article if the profit by selling it for tk 250 is 25%

ক
ক) Tk. 150
খ
খ) Tk. 180
গ
গ) Tk. 200
ঘ
ঘ) Tk. 210

ব্যাখ্যা

For 25% profit,
If the selling price is 125 tk, then buying price is 100 tk
So, when the selling price is 250 tk, buying price is (100×250)/125 = 200 tk

১,৩২০.

An article 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 Tk. 120
খ
Profit Tk. 120
গ
Loss Tk. 80
ঘ
Profit Tk. 80

ব্যাখ্যা

Question: An article 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 article. C.P. = 2400 × (100/125) = 1920.

New selling price = Tk. 1800
∴ Loss = 1920 - 1800 = 120

১,৩২১.

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

ক
ক) 20%
খ
খ) 25%
গ
গ) 30%
ঘ
ঘ) 15%

ব্যাখ্যা

Let C.P. of each books Tk. 1
C.P. of 20 books Tk. 20
S.P. of 20 books Tk. 15
Loss = TK. (20 - 15) = Tk.5

Loss% = {(5/20) × 100}% = 25%

১,৩২২.

A merchant sells one table for Tk. 1200 at a profit of 25% and another for Tk. 1500 at a loss of 10%. His total gain or loss percentage is-

ক
3.14% gain
খ
2.78% gain
গ
4.82% loss
ঘ
1.73% loss

ব্যাখ্যা

Question: A merchant sells one table for Tk. 1200 at a profit of 25% and another for Tk. 1500 at a loss of 10%. His total gain or loss percentage is-

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

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

১,৩২৩.

Abir scored 30% marks and failed by 15 marks. Sunny scored 40% marks and obtained 35 marks more than those required to pass. The pass percentage is-

ক
25%
খ
30%
গ
32%
ঘ
33%

ব্যাখ্যা

Question: Abir scored 30% marks and failed by 15 marks. Sunny scored 40% marks and obtained 35 marks more than those required to pass. The pass percentage is-

Solution:
Let, total mark is x

Now
0.3x + 15 = 0.4x - 35
⇒ 0.4x - 0.3x = 35 + 15
⇒ 0.1x = 50
⇒ x = 50/0.1
∴ x = 500

Pass mark = 0.3 × 500 + 15
= 150 + 15
= 165

Pass percentage = (165/500) × 100%
= 33%

১,৩২৪.

এক দোকানদারের দাবি, তিনি একটি পণ্য ২৩ টাকা প্রতি কেজি বিক্রি করেন, যদিও তার জন্য এটি খরচ হচ্ছে ২৫ টাকা প্রতি কেজি। তিনি বলেন, গ্রাহকদের ভালো সুবিধা দেয়ার জন্য তিনি এই ক্ষতি করছেন। তবে, তদন্ত করে দেখা যায় যে দোকানদার ১ কেজির জায়গায় ৮০০ গ্রাম ওজন ব্যবহার করছেন। তাহলে, দোকানদার কতটা লাভ বা ক্ষতি করছেন?

ক
১৫% লাভ
খ
১০% লাভ
গ
১০% ক্ষতি
ঘ
৮% ক্ষতি
ঙ
কোনটি নয়

ব্যাখ্যা

প্রশ্ন: এক দোকানদারের দাবি, তিনি একটি পণ্য ২৩ টাকা প্রতি কেজি বিক্রি করেন, যদিও তার জন্য এটি খরচ হচ্ছে ২৫ টাকা প্রতি কেজি। তিনি বলেন, গ্রাহকদের ভালো সুবিধা দেয়ার জন্য তিনি এই ক্ষতি করছেন। তবে, তদন্ত করে দেখা যায় যে দোকানদার ১ কেজির জায়গায় ৮০০ গ্রাম ওজন ব্যবহার করছেন। তাহলে, দোকানদার কতটা লাভ বা ক্ষতি করছেন?

সমাধান:
০.৮ কেজির বিক্রয় মূল্য = ২৩ টাকা

এখন,
১ কেজির বিক্রয় মূল্য = ২৩/০.৮ টাকা
= ১১৫/৪ টাকা
= ২৮.৭৫ টাকা

∴ শতকরা লাভ = {(২৮.৭৫ - ২৫)/২৫} × ১০০%
= (৩.৭৫/২৫) × ১০০%
= ১৫%

১,৩২৫.

40% of a number when subtracted from 140, gives the number itself. Find the number.

ক
ক) 95
খ
খ) 100
গ
গ) 110
ঘ
ঘ) 90

ব্যাখ্যা

Question: 40% of a number when subtracted from 140, gives the number itself. Find the number.

Solution:
ধরি, সংখ্যাটি = ক
তাহলে,
১৪০ - (ক এর ৪০%) = ক
১৪০ - ৪০ক/১০০ = ক
১৪০০০ - ৪০ক = ১০০ক
১৪০ক = ১৪০০০
ক = ১০০

১,৩২৬.

In a shipment of 120 machine parts, 5 percent were defective. In a shipment of 80 machine parts, 10 percent were defective. For the two shipments combined, what percent of the machine parts were defective?

ক
6.5%
খ
7.0%
গ
7.5%
ঘ
8.0%
ঙ
None of these

ব্যাখ্যা

Question: In a shipment of 120 machine parts, 5 percent were defective. In a shipment of 80 machine parts, 10 percent were defective. For the two shipments combined, what percent of the machine parts were defective?

Solution:
Defective machine in 1st shipment = 5% of 120 = 6

Defective machine in 2nd shipment = 10% of 80 = 8

Total Defective machine = (6 + 8) = 14

Percentage of combined defective machine = (14/200) × 100% = 7%

১,৩২৭.

A total profit of Tk. 5400 is to be distributed amongst A, B and C such that A : B = 5 : 4 and B : C = 8 : 9. The share of B in the profit is:

ক
ক) Tk. 1200
খ
খ) Tk. 1600
গ
গ) Tk. 1800
ঘ
ঘ) Tk. 800

ব্যাখ্যা

Question: A total profit of Tk. 5400 is to be distributed amongst A, B and C such that A : B = 5 : 4 and B : C = 8 : 9. The share of B in the profit is:

Solution:
A Total Profit = Tk. 5400

Profit ratio,
A : B = 5 : 4
B : C = 8 : 9
As B is common in both ratio, we make B equal in both ratio by multiplying One B in another.
A : B = (5 × 8) : (4 × 8) = 40 : 32
B : C = (8 × 4) : (9 × 4) = 32 : 36

So, ratio of A : B : C = 40 : 32 : 36 = 10 : 8 : 9

Now,
B shares in profit = (5400 × 8)/27
= Tk. 1600

১,৩২৮.

The cost of a milk and water mixture in a 7 : 3 ratio is Tk. 500. Adding 2 liters of water increases profit. Find the profit percentage.

ক
40%
খ
32%
গ
30%
ঘ
10%
ঙ
20%

ব্যাখ্যা

Question: The cost of a milk and water mixture in a 7:3 ratio is Tk. 500. Adding 2 liters of water increases profit. Find the profit percentage.

Solution:
Let
Milk = 7 liters
Water = 3 liters
Original mixture quantity = 10 liters

Cost of original mixture = 500 Taka
Cost per liter = 500 / 10 = 50 Taka

Water added = 2 liters
New total water = 3 + 2 = 5 liters
Milk remains = 7 liters
Total mixture = 7 + 5 = 12 liters

Total Selling Price = 12 × 50 = 600 Taka

Profit = SP - CP = 600 - 500 = 100
Profit % = (100/500) × 100 = 20%

∴ Profit percent = 20%

১,৩২৯.

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

ক
ক) 60%
খ
খ) 50%
গ
গ) 40%
ঘ
ঘ) 30%

ব্যাখ্যা

প্রশ্ন: In a transaction, the profit percentage is 80% of the cost. If the cost further increases by 20% but the selling price remains the same, how much is the decrease in profit percentage?

সমাধান:
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%.

১,৩৩০.

Three-fourths of a number is equal to 60% of another number and the difference between these two number is 20. What is the sum of these two numbers?

ক
170
খ
180
গ
190
ঘ
Cannot be determined

ব্যাখ্যা

Question: Three-fourths of a number is equal to 60% of another number and the difference between these two number is 20. What is the sum of these two numbers?

Solution:
Let the numbers be x and x + 20

Then,
3x/4 = 60% of (x + 20)
⇒ 3x/4 = 60(x + 20)/100
⇒ 3x/4 = 3(x + 20)/5
⇒ x/4 = (x + 20)/5
⇒ 5x = 4x + 80
⇒ 5x - 4x = 80
⇒ x = 80

The sum of these two numbers = x + x + 20
= 2x + 20
= 2 × 80 + 20
= 160 + 20
= 180

১,৩৩১.

Suman buys 160 chocolates for Tk. 480. She wanted to earn 30% profit by selling them. But Rakesh visited her and she gave him 25% of those chocolates at the cost price itself. But even after doing this, she earned a profit of 30% as decided. For how much did she sell each chocolate?

ক
Tk. 3
খ
Tk. 4.2
গ
Tk. 3.4
ঘ
Tk. 4.8
ঙ
None

ব্যাখ্যা

Question: Suman buys 160 chocolates for Tk. 480. She wanted to earn 30% profit by selling them. But Rakesh visited her and she gave him 25% of those chocolates at the cost price itself. But even after doing this, she earned a profit of 30% as decided. For how much did she sell each chocolate?

Solution:
Total chocolates = 160
Cost price (CP) of all chocolates = Tk. 480
CP per chocolate = 480/160 = Tk. 3
Desired profit = 30%
Given to Rakesh = 25% of chocolates at CP
25% of 160 = 40 chocolates
Remaining chocolates = 160 - 40 = 120 chocolates

CP for 40 chocolates = 40 × Tk. 3 = Tk. 120
CP for 120 chocolates = 120 × Tk. 3 = Tk. 360

To achieve 30% profit overall:
Let selling price (SP) per chocolate = x
Total revenue = (40 × 3) + (120 × x)
Total revenue = 120 + 120x

For 30% profit:
Total revenue = CP + 30% of CP
120 + 120x = 480 + (0.3 × 480)
120 + 120x = 480 + 144
120x = 504
x = 4.2
Therefore, Suman sold each remaining chocolate for Tk. 4.2

১,৩৩২.

Mehedi purchased two articles at the same price and sold one at a profit of 20% and the other at a profit of 22.5%. If the difference between the two selling price is Tk. 150, what is the cost price of each of the articles?

ক
Tk. 6000
খ
Tk. 5000
গ
Tk. 4000
ঘ
Tk. 3000

ব্যাখ্যা

Question: Mehedi purchased two articles at the same price and sold one at a profit of 20% and the other at a profit of 22.5%. If the difference between the two selling price is Tk. 150, what is the cost price of each of the articles?

Solution:
Let the cost price of each of the articles = 100.
The selling price of the first watch = 120
and the selling price of the second watch = 122.5
The difference in the selling price = 122.5 - 120 = 2.5

The difference in the selling price = 2.5 if the cost price = 100
If the difference in selling price = 150, then the cost price = (150 × 100)/2.5 = 6000

১,৩৩৩.

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
5%
গ
7%
ঘ
6%
ঙ
None

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%.

১,৩৩৪.

15% of 40% of a number is 120. What is 24% of that number?

ক
2000
খ
1250
গ
600
ঘ
480

ব্যাখ্যা

Question: 15% of 40% of a number is 120. What is 24% of that number?

Solution:
let, a number is x

x × 0.15 × 0.4 = 120
⇒ x = 120/( 0.15 × 0.4)
= 2000

24% of that number is = 2000 × 0.24
= 480

১,৩৩৫.

40 litres of a mixture of milk and water contains 10% of water, the water to be added, to make the water content 20% in the new mixture. Find how many litres water will be added ?

ক
ক) 6 litres
খ
খ) 6.5 litres
গ
গ) 5.5 litres
ঘ
ঘ) 5 litres

ব্যাখ্যা

Water content in 40 litres of mixture.
= 40×(10/100) =4 litres
Milk in the mixture.
= 40−4=36 litres
Let x litres of water is mixed
⇒(4+x)/(40+x)=20/100
⇒x=5 litres

১,৩৩৬.

P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work?

ক
9
খ
11
গ
13
ঘ
15

ব্যাখ্যা

Work done by P in 1 day = 1/23
Let work done by Q in 1 day = q
q × (130/100) = 1/23
⇒ q = 100/(23 × 130)
= 10/(23 × 13)
Work done by P and Q in 1 day = 1/23 + 10/(23 × 13)
= 23/(23 × 13)
= 1/13
⇒ P and Q together can do the work in 13 days

১,৩৩৭.

What is the rate of discount is a car that had a regular price of Tk. 3,000 is sold for Tk.2,790?

ক
ক) 15%
খ
খ) 7%
গ
গ) 12%
ঘ
ঘ) 9%

ব্যাখ্যা

প্রশ্ন : What is the rate of discount is a car that had a regular price of Tk. 3,000 is sold for Tk.2,790?

সমাধান :

লিখিতমূল্য = 3000 টাকা
বিক্রয় মূল্য = 2790 টাকা

ছাড় = (3000 - 2790) টাকা
= 210 টাকা
ছাড়ের হার = {(210/3000) × 100}%
=7%

১,৩৩৮.

A shopkeeper earns a profit of 10% after allowing a discount of 20% on the market price. The cost price of the product whose market price is Tk. 1100, is =?

ক
ক) 800Tk.
খ
খ) 750Tk.
গ
গ) 850Tk.
ঘ
ঘ) 880Tk.

ব্যাখ্যা

Question: A shopkeeper earns a profit of 10% after allowing a discount of 20% on the market price. The cost price of the product whose market price is Tk. 1100, is =?

Solution:
Market price of the product is = Tk. 1100
After discount selling price of the product is = (1100 × 80)/100
= 880 Tk.

Cost price of the product is = (880 × 100)/110 = 800Tk.

১,৩৩৯.

The sale price of an article including the Sales Tax is Tk. 616. The rate of Sales Tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is-

ক
Tk. 500
খ
Tk. 550
গ
Tk. 400
ঘ
Tk. 600

ব্যাখ্যা

Question: The sale price of an article including the Sales Tax is Tk. 616. The rate of Sales Tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is-

Solution:
Let,
The cost price be x.
Selling price = x + 12% of x
= x + (12x/100)
= 28x/25

ATQ,
(28x/25) + 10% of (28x/25) = 616
⇒ (28x/25) + (280x/2500) = 616
⇒ (28x/25) + (14x/125) = 616
⇒ (140x + 14x)/125 = 616
⇒ 154x = 77000
∴ x = 500

∴ Cost price tk. 500.

১,৩৪০.

Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solutions Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new liquid solution is liquid X?

ক
30%
খ
33.33%
গ
37.5%
ঘ
40%

ব্যাখ্যা

Question: Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solutions Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new liquid solution is liquid X?

Solution:
At the beggining, we have 8 KG of solution Y,
70% of 8 KG = 5.6 KG of Water
30% of 8 KG = 2.4 KG of X

2KG of water evaporate:
now remaining
5.6 KG - 2 KG = 3.6 KG of Water
2.4 KG of X

2KG of liquid are added:
Now,
3.6 KG + 2 × 0.70 = 5 KG of Water
2.4 KG + 2 × 0.30 = 3 KG of X

So we have 3 KG of X in 8 KG (3 + 5) solution.
Therefore X concentration is (3/8) × 100% = 37.5%

১,৩৪১.

Due to a decrease of 10% in the price of rice, 3 more quintals of rice can be bought for Tk. 1500. What is the present price of 12 quintals of rice?

ক
ক) Tk. 200
খ
খ) Tk. 600
গ
গ) Tk. 400
ঘ
ঘ) Tk. 210

ব্যাখ্যা

Question: Due to a decrease of 10% in the price of rice, 3 more quintals of rice can be bought for Tk. 1500. What is the present price of 12 quintals of rice?

Solution:
৩ কুইণ্টাল চালের দাম = ১৫০০ এর ১০%
= ১৫০ টাকা
∴ ১ কুইণ্টাল চালের দাম = ১৫০/৩ টাকা
∴ ১২ কুইণ্টাল চালের দাম = (১৫০ × ১২)/৩ টাকা
= ৬০০ টাকা

১,৩৪২.

I'd called her yesterday, ______?

ক
wouldn't I
খ
had I
গ
would I
ঘ
hadn't I

ব্যাখ্যা

• Tag question করার নিয়ম:
- Tag question ব্যবহার করা হয় উক্তিটি সত্য না মিথ্যা তা নিশ্চিত করার জন্য।
- Statement positive হলে tag question টি negative হবে।
- Subject ও tense অনুসারে auxiliary verb দ্বারা tag question হয়।

• Confusing Contraction sentence এর tag question করার নিয়ম:
- যদি subject এরপর 'd থাকে অর্থাৎ, verb টি base form এ আসে, তাহলে এটিকে modal auxiliary হিসেবে would ধরতে হবে।
- Example: If I were a rich man, I'd establish a hospital, wouldn't I?

- তবে 'd এরপরের verb টি যদি past participle form এ থাকে তাহলে তাকে past perfect tense এর had হিসেবে ধরতে হবে।
- Example: I'd reached there in time, hadn't I?

• Correct answer: I had called her yesterday, hadn't I?

Source: Advanced Learner's Communicative English Grammar & Composition By Chowdhury & Hossain.

১,৩৪৩.

Mahin loses one-seventh of the cost by selling a pen for Tk.144. If the pen is sold for Tk. 189, what is the gain percent?

ক
ক) 12.5%
খ
খ) 15.0%
গ
গ) 15.5%
ঘ
ঘ) 13.0%

ব্যাখ্যা

Let the cost price be Tk. x
⇒ Loss = x/7

⇒ Selling price = x – (x/7)
⇒ 144 = 6x/7
⇒ x = 168

⇒ New selling price = Tk. 189
⇒ Gain % = {(189 – 168)/168} × 100
= 12.5%

১,৩৪৪.

A student scores 55% marks in 8 papers of 100 marks each. He scores 15% of the total marks in Bangla How much does he score in Bangla?

ক
76
খ
72
গ
66
ঘ
64

ব্যাখ্যা

Question: A student scores 55% marks in 8 papers of 100 marks each. He scores 15% of the total marks in Bangla How much does he score in Bangla?

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

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

১,৩৪৫.

The cost price of a product is 65% of the market price. How much is the gain in percent if the product is sold allowing a discount of 15%?

ক
ক) 30.77%
খ
খ) 34.51%
গ
গ) 37.5%
ঘ
ঘ) 32.51%

ব্যাখ্যা

Question: The cost price of a product is 65% of the market price. How much is the gain in percent if the product is sold allowing a discount of 15%?

Solution:
ধরি
পণ্যটির তালিকামূল্য 100 টাকা
পণ্যটির ক্রয়মূল্য = 65 টাকা

15% হ্রাসে,
পণ্যটির মূল্য = (100 - 15) টাকা = 85 টাকা
লাভ = 85 - 65 = 20 টাকা
শতকরা লাভ = {(20/65) × 100%}
= 30.77%

১,৩৪৬.

If x = 50%, by what percent is x larger than x²?

ক
ক) 1%
খ
খ) 100%
গ
গ) 25%
ঘ
ঘ) None

ব্যাখ্যা

Question: If x = 50%, by what percent is x larger than x²?

Solution:
x = 50%
⇒ x = 50/100 = 1/2
⇒ x² = 1/4 = 1/4 × 100% = 25%

x is larger than x² = (50% - 25%) = 25%

x is larger than x² (in percentage) = (25/25 ×100)% = 100%

১,৩৪৭.

A manufacturer sells three products i.e. A, B and C. Product A costs 200 and sells for 250, Product B costs 150 and sells for 180, product C costs 100 and sells for 110. On which product, he has maximum percentage of profit?

ক
ক) B only
খ
খ) A and B both
গ
গ) A only
ঘ
ঘ) C only

ব্যাখ্যা

Question: A manufacturer sells three products i.e. A, B and C. Product A costs 200 and sells for 250, Product B costs 150 and sells for 180, product C costs 100 and sells for 110. On which product, he has maximum percentage of profit?

Solution:
প্রোডাক্ট A তে,
লাভ = ২৫০ - ২০০ = ৫০ টাকা
শতকরা লাভ = (৫০ × ১০০)/২০০ = ২৫%

প্রোডাক্ট B তে,
লাভ = ১৮০ - ১৫০ = ৩০ টাকা
শতকরা লাভ = (৩০ × ১০০)/১৫০ = ২০%

প্রোডাক্ট C তে,
লাভ = ১১০ - ১০০ = ১০ টাকা
শতকরা লাভ = (১০ × ১০০)/১০০ = ১০%

সুতরাং প্রোডাক্ট A তে লাভ বেশি হবে।

১,৩৪৮.

A and B share profits in the ratio 7 : 3. If 12% of the total profit is given to charity and A’s share is Tk. 3080, find the total profit.

ক
Tk. 4500
খ
Tk. 5000
গ
Tk. 6000
ঘ
Tk. 6500

ব্যাখ্যা

Question: A and B share profits in the ratio 7 : 3. If 12% of the total profit is given to charity and A’s share is Tk. 3080, find the total profit.

Solution:
Let
total profit = Tk. x
∴ Remaining after charity = 88% of x = 22x/25

ATQ,
(22x/25) of (7/10) = 3080
⇒ 154x/250 = 3080
⇒ 154x = 3080 × 250
⇒ x = (3080 × 250)/154
∴ x = 5000

∴ the total profit = Tk. 5000

১,৩৪৯.

A bookseller procures 40 books for 3600 Tk and sells them at a profit equal to the selling price of 4 books. What is the selling price of one quarter dozen books, if the price of each book is same?

ক
25 Tk
খ
90 Tk
গ
100 Tk
ঘ
300 Tk
ঙ
1200 Tk

ব্যাখ্যা

Question: A bookseller procures 40 books for 3600 Tk and sells them at a profit equal to the selling price of 4 books. What is the selling price of one quarter dozen books, if the price of each book is same?

Solution:
Cost price of each book = 3600/40 Tk
= 90 Tk

Now,
Selling Price of 40 books = CP of 40 books + SP of 4 books.
Selling Price of 40 books - SP of 4 books = CP of 40 books.
SP of 36 books = 3600 Tk
SP of 1 book = 3600/36 Tk
= 100 Tk

Selling price of one dozen books = 12 × 100 = 1200 Tk
∴ Selling price of one quarter dozen books = (1/4) × 1200 = 300 Tk

১,৩৫০.

An employer pays 3 workers A, B, and C a total of TK. 48,000 a week. A is paid 150% of the amount B is paid and 60% of the amount C is paid. How much does A make a week?

ক
12400 tk
খ
13200 tk
গ
14400 tk
ঘ
15600 tk

ব্যাখ্যা

Question: An employer pays 3 workers A, B, and C a total of TK. 48,000 a week. A is paid 150% of the amount B is paid and 60% of the amount C is paid. How much does A make a week?

Solution:
A = 159% of B
⇒ A = 150B/100
⇒ A/B = 150/100
∴ A : B = 3 : 2

A = 60% of C
⇒ A = 60C/100
⇒ A/C = 60/100
∴ A : C = 3 : 5

∴ A : B : C = 3 : 2 : 5

A makes the week = (3/10) × 48000
= 14400 tk

১,৩৫১.

A wholesaler buys a laptop for Tk. 40,000 and sells it to a retailer at a profit of 20%. The retailer then sells it to a customer at a profit of 15%. How much does the customer pay to the retailer?

ক
Tk. 52,600
খ
Tk. 60,000
গ
Tk. 55,200
ঘ
Tk. 58,500

ব্যাখ্যা

Question: A wholesaler buys a laptop for Tk. 40,000 and sells it to a retailer at a profit of 20%. The retailer then sells it to a customer at a profit of 15%. How much does the customer pay to the retailer?

Solution:
পাইকারি বিক্রেতার ক্রয়মূল্য = 40,000 টাকা
20% লাভে পাইকারি বিক্রেতার বিক্রয়মূল্য (যা খুচরা বিক্রেতার ক্রয়মূল্য) = 40,000 + 40,000 এর 20%
= 40,000 + (40,000 × 20/100)
= 40,000 + 8,000 = 48,000 টাকা

∴ খুচরা বিক্রেতার ক্রয়মূল্য = 48,000 টাকা

আবার, খুচরা বিক্রেতা 15% লাভে এটি বিক্রি করেন।
∴ 15% লাভে খুচরা বিক্রেতার বিক্রয়মূল্য (যা ক্রেতার পরিশোধিত মূল্য) = 48,000 + 48,000 এর 15%
= 48,000 + (48,000 × 15/100)
= 48,000 + 7,200 = 55,200 টাকা

∴ ক্রেতা খুচরা বিক্রেতাকে 55,200 টাকা প্রদান করেন।

১,৩৫২.

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

ক
ক) 56.25%
খ
খ) 25.56%
গ
গ) 50.25%
ঘ
ঘ) 54.25%

ব্যাখ্যা

Let the cost price of goods be 100 taka.
At 25% profit,
if cost price of goods is 100 taka, selling price of goods is (100 + 25) taka or 125 taka.

At a discount 20%,
80% of goods' price = 125 taka.
100% of goods' price shall be (125×100/80) taka or 156.25 taka.
profit percentage would be (156.25 - 100) taka or 56.25 taka.

১,৩৫৩.

In a market survey, 30% of respondents opted for product P and 50% opted for product Q. The remaining respondents were uncertain. If the difference between the number of respondents who opted for product Q and those who were uncertain is 420, how many respondents were surveyed?

ক
600
খ
900
গ
1200
ঘ
1400
ঙ
1700

ব্যাখ্যা

Question: In a market survey, 30% of respondents opted for product P and 50% opted for product Q. The remaining respondents were uncertain. If the difference between the number of respondents who opted for product Q and those who were uncertain is 420, how many respondents were surveyed?

Solution:
Here, product P opted for 30% respondents & product Q opted for 50% respondents.

Uncertain respondents = (100 - (30 + 50))% = 20%
The difference between those who opted for product Q and those who were uncertain = (50 - 20)% = 30%

Let total number of respondents = a
∴ a × 30% = 420
⇒ 30a/100 = 420
⇒ a = (420 × 100)/30
⇒ a = 1400

১,৩৫৪.

The profit earned after selling an article for Tk. 1754 is the same as loss incurred after selling the article for Tk. 1492. What is the cost price of the article?

ক
ক) Tk. 1689
খ
খ) Tk. 2623
গ
গ) Tk. 1623
ঘ
ঘ) Tk. 3246

ব্যাখ্যা

Question: The profit earned after selling an article for Tk. 1754 is the same as loss incurred after selling the article for Tk. 1492. What is the cost price of the article?

Solution:
Let,
The cost price of the article be Tk. x.

ATQ,
x - 1492 = 1754 - x
⇒ 2x = 1754 + 1492
⇒ 2x = 3246
⇒ x = 3246/2
∴ x = 1623

∴ The cost price of the article is Tk. 1623.

১,৩৫৫.

If 50% of (x - y) = 30% of (x + y), then what percent of x is y?

ক
25
খ
30
গ
35
ঘ
40

ব্যাখ্যা

Question: If 50% of (x - y) = 30% of (x + y), then what percent of x is y?

Solution:
50% of (x - y) = 30% of (x + y)
50(x - y)/100 = 30(x + y)/100
5(x - y) = 3(x + y)
5x - 5y = 3x + 3y
5x - 3x = 5y + 3y
2x = 8y
x/y = 8/2
x = 4y

Percent of x is y = (1/4) × 100%
= 25%

১,৩৫৬.

We rarely go out during exams, ______?

ক
don't we
খ
did we
গ
do we
ঘ
does we

ব্যাখ্যা

• Correct sentence: We rarely go out during exams, do we?

• Tag question করার নিয়ম:
- সাধারণত Tag question ব্যবহৃত হয় পূর্বে উল্লেখিত কোন উক্তি সত্য না মিথ্যা তা নিশ্চিত হওয়ার জন্য।
- Tag question এর subject সর্বদা মূল sentence এর subject এর pronoun হয়।
- Tag question গঠনে auxiliary verb ব্যবহৃত হয় এবং auxiliary verb এর সংক্ষিপ্ত রূপ হয়।
- Statement positive হলে tag question টা negative হবে। আবার statement negative হলে tag question positive হবে।

• hardly, rarely, scarcely, seldom ইত্যাদি কোনো sentence এ থাকলে, ওই sentence "negative' expression দেয়।
- এর ফলে প্রশ্ন প্রদও বাক্যটির tag 'affirmative' হয়েছে।
- Sentence টিতে subject We হওয়ার কারণে Auxiliary verb 'do' হয়েছে।
- অর্থাৎ, Tag question এর নিয়মানুযায়ী বাক্যটি Negative হওয়ায় Tag question Affirmative হয়েছে।

Source: Advanced Learner's Grammar and Composition by Chowdhury and Hossain.

১,৩৫৭.

A shopkeeper incurs a loss by selling an article for Tk 720. If he had sold it for Tk 1080, he would have made a profit which is five times the initial loss. At what price should he sell the article to make 15% profit?

ক
Tk. 875
খ
Tk. 897
গ
Tk. 905
ঘ
Tk. 920

ব্যাখ্যা

Question: A shopkeeper incurs a loss by selling an article for Tk 720. If he had sold it for Tk 1080, he would have made a profit which is five times the initial loss. At what price should he sell the article to make 15% profit?

Solution:
ধরি, পণ্যের ক্রয়মূল্য = x টাকা
720 টাকায় বিক্রি করলে ক্ষতি = x - 720 টাকা
1080 টাকায় বিক্রি করলে লাভ = 1080 - x টাকা

প্রশ্নমতে,
1080 - x = 5(x - 720)
⇒ 1080 - x = 5x - 3600
⇒ 1080 + 3600 = 5x + x
⇒ 4680 = 6x
∴ x = 780 টাকা

এখন, 15% লাভে,
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য 115 টাকা
ক্রয়মূল্য 1 টাকা হলে বিক্রয়মূল্য (115/100) টাকা
∴ ক্রয়মূল্য 780 টাকা হলে বিক্রয়মূল্য (115 × 780)/100 টাকা
= 897 টাকা

১,৩৫৮.

If a man sells a chair for Tk. 600 and he would loss 20%, then at what price should he sell it to gain 20%?

ক
Tk. 800
খ
Tk. 850
গ
Tk. 1050
ঘ
Tk. 900

ব্যাখ্যা

Question: If a man sells a chair for Tk. 600 and he would loss 20%, then at what price should he sell it to gain 20%?

Solution:
Let
the cost price of the chair be x.

Selling price = x - 20% of x
⇒ 600 = x - (20x/100)
⇒ 600 = x - (x/5)
⇒ 600 = 4x/5
⇒ 4x = 3000
∴ x = 750

To gain 20%, the selling price should be = 750 + 20% of 750
= 750 + {(20/100) of 750}
= 750 + 150
= Tk. 900

১,৩৫৯.

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

ক
4%
খ
6.67%
গ
8%
ঘ
12%

ব্যাখ্যা

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

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

let second discount is x%

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

১,৩৬০.

Jalal bought a bicycle for Taka. 8000 and then sold it at a loss of Taka. 1200. What was the selling price of the bicycle?

ক
Tk. 6800
খ
Tk. 5800
গ
Tk. 800
ঘ
Tk. 680

ব্যাখ্যা

Question: Jalal bought a bicycle for Tk. 8000 and then sold it at a loss of Tk. 1200. What was the selling price of the bicycle?

Answer:
Given,
Cost Price (CP) = 8000 Taka
Loss = 1200 Taka
Using Formula
Selling Price (SP) = Cost Price - Loss
⇒ Selling Price (SP) = Tk. 8000 - Tk. 1200
⇒ Selling Price (SP) = Tk. 6800

Therefore, the selling price of the bicycle is Tk. 6800.

১,৩৬১.

If A = x% of y and B = y% of x, then which of the following is true?

ক
A is smaller than B
খ
If x is smaller than y, then A is greater than B.
গ
A is greater than B
ঘ
None of these

ব্যাখ্যা

Question: If A = x% of y and B = y% of x, then which of the following is true?

Solution:
Given that,
A = x% of y
= (x/100) × y
= (xy)/100

And,
B = y% of x
= (y/100) × x
= (yx)/100
= (xy)/100

So, A = (xy)/100 and B = (xy)/100
⇒ A = B

১,৩৬২.

By selling a bicycle for Tk. 2,850 a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be

ক
Tk. 2,500
খ
Tk. 2,600
গ
Tk. 2,700
ঘ
Tk. 2,900

ব্যাখ্যা

Question: By selling a bicycle for Tk. 2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be

Solution:
Let Cost Price was x
ATQ,
x + 14% of x = 2850
⇒ x + 14x/100 = 2850
⇒ x + 0.14x = 2850
⇒ 1.14x = 2850
⇒ x = 2850/1.14
∴ x = 2500

So, Cost Price = 2500
Now, Selling Price When profit remains at 8%,
= 2500 + 8% of 2500
= 2500 + 200
= Tk. 2700

১,৩৬৩.

Shishir bought a book and sold it at a loss of 10%. If he had bought it for 20% less and sold it for tk 55 more, he would have made a profit of 40%, What was the cost of the book?

ক
200 tk
খ
250 tk
গ
300 tk
ঘ
350 tk
ঙ
400 tk

ব্যাখ্যা

Question: Shishir bought a book and sold it at a loss of 10%. If he had bought it for 20% less and sold it for tk 55 more, he would have made a profit of 40%, What was the cost of the book?

Solution:
Let the cost price of the book be x tk.
The selling price of the book when sold at a 10% loss is 0.92 tk.

If the book had been bought for 20% less, the cost price would be 0.8x tk.
If the selling price had been 55 tk more, the selling price would be 0.9x + 55 tk.
According to the problem, in this case, Shishir would have made a profit of 40%, so the selling price would be 1.4 × 0.8x = 1.12x tk.

ATQ,
0.9x + 55 = 1.12x
⇒ 1.12x - 0.9x = 55
⇒ 0.22x = 55
⇒ x = 55/0.22
⇒ x = 5500/22
∴ x = 250 tk

১,৩৬৪.

A person bought an article for Tk. 1200 and sold it at a profit of 15%. The buyer sold it to a third person at a loss of 5%. Calculate the last selling price?

ক
ক) Tk. 1310
খ
খ) Tk. 1311
গ
গ) Tk. 1380
ঘ
ঘ) Tk. 1280

ব্যাখ্যা

Question: A person bought an article for Tk. 1200 and sold it at a profit of 15%. The buyer sold it to a third person at a loss of 5%. Calculate the last selling price?

Solution:
১৫% লাভে,
১০০ টাকার দ্রব্যের বিক্রয়মূল্য = ১১৫ টাকা
১ টাকার দ্রব্যের বিক্রয়মূল্য = ১১৫/১০০ টাকা
∴ ১২০০ টাকার দ্রব্যের বিক্রয়মূল্য = (১১৫ × ১২০০)/১০০ টাকা
= ১৩৮০ টাকা

৫% ক্ষতিতে,
১০০ টাকার দ্রব্যের বিক্রয়মূল্য = ৯৫ টাকা
১ টাকার দ্রব্যের বিক্রয়মূল্য = ৯৫/১০০ টাকা
∴ ১৩৮০ টাকার দ্রব্যের বিক্রয়মূল্য = (৯৫ × ১৩৮০)/১০০ টাকা
= ১৩১১ টাকা

১,৩৬৫.

Three partners A, B, C start a business. B's Capital is four times C's capital and twice A's capital is equal to thrice B's capital. If the total profit is Tk. 28600 at the end of a year, Find out B's share in it.

ক
Tk. 8400
খ
Tk. 9400
গ
Tk. 10400
ঘ
Tk. 11400

ব্যাখ্যা

Question: Three partners A, B, C start a business. B's Capital is four times C's capital and twice A's capital is equal to thrice B's capital. If the total profit is Tk. 28600 at the end of a year, Find out B's share in it.

Solution:
Let
C's capital = x then
B's capital = 4x
A's capital = 6x
A : B : C = 6x : 4x : x
= 6 : 4 : 1

B's share = 28600 × 4/11
= Tk. 10400

১,৩৬৬.

The population of a town 2 years ago was 62,500. Due to migration to big cities, it decreases every year at the rate of 4%. The present population of the town is -

ক
ক) 56,700
খ
খ) 57,600
গ
গ) 58,800
ঘ
ঘ) 60,000

ব্যাখ্যা

Present population
=62500 × {1 - (4/100)}²
= 62500 × (24/25) × (24/25)
= 57600.

১,৩৬৭.

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

ক
ক) 56.25%
খ
খ) 57%
গ
গ) 52.50%
ঘ
ঘ) None of these

ব্যাখ্যা

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

Solution:
ধরি,
দ্রব্যটির বাজার মূল্য = 100 টাকা
∴ 20% ছাড়ে বিক্রয়মূল্য = (100 - 20) = 80 টাকা।

আবার, ধরি,
দ্রব্যটির উৎপাদন খরচ = x টাকা।

প্রশ্নমতে,
∴ x + x এর 25/100 = 80
বা, x + (x/4) = 80
বা, 5x/4 = 80
∴ x = 64

∴ বাজার মূল্যে পন্যটি বিক্রি করলে,
লাভ =(100 - 64) = 36 টাকা।

∴ 64 টাকায় লাভ হয় = 36 টাকা
∴ 100 টাকায় লাভ হয় = (36 × 100)/64
= 56.25%

১,৩৬৮.

In a survey of 400 students, 65% play basketball, 45% play football, and 15% play neither sport. What percent of students play both sports?

ক
20%
খ
25%
গ
30%
ঘ
15%

ব্যাখ্যা

Question: In a survey of 400 students, 65% play basketball, 45% play football, and 15% play neither sport. What percent of students play both sports?

Solution:
Let,
x% students play both sports
∴ (65 - x)% + (45 - x)% + x% + 15% = 100%
⇒ 65% + 45% + 15% - x% = 100%
⇒ 125% - x% = 100%
∴ x% = 125% - 100% = 25%

১,৩৬৯.

If the price of onion goes up by 25%, by how much should usage be reduced in order to keep the total expense for onion as before?

ক
ক) 33(1/3)%
খ
খ) 25%
গ
গ) 20%
ঘ
ঘ) 24%

ব্যাখ্যা

পিয়াজের দাম বেড়ে 100 থেকে 125 হলো
∴ খরচ সমান রাখতে হলে, এখন 125 টাকায় কিনা যায় 1 অংশ
∴ 100 টাকায় কিনা যায় (1/125) × 100 অংশ
= 4/5 অংশ
∴ ব্যবহার কমাতে হবে = 1 - 4/5
= 1/5 অংশ।
অতএব, 1/5 × 100%
= 20% কমাতে হবে।

১,৩৭০.

A firm pays fixed costs of Tk. 1500 plus another Tk. 60 for each unit produced. How much can it produce for a budget of Tk. 4,800?

ক
ক) 42
খ
খ) 55
গ
গ) 67
ঘ
ঘ) 71

ব্যাখ্যা

1500 টাকা হলো fixed cost এবং প্রতি ইউনিট উৎপাদনের জন্য লাগে, ৬০ টাকা।
বাজেট ৪৮০০ টাকা হলে,
প্রশ্নমতে, 1500+60x = 4800
বা, x = 3300/60 = 55.

১,৩৭১.

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

ক
920
খ
910
গ
810
ঘ
850

ব্যাখ্যা

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

Solution:
pass mark = 767 + 313
= 1080

0.6 × total marks = 1080
⇒ total marks = 1080/0.6
= 1800

the minimum passing marks for girls is = 1800 × 0.45
= 810

১,৩৭২.

A trader buys some goods for Tk. 150. If the overhead expenses be 12% of cost price, then at what price should it be sold to earn 10%?

ক
ক) 184.80
খ
খ) 185.80
গ
গ) 187.80
ঘ
ঘ) 188.80

ব্যাখ্যা

Total C.P. = Cost + Overhead Expenses
= Tk. (150 + 12% of 150)
= Tk. (150 + 18)
= Tk. 168
∴S.P.=Tk.(110/100×168)=Tk. 184.80

১,৩৭৩.

A reduction of 21% in the price of pulse enables a person to buy 10.5 kg more for TK. 100. What is the reduced rate per kg of pulse?

ক
ΤΚ. 2.50
খ
ΤΚ. 2.25
গ
TK. 2
ঘ
Tk. 2.30
ঙ
None of these

ব্যাখ্যা

Question: A reduction of 21% in the price of pulse enables a person to buy 10.5 kg more for TK. 100. How much is reduced per kg of pulse?

Solution:
21% মূল্য হ্রাসে,
পূর্বের 100 টাকার দ্রব্য বর্তমানে পাওয়া যায় 79 টাকায়

100 টাকায় এখন পূর্বাপেক্ষা 10.5 কেজি দ্রব্য বেশি পাওয়া যায়।

10.5 কেজির বর্তমান মূল্য 21 টাকা
1 কেজির বর্তমান মূল্য 21/10.5 টাকা
= 2 টাকা

১,৩৭৪.

At a club, 70% of the members are women and 60% of the members are married. If ⅔ of the men are single, what fraction of the women are married?

ক
ক) 5/7
খ
খ) 7/10
গ
গ) 1/3
ঘ
ঘ) 7/30

ব্যাখ্যা

ধরি,
মোট member = 100
∴ মহিলা member = 70 এবং পুরুষ member = 30 জন।
30 জন পুরুষের মধ্যে অবিবাহিত = 30 × 2/3 = 20 জন।
সুতরাং বিবাহিত = 10 জন।
মোট বিবাহিত = 60 জন।
∴ মহিলাদের মধ্যে বিবাহিত = 60 - 10 = 50 জন।
∴ নির্ণেয় fraction = 50/70
= 5/7

১,৩৭৫.

The cost price of 8 apples equals the selling price of 7 apples. The profit or loss percent in the transaction is?

ক
29.29%
খ
24.29%
গ
15.29%
ঘ
14.29%

ব্যাখ্যা

Question: The cost price of 8 apples equals the selling price of 7 apples. The profit or loss percent in the transaction is?

Solution:
দেওয়া আছে,
8টি আপেলের ক্রয়মূল্য = 7টি আপেলের বিক্রয়মূল্য

ধরি, 1টি আপেলের ক্রয়মূল্য = x টাকা
তাহলে,
8টি আপেলের ক্রয়মূল্য = 8x টাকা
7টি আপেলের বিক্রয়মূল্য = 8x টাকা

∴ 1টি আপেলের বিক্রয়মূল্য = 8x / 7 টাকা

∴ লাভ = বিক্রয়মূল্য − ক্রয়মূল্য
= (8x/7) − x
= (8x − 7x)/7
= x/7

∴ x টাকায় লাভ হয় x/7 টাকা
1 টাকায় লাভ হয় = (x/7)/x = 1/7
100 টাকায় লাভ হয় = (1/7) × 100 ≈ 14.29 টাকা

∴ লাভ হয় ≈ 14.29%

১,৩৭৬.

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

ক
56.25%
খ
25.56%
গ
50.25%
ঘ
54.25%
ঙ
55.50%

ব্যাখ্যা

১,৩৭৭.

The price of an article was first increased by 10% and then again by 20%. If the last increased price was Tk. 33, the original price was:

ক
ক) Tk. 20
খ
খ) Tk. 25.50
গ
গ) Tk. 25
ঘ
ঘ) Tk. 22

ব্যাখ্যা

Question: The price of an article was first increased by 10% and then again by 20%. If the last increased price was Tk. 33, the original price was:

Solution:
Let the original price = 100x
Article price 1st increased by 10%.
Price of article become = 100x + 100x of 10%
= 100x + (100x × 10)/100
= 110x

And then the article price increased by 20%
Price of article become = 110x + 110x of 20%
= 110x + (110x × 20)/100
= 132x

ATQ,
132x = 33
⇒ x = 33/132
∴ x = 1/4

Therefore Original price of Article is
= 100 × 1/4
= Tk. 25

১,৩৭৮.

A salesperson earns a 7.5% commission on sales. If he earned Tk. 1125 in commission, what was the total value of the goods he sold?

ক
Tk. 7500
খ
Tk. 18000
গ
Tk. 13500
ঘ
Tk. 15000

ব্যাখ্যা

Question: A salesperson earns a 7.5% commission on sales. If he earned Tk. 1125 in commission, what was the total value of the goods he sold?

Solution:
Given that,
Commission rate = 7.5%
Commission earned = Tk. 1125

Let the total sales amount be x.
Then,
(7.5/100) × x = 1125
⇒ x = (1125 × 100)/7.5
⇒ x = 15000

So the total value of the goods he sold was Tk. 15000

১,৩৭৯.

45% of a number is 1350. What is 75% of that number?

ক
2120
খ
2250
গ
2340
ঘ
2410

ব্যাখ্যা

Question: 45% of a number is 1350. What is 75% of that number?

Solution:
Let the number be x
Then,
45% of x = 1350
45x/100 = 1350
x = (1350 × 100)/45
x = 3000

75% of 3000 = 3000 × (75/100)
= 2250

১,৩৮০.

A watch is sold for Tk. 840, and the seller makes a profit of 20% on the cost price. What will be the new selling price if he reduces the profit to 5%?

ক
795 Tk.
খ
772 Tk.
গ
750 Tk.
ঘ
735 Tk.

ব্যাখ্যা

Question: A watch is sold for Tk. 840, and the seller makes a profit of 20% on the cost price. What will be the new selling price if he reduces the profit to 5%?

Solution:
At 20% profit,
Selling Price = 120% of Cost Price

∴ Cost Price= (100/120) × Selling Price
= (100/120) × 840
= 700 Tk.

Now, if the seller wants 5% profit,
∴ New Selling Price = 700 + (5% of 700)
= 700 + {(5/100) × 700}
= 700 + 35
= 735 Tk.

১,৩৮১.

Two students appeared at an examination. One of them secured 7 marks more than the other and his marks was 52% of the sum of their marks. The marks obtained by them are-

ক
54, 61
খ
61, 68
গ
71, 78
ঘ
84, 91

ব্যাখ্যা

Question: Two students appeared at an examination. One of them secured 7 marks more than the other and his marks was 52% of the sum of their marks. The marks obtained by them are-

Solution:

ধরি,
তাদের প্রাপ্ত নাম্বার যথাক্রমে x এবং x + 7

প্রশ্নমতে,
x + 7 = (52/100) × (x + x + 7)
⇒ x + 7 = (13/25) × (2x + 7)
⇒ 25x + 175 = 26x + 91
⇒ 26x - 25x = 175 - 91
⇒ x = 84

∴ অপর জনের প্রাপ্ত নাম্বার = 84 + 7
= 91

১,৩৮২.

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

ক
20%
খ
30%
গ
40%
ঘ
50%

ব্যাখ্যা

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

solution:
let the rate be R%

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

১,৩৮৩.

Rafi went to the stationers and bought things worth Tk. 25 out of which 30 paisa went on sales tax on taxable purchases. if the tax rate was 6%, then what was the cost of the tax-free items?

ক
Tk. 20
খ
Tk. 19.7
গ
Tk. 15.5
ঘ
Tk. 15

ব্যাখ্যা

Question: Rafi went to the stationers and bought things worth Tk. 25 out of which 30 paisa went on sales tax on taxable purchases. if the tax rate was 6%, then what was the cost of the tax-free items?

Solution:
Let, cost of taxable purchases is x taka

ATQ,
0.06x = 30/100
⇒ x = 30/(100 × 0.06)
= 5 taka

∴ The cost of the tax-free items was = 25 - 5 - 0.3
= Tk. 19.7

১,৩৮৪.

A dishonest shopkeeper sells his grocery using weights 10% less than true weights and makes a profit of 30%. Find his total gain percentage.

ক
ক) 49.4%
খ
খ) 44.44%
গ
গ) 55.55%
ঘ
ঘ) 39.88%

ব্যাখ্যা

Let the weight of the grocery bag be 1000 gm.
Now, the shopkeeper sells his grocery using weights 10% less than true weights.
Hence, actual weight of bag = 90% of 1000 gm = 900 gm
If each gram = Tk.1, C.P. of each bag containing 900 gm = Tk. 900
The shopkeeper sells with a gain of 30% on true C.P.

Calculate the S.P.
Selling price = 100 + gain% × C.P.
Therefore,
Selling price = (130/100) × Tk. 1000
= Tk. 1300
Gain = S.P. - C.P. = 1300 - 900 = Tk. 400
Gain% = (400/900) × 100
= 44.44%

১,৩৮৫.

Increasing the original price of an item by 10%, then decreasing by 20% and then again increasing the price by 10% is equivalent:

ক
ক) 4.4% increase
খ
খ) 3.2% decrease
গ
গ) 3.5% decrease
ঘ
ঘ) None of these

ব্যাখ্যা

Question: Increasing the original price of an item by 10%, then decreasing by 20% and then again increasing the price by 10% is equivalent -

Solution:
ধরি,
প্রাথমিক দাম = ১০০ টাকা
১০% বৃদ্ধি করলে = ১০০ + (১০০ এর ১০%)
= ১১০ টাকা

২০% হ্রাস করলে দাম = ১১০ - (১১০ এর ২০%)
= ১১০ - ২২ = ৮৮ টাকা

১০% বৃদ্ধি করলে = ৮৮ + (৮৮ এর ১০%)
= ৮৮ + ৮.৮
= ৯৬.৮ টাকা

∴ হ্রাস = (১০০ - ৯৬.৮) = ৩.২ টাকা

শতকরা হ্রাস = ৩.২%

১,৩৮৬.

Which of the following is equal to 85 percent of 160?

ক
1.88
খ
13.6
গ
136
ঘ
188

ব্যাখ্যা

Question: Which of the following is equal to 85 percent of 160?

Solution:
85% of 160
= (85/100) × 160
= 136

১,৩৮৭.

85% of a number is added to 48, the result is the same number. Find the number.

ক
ক) 240
খ
খ) 160
গ
গ) 180
ঘ
ঘ) 320

ব্যাখ্যা

Question: 85% of a number is added to 48, the result is the same number. Find the number.

Solution:

ধরি,
সংখ্যাটি x

প্রশ্নমতে,
x এর 85% + 48 = x
বা, (85x/100) + 48 = x
বা, (17x /20) + 48 = x
বা, x - (17x /20) = 48
বা, (20x - 17x)/20 = 48
বা, 3x/20 = 48
বা, x/20 = 16
বা, x = 320

১,৩৮৮.

Peter purchased a machine for TK. 80,000 and spent TK. 5,000 on repair and TK. 1,000 on transport and sold it with 25% profit. At what price did he sell the machine?

ক
ক) TK. 1,06,250
খ
খ) TK. 1,07,500
গ
গ) TK. 1,17,500
ঘ
ঘ) TK. 1,05,100

ব্যাখ্যা

Cost price = 80000 + 5000 + 1000 = 86000
Given, profit = 25%
∴ Selling price = 86000 + 86000×(25/100)
= Tk. 107500

১,৩৮৯.

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 profit of Tk. 96 . How many eggs did he buy?

ক
ক) 144
খ
খ) 288
গ
গ) 148
ঘ
ঘ) 256

ব্যাখ্যা

Question: 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 profir of Tk. 96 . How many eggs did he buy?

Solution:
Let
Numbers of eggs he bought = x

Now
4( x - 12) - 3x = 96
4x - 48 - 3x = 96
x = 96 + 48
x = 144

১,৩৯০.

(a% of 10b) + (b% of a) is equal to:

ক
a% of b
খ
11% of ab
গ
2% of 100ab
ঘ
100% of ab

ব্যাখ্যা

Question: (a% of 10b) + (b% of a) is equal to:

Solution:
According to question
(a% of 10b) + (b% of a)
= 10b × (a/100) + a × (b/100)
= (ab/10) + (ab/100)
= [(10ab + ab)]/100
= 11ab/100
= 11ab%

Or, we can write 11% of ab.

১,৩৯১.

An article is listed at Tk. 900 and two successive discounts of 8% and 8% are given on it. How much would the seller gain or lose, if he gives a single discount of 16%, instead of two discounts?

ক
loss of Tk. 5.76
খ
gain of Tk. 5.76
গ
gain of Tk. 4.76
ঘ
loss of Tk. 3.76

ব্যাখ্যা

Question: An article is listed at Tk. 900 and two successive discounts of 8% and 8% are given on it. How much would the seller gain or lose, if he gives a single discount of 16%, instead of two discounts?

Solution:
After first 8% discount = 900 - 900 × 0.08
= 828 taka

After second 8% discount = 828 - 828 × 0.08
= 761.76 taka

After 16% discount = 900 - 900 × 0.16
= 756 taka

loss = Tk. (761.76 - 756)
= Tk. 5.76

১,৩৯২.

20% of 45 + 45% of 120 = ?

ক
30
খ
33
গ
55
ঘ
62
ঙ
63

ব্যাখ্যা

Question: 20% of 45 + 45% of 120 = ?

Solution:
20% of 45 + 45% of 120
= {(20/100) × 45} + {(45/100) × 120}
= 9 + 54
= 63

১,৩৯৩.

If the average of a number, 75% of that number, and 50% of the same number is 420, then what is the number?

ক
520
খ
560
গ
600
ঘ
640

ব্যাখ্যা

Question: If the average of a number, 75% of that number, and 50% of the same number is 420, then what is the number?

Solution:
Let
the number be x

ATQ,
(x + 75% of x + 50% of x)/3 = 420
⇒ (x + 3x/4 + x/2)/3 = 420
⇒ {(4x + 3x + 2x)/4}/3 = 420
⇒ 9x/12 = 420
⇒ x = (420 × 12)/9
⇒ x = 560

∴ The number is 560

১,৩৯৪.

3 liters of water is added to 11 liters of a solution containing 42% of alcohol in the water. The percentage of alcohol in the new mixture is -

ক
ক) 32%
খ
খ) 75%
গ
গ) 33%
ঘ
ঘ) 38%

ব্যাখ্যা

We have an 11-liter solution containing 42% of alcohol in the water.
=> quantity of alcohol in the solution = (11 × 42)/100
Now 3 liter of water is added to the solution.
=> Total quantity of the new solution = 11 + 3 = 14
Percentage of alcohol in the new solution = {(11 × 42)/100}/14 × 100
= (11 × 3)/100
= 33%

১,৩৯৫.

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

ক
56%
খ
52%
গ
50%
ঘ
48%

ব্যাখ্যা

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

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

Total number of students = 120 + 80
= 200

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

১,৩৯৬.

Rohit multiplies a number by 2 instead of dividing the number by 2. Resultant number is what percentage of the correct value?

ক
200%
খ
300%
গ
50%
ঘ
400%

ব্যাখ্যা

Question: Rohit multiplies a number by 2 instead of dividing the number by 2. Resultant number is what percentage of the correct value?

Solution:
Let the number be x.
Correct value = x/2
Resultant number = 2 × x

According to Question,
Required percentage = Resultant number/Correct value × 100%
⇒ Required percentage = [(2x)/(x/2)] × 100%
⇒ Required percentage = 400%

১,৩৯৭.

7 is 5% of what number?

ক
ক) 128
খ
খ) 156
গ
গ) 140
ঘ
ঘ) 135

ব্যাখ্যা

Question: 7 is 5% of what number?

Solution:
ধরি, ৭, x এর ৫%

x এর ৫% = ৭
⇒ x × ৫/১০০ = ৭
⇒ x/২০ = ৭
⇒ x = ২০ × ৭
= ১৪০

১,৩৯৮.

For the sale season, a mall first increased the rate of its products by 10% and then offered a discount of 10%. What is the change in the rate of products in comparison to the original?

ক
ক) 1%
খ
খ) 1.11%
গ
গ) 3.5%
ঘ
ঘ) 5%

ব্যাখ্যা

Let the original price be 100
Increase of 10% means the price now = 100 + (10% of 100) = Tk. 110
Now decrease of 10% means price now = Tk. 110 - (10% of 110)
= 110 - 11
= Tk. 99
So change in price = 100 - 99 = Tk. 1
1 is 1 percent of 100.
It is 1%
So change in price is 1%.

১,৩৯৯.

The price of a notebook is Tk. 80. If you buy more than 5 notebooks, you will get a 15% discount. How much do you have to pay if you buy 10 notebooks?

ক
640 tk
খ
680 tk
গ
720 tk
ঘ
740 tk

ব্যাখ্যা

Question: The price of a notebook is Tk. 80. If you buy more than 5 notebooks, you will get a 15% discount. How much do you have to pay if you buy 10 notebooks?

Solution:
The price of 1 notebook = 80
∴ The price of 10 notebook = 80 × 10 = 800

If price 100 then have to be paid = 85
If price 1 then have to be paid = 85/100
If price 800 then have to be paid = (85 × 800)/100
= 680 tk

Therefore, you have to pay Tk. 680 if you buy 10 notebooks.

১,৪০০.

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
ক) 400 kg
খ
খ) 560 kg
গ
গ) 600 kg
ঘ
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
Then 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) + 1180 - (118y/100) = 1140
1180 - 1140 = (118y/100) - (108y/100)
40 = 10y/100
40 = y/10
y = 400

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