Percentage and Profit & Loss

PrepBank · পাতা ৭ / ১৭ · ৬০১–৭০০ / ১,৬৯৬

৬০১.

30% of 10 is 10% of which ?

ক
ক) 30
খ
খ) 40
গ
গ) 60
ঘ
ঘ) 600

সঠিক উত্তর: ক

ক) 30

উত্তর

সঠিক উত্তর: ক

ক) 30

ক

ব্যাখ্যা

Question: 30% of 10 is 10% of which ?

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

৬০২.

A fruit seller buys apples at a rate of 2 apples for a Taka and sells them at a rate of 5 apples for 3 Taka. What is her profit margin (based on cost price)?

ক
ক) 25%
খ
খ) 20%
গ
গ) 30%
ঘ
ঘ) 10%

সঠিক উত্তর: খ

খ) 20%

উত্তর

সঠিক উত্তর: খ

খ) 20%

খ

ব্যাখ্যা

Question: A fruit seller buys apples at a rate of 2 apples for a Taka and sells them at a rate of 5 apples for 3 Taka. What is her profit margin (based on cost price)?

Solution:
২টি আপেলের ক্রয়মূল্য = ১ টাকা
১টি আপেলের ক্রয়মূল্য = ১/২ টাকা

Then,
৫টি আপেলের বিক্রয়মূল্য = ৩ টাকা
১টি আপেলের বিক্রয়মূল্য = ৩/৫ টাকা
সুতরাং, লাভ =৩/৫ - ১/২ = ১/১০ টাকা

অতএব শতকরা লাভ = {(১/১০)/(১/২)} × ১০০ = ২০%

৬০৩.

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%
গ
8%
ঘ
10%

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

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

৬০৪.

What is the rate of discount is a car that had a regular price of Tk. 30,00,000 is sold for Tk. 27,90,000?

ক
ক) 5%
খ
খ) 6%
গ
গ) 7%
ঘ
ঘ) 8%

সঠিক উত্তর: গ

গ) 7%

উত্তর

সঠিক উত্তর: গ

গ) 7%

গ

ব্যাখ্যা

Discount = Tk. (30,00,000 - 27,90,000) = Tk. 2,10,000
Therefore, rate of discount = (2,10,000/30,00,000) × 100% = 7%

৬০৫.

A’s salary is 25% more than B’s, and B’s salary is 20% less than C’s. If C’s salary is 50,000 Taka, find A’s salary.

ক
Tk. 30,000
খ
Tk. 35,000
গ
Tk. 40,000
ঘ
Tk. 50,000

সঠিক উত্তর: ঘ

Tk. 50,000

উত্তর

সঠিক উত্তর: ঘ

Tk. 50,000

ঘ

ব্যাখ্যা

Question: A’s salary is 25% more than B’s, and B’s salary is 20% less than C’s. If C’s salary is 50,000 Taka, find A’s salary.

Solution:
B’s salary is 20% less than C’s:
B = C × (1 - 20/100) = 50,000 × 0.8 = 40,000 Taka

A’s salary is 25% more than B’s:
A = B × (1 + 25/100) = 40,000 × 1.25 = 50,000 Taka

∴ A’s salary = 50,000 Taka

৬০৬.

A bookseller procures 40 books for Tk. 3200 and sells them at a profit equal to the selling price of 8 books. What is the selling price of one dozen books, if the price of each book is same?

ক
ক) Tk. 600
খ
খ) Tk. 800
গ
গ) Tk. 1200
ঘ
ঘ) Tk. 900

সঠিক উত্তর: গ

গ) Tk. 1200

উত্তর

সঠিক উত্তর: গ

গ) Tk. 1200

গ

ব্যাখ্যা

Question: A bookseller procures 40 books for Tk. 3200 and sells them at a profit equal to the selling price of 8 books. What is the selling price of one dozen books, if the price of each book is same?

Solution:
Cost price of each book = 3200/40
= Tk. 80.

ATQ,
Selling Price of 40 books = Cost price of 40 books + Selling Price of 8 books.
Or, Selling Price of 40 books - SP of 8 books = CP of 40 books.
Or, Selling Price of 32 books = Tk. 3200
Or, Selling Price of 1 book = 3200/32
= Tk. 100.

∴ Selling price of one dozen or 12 book = 12 × 100 = Tk. 1200.

৬০৭.

The price of a dress was first discounted by a certain percent and later by 25 percent of the discounted price. If these two discounts are equivalent to a single discount of 40 percent of the original price, what was the first discount?

ক
10%
খ
15%
গ
20%
ঘ
30%

সঠিক উত্তর: গ

20%

উত্তর

সঠিক উত্তর: গ

20%

গ

ব্যাখ্যা

Question: The price of a dress was first discounted by a certain percent and later by 25 percent of the discounted price. If these two discounts are equivalent to a single discount of 40 percent of the original price, what was the first discount?

Solution:
Let
n denote the original price of the shirt and
let the first discount be x percent.
Then, after the first discount, the price is reduced to n(1 - x/100).
After the second discount, the price is reduced to n(1 - x/100)(1 - 25/100) = n(1 - x/100)(75/100) = n(1 - x/100)(3/4).

Since the two discounts are equivalent to a single discount of 40 percent of the original price, we have:
n(1 - x/100)(3/4) = (60/100)n
⇒ (1 - x/100)(3/4) = 3/5
⇒ 1 - x/100 = 4/5
⇒ x/100 = 1/5
∴ x = 100/5 = 20

৬০৮.

If 4 (A's capital) = 6 (B's capital) = 10 (C's capital), then out of a profit of Tk. 4,340, B will receive__

ক
ক) Tk. 900
খ
খ) Tk. 1000
গ
গ) Tk. 1200
ঘ
ঘ) Tk. 1400

সঠিক উত্তর: ঘ

ঘ) Tk. 1400

উত্তর

সঠিক উত্তর: ঘ

ঘ) Tk. 1400

ঘ

ব্যাখ্যা

Let
4A = 6B = 1OC = k.
A = k/4, B = k/6, and C = k/10 .
A : B : C = k/4 : k/6 : k/10
= (k/4) × 60 : (k/6) × 60 : (k/10) × 60
= 15 : 10 : 6.

Hence, B's share (4,340 × 10/31) = Tk. 1400

৬০৯.

A shopkeeper marks his goods 20% above the cost price, but allows 10% discount for cash purchase. What percent profit does he make?

ক
12%
খ
8%
গ
7%
ঘ
6%

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: A shopkeeper marks his goods 20% above the cost price, but allows 10% discount for cash purchase. What percent profit does he make?

Solution:
At 20% above,
The market price of goods = 100 + 20 = Tk. 120

At 10% discount,
Selling price = 120 - 10% of 120
= 120 - 12
= Tk. 108

∴ Profit = 108 - 100 = Tk. 8
Profit % = (8/100) × 100
= 8%

৬১০.

In an examination 77% candidates passed in English and 87% candidates passed in Mathematics. If 69% candidates passed in both these subjects, then what percent of candidates failed in both the subjects?

ক
2%
খ
8%
গ
7%
ঘ
5%

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: In an examination 77% candidates passed in English and 87% candidates passed in Mathematics. If 69% candidates passed in both these subjects, then what percent of candidates failed in both the subjects?

Solution:
Given that,
Students passed in English = 77%
Students passed in Math's = 87%
Students passed in both subjects = 69%
Then, number of students passed in at least one subject
= (77 + 87) - 69
= 95%

Thus, students failed in both subjects = 100 - 95 = 5%

৬১১.

Mr. Ali is a trader. He mixes 26 kg of rice at Tk. 20 per kg with 30 kg of rice of other variety at Tk. 36 per kg and sells the mixture at Tk. 32 per kg. His profit percent is-

ক
12%
খ
7%
গ
9%
ঘ
6%

সঠিক উত্তর: ক

12%

উত্তর

সঠিক উত্তর: ক

12%

ক

ব্যাখ্যা

Question: Mr. Ali is a trader. He mixes 26 kg of rice at Tk. 20 per kg with 30 kg of rice of other variety at Tk. 36 per kg and sells the mixture at Tk. 32 per kg. His profit percent is-

Solution:
Cost Price of 56 kg rice = {(26 × 20) + (30 × 36)}
= (520 + 1080)
= 1600 taka

Selling Price of 56 kg rice = (56 × 32)
= 1792 taka

∴ Profit = 1792 - 1600
= 192 taka

∴ Profit percentage = (192/1600) × 100%
= 12%

৬১২.

After selling a saree for Tk. 3360 a shopkeeper suffers a loss of 16%. If he wants to earn 15% profit after giving the discount of 8%, what will be the marked price of the saree?

ক
Tk. 4800
খ
Tk. 5000
গ
Tk. 5500
ঘ
Tk. 4000

সঠিক উত্তর: খ

Tk. 5000

উত্তর

সঠিক উত্তর: খ

Tk. 5000

খ

ব্যাখ্যা

Question: After selling a saree for Tk. 3360 a shopkeeper suffers a loss of 16%. If he wants to earn 15% profit after giving the discount of 8%, what will be the marked price of the saree?

Solution:
After selling a saree for Tk. 3360 a shopkeeper suffers a loss of 16%.

Selling price Tk. 84 when Cost price = Tk. 100
∴ Selling price Tk. 3360 when Cost price = Tk. (100 × 3360)/84
= Tk. 4000

15% profit,
Cost price Tk. 100 then Selling price = Tk. 115
∴ Cost price Tk. 4000 then Selling price = Tk. (115 × 4000)/100
= Tk. 4600

discount 8%,
Selling price Tk. 92 When Marked price = Tk. 100
∴ Selling price Tk. 4600 When Marked price = Tk. (100 × 4600)/92
= Tk. 5000

৬১৩.

If 20% of p = q, then q% of 20 is the same as:

ক
4% of p
খ
5% of p
গ
10% of p
ঘ
20% of p
ঙ
None

সঠিক উত্তর: ক

4% of p

উত্তর

সঠিক উত্তর: ক

4% of p

ক

ব্যাখ্যা

Question: If 20% of p = q, then q% of 20 is the same as:

Solution:
20% of p = q
⇒ (20 × p)/100 = q
⇒ p/5 = q

q% of 20 = (q/100) × 20 = q/5 = (p/5)/5 = p/25 = (p/25) × 100% = p × 4% = 4% of p

৬১৪.

The price of a stock increased by 20% in January and then decreased by 10% in February. If the price of the stock was Tk. 108 at the end of February, what was the price at the beginning of January?

ক
Tk. 90
খ
Tk. 96
গ
Tk. 100
ঘ
Tk. 102

সঠিক উত্তর: গ

Tk. 100

উত্তর

সঠিক উত্তর: গ

Tk. 100

গ

ব্যাখ্যা

Question: The price of a stock increased by 20% in January and then decreased by 10% in February. If the price of the stock was Tk. 108 at the end of February, what was the price at the beginning of January?

Solution:
Let the beginning price of January = 100x
The price of a stock increased by 20% in January.
Price of stock become = 100x + 100x of 20%
= 100x + (100x × 20)/100
= 120x

And then the stock price decreased by 10% in February
Price of stock become = 120x - 120x of 10%
= 120x - (120x × 10)/100
= 108x

ATQ,
108x = 108
⇒ x = 108/108
∴ x = 1

Therefore the price at the beginning of January
= 100 × 1
= Tk. 100

The price at the beginning of January was Tk. 100.

৬১৫.

নিচের কোন ভগ্নাংশ বৃহত্তম?

ক
১/২
খ
৭/১২
গ
৫/৯
ঘ
৩/৪

সঠিক উত্তর: ঘ

৩/৪

উত্তর

সঠিক উত্তর: ঘ

৩/৪

ঘ

ব্যাখ্যা

প্রশ্ন: নিচের কোন ভগ্নাংশ বৃহত্তম?

সমাধান:
১/২ = ০.৫
৭/১২ = ০.৫৮
৫/৯ = ০.৫৬
৩/৪ = ০.৭৫

এখানে,
০.৫ < ০.৫৬ < ০.৫৮ < ০.৭৫

∴ বৃহত্তম ভগ্নাংশটি = ৩/৪

৬১৬.

If 12 equally priced melons cost a total of $9.60, then what is the cost of 11 of these melons?

ক
ক) $8.04
খ
খ) $7.20
গ
গ) $8.37
ঘ
ঘ) $8.80

সঠিক উত্তর: ঘ

ঘ) $8.80

উত্তর

সঠিক উত্তর: ঘ

ঘ) $8.80

ঘ

ব্যাখ্যা

Question: If 12 equally priced melons cost a total of $9.60, then what is the cost of 11 of these melons?

Solution:
প্রতিটি তরমুজের মূল্য = 9.6/12 = .8
সুতরাং, ১১টি তরমুজের মূল্য = .8 × 11 = 8.8

৬১৭.

A mixture of 30 kg of milk and water contains 20% water. How much water must be added to this mixture to raise the percentage of water to 25%?

ক
ক) 4 kg
খ
খ) 5 kg
গ
গ) 3 kg
ঘ
ঘ) 2 kg

সঠিক উত্তর: ঘ

ঘ) 2 kg

উত্তর

সঠিক উত্তর: ঘ

ঘ) 2 kg

ঘ

ব্যাখ্যা

Question: A mixture of 30 kg of milk and water contains 20% water. How much water must be added to this mixture to raise the percentage of water to 25%?

Solution:
30 কেজি মিশ্রণে পানির পরিমাণ = 30 × 20/100 = 6 কেজি
ধরি,
মিশ্রণে x কেজি পানি মেশালে পানির পরিমাণ হবে 25%

প্রশ্নমতে,
(6 + x) = (25/100) (30 + x)
6 + x = (30 + x)/4
4x + 24 = 30 + x
4x - x = 30 - 24
3x = 6
x = 2

∴ মিশ্রণে 2 কেজি পানি মেশালে পানির পরিমাণ হবে 25%

৬১৮.

A man sold 18 cots for Tk. 14,700, gaining thereby the cost price of 3 cots. The cost price of a cot is-

ক
ক) Tk. 600
খ
খ) Tk. 700
গ
গ) Tk. 800
ঘ
ঘ) Tk. 900

সঠিক উত্তর: খ

খ) Tk. 700

উত্তর

সঠিক উত্তর: খ

খ) Tk. 700

খ

ব্যাখ্যা

Here
(S.P of 18 cots) - (C.P of 18 cots) = C.P of 3cots
S.P of 18 cots = C.P of 21 cots

S.P of 18 cots = Tk. 14,700

C.P of 21 cots = Tk. 14,700
C.P of 1 cot = Tk. (14,700/21)
= Tk. 700

৬১৯.

In a shop, shirts are usually sold at 40% above the cost price. During a sale, the shopkeeper offers a discount of 10% off the usual selling price. If he manages to sell 72 shirts for tk 13,608, then his cost price per shirt, (in tk) is

ক
135 tk
খ
150 tk
গ
145 tk
ঘ
155 tk

সঠিক উত্তর: খ

150 tk

উত্তর

সঠিক উত্তর: খ

150 tk

খ

ব্যাখ্যা

Question: In a shop, shirts are usually sold at 40% above the cost price. During a sale, the shopkeeper offers a discount of 10% off the usual selling price. If he manages to sell 72 shirts for tk 13,608, then his cost price per shirt, (in tk) is

Solution:
Let the CP of each shirt be tk 100, then SP = 140.

∴ New SP = (140 × 90)/100
= 126 tk

∴ When S.P. is tk 126, C.P. = tk 100
∴ When S.P. is tk 13608/72, then C.P. = (100/126) × (13608/72)
= 150 tk

৬২০.

If A bought an article at Tk. 200 and sold it to B at 20% profit. Again B sold the article at 10% profit to C. Find the amount paid by C.

ক
Tk. 250
খ
Tk. 256
গ
Tk. 264
ঘ
Tk. 268

সঠিক উত্তর: গ

Tk. 264

উত্তর

সঠিক উত্তর: গ

Tk. 264

গ

ব্যাখ্যা

Question: If A bought an article at Tk. 200 and sold it to B at 20% profit. Again B sold the article at 10% profit to C. Find the amount paid by C.

Solution:
Price paid by B = 200 + (200/100 × 20) = 200 + 40 = 240

∴ Price paid by C = 240 + (240/100 × 10) = 240 + 24 = 264

৬২১.

A product is bought and sold at the profit of 15% the ratio of selling and buying cost is -

ক
ক) 17:20
খ
খ) 23:20
গ
গ) 20:23
ঘ
ঘ) 20:17

সঠিক উত্তর: খ

খ) 23:20

উত্তর

সঠিক উত্তর: খ

খ) 23:20

খ

ব্যাখ্যা

Let, the cost price be = 100 and selling price = 115
Their ratio = sp : cp = 115 : 100 = 23 : 20

৬২২.

A man sells one camera A for Tk. 7500 at a gain of 20% and another camera B for Tk. 8550 at a loss of 5%. Find his total loss or gain%.

ক
ক) 2.7%
খ
খ) 5.2%
গ
গ) 4..2%
ঘ
ঘ) 5.1%

সঠিক উত্তর: খ

খ) 5.2%

উত্তর

সঠিক উত্তর: খ

খ) 5.2%

খ

ব্যাখ্যা

Here,
we just know the selling price and the gain and loss incurred, on two cameras.
Therefore,
first calculate the cost price of both the cameras, because gain or loss is calculated on the cost price of the material.
When a shopkeeper earns profit, Cost Price = 100/(100 + Gain%) × S.P.
When shopkeeper incurs a loss, Cost Price = 100/(100 – Loss%) × S.P.

C.P. of camera A = 100/(100 +20) × 7500
= 100/120 × 7500
= Tk. 6250
C.P of camera B = 100/(100 – 5) × 8550
= 100/95 × 8550
= Tk. 9000

Total C.P. = Cost of camera A + Cost of camera B
Total C.P. = 6250 + 9000 = Tk. 15250
Total S.P. = 7500 + 8550 = Tk. 16050
Selling Price > Cost Price, hence man gains during this transaction.

Gain = S.P. – C.P.
= 16050 – 15250
= Tk. 800
Gain% = Gain/C.P. × 100
Gain% = 800/15250 × 100
= 5.24%

৬২৩.

A salesman sells two shirts at BDT 594 each. On one he gains 10% and on the other, he loses 10%. Find his gain or loss percent on the whole.

ক
ক) 1% loss
খ
খ) 1% profit
গ
গ) 99% loss
ঘ
ঘ) 99% profit

সঠিক উত্তর: ক

ক) 1% loss

উত্তর

সঠিক উত্তর: ক

ক) 1% loss

ক

ব্যাখ্যা

At 10% profit, The cost price of the first shirt
= 100/(100 + 10) × 594
= Tk. 540

At 10% loss, The cost price of the second shirt
= 100/(100 - 10) × 594
= Tk. 660

Now, the total cost price of two shirts
= 540 + 660
= Tk. 1200

and the total sell price of two shirts
= 594 × 2
= Tk. 1188

Loss = 1200 - 1188
= Tk. 12

Percentage of loss = (12/1200 × 100)%
= 1%
--------------------------------------------------------
Shortcut:
Loss percentage = (common gain or loss/10)% = (10/10)% = 1%
[ When a salesman sells two shirts at same price each and on one there is gain is equal to on other there is loss in percentage, then there shall be always loss percent on the whole and loss percentage will be (common gain or loss/10)% ]

৬২৪.

When the selling price is doubled, the profit becomes threefold. What is the percentage profit?

ক
65%
খ
100%
গ
120%
ঘ
250%

সঠিক উত্তর: খ

100%

উত্তর

সঠিক উত্তর: খ

100%

খ

ব্যাখ্যা

Question: When the selling price is doubled, the profit becomes threefold. What is the percentage profit?

Solution:
ধরি,
ক্রয়মূল্য = 100 টাকা
বিক্রয়মূল্য = (100 + x) টাকা

∴ লাভ = (100 + x) - 100 টাকা = x টাকা

প্রশ্নমতে,
3x = 2(100 + x) - 100
⇒ 3x = 200 + 2x - 100
⇒ 3x = 100 + 2x
⇒ 3x - 2x = 100
⇒ x = 100

∴ লাভ = 100 টাকা

এখন,
লাভের হার = (লাভ/ক্রয়মূল্য) × 100%
= (100/100) × 100%
= 100%

∴ লাভের শতকরা হার = 100%

৬২৫.

What percentage of numbers from 1 to 50 has 3 or 7 in the unit's digit?

ক
25%
খ
12%
গ
15%
ঘ
20%

সঠিক উত্তর: ঘ

20%

উত্তর

সঠিক উত্তর: ঘ

20%

ঘ

ব্যাখ্যা

Question: What percentage of numbers from 1 to 50 has 3 or 7 in the unit's digit?

Solution:
We can list the numbers from 1 to 50 and identify those that have 3 or 7 in the unit's place:

Numbers with 3 in the unit's digit:3, 13, 23, 33, 43
Numbers with 7 in the unit's digit: 7, 17, 27, 37, 47

So, the numbers with 3 or 7 in the unit's digit are:
3, 7, 13, 17, 23, 27, 33, 37, 43, 47

There are 10 such numbers.

There are 50 numbers in total from 1 to 50. The percentage of numbers that have 3 or 7 in the unit's digit is: (10/50) × 100%
= 20%

৬২৬.

A trader marked the price of his commodity so as to include a profit of 25%. He allowed a discount of 16% on the marked price. His actual profit was:

ক
5%
খ
10%
গ
12%
ঘ
20%

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: A trader marked the price of his commodity so as to include a profit of 25%. He allowed a discount of 16% on the marked price. His actual profit was:

Solution:
let, cost price 100 taka
marked price = 100 + 25
= 125 taka

After 16% discount selling price = 125 - 125 × 16/100
= 125 - 20
= 105 taka

actual profit = (105 - 100) = 5 taka

৬২৭.

A man purchased a cow for Tk. 3000 and sold it the same day for Tk. 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of

ক
ক) 0%
খ
খ) 5%
গ
গ) 7.5%
ঘ
ঘ) 10%

সঠিক উত্তর: ক

ক) 0%

উত্তর

সঠিক উত্তর: ক

ক) 0%

ক

ব্যাখ্যা

Cost price = Tk 3000
Selling price = [{3600 × 100}/{100 + (10 × 2)}]
= Tk. 3000
Gain = 0%.

৬২৮.

A city's population increases by 10% each year. If its present population is 50,000, what will be the population after 2 years?

ক
59400
খ
60500
গ
61600
ঘ
63600
ঙ
None

সঠিক উত্তর: খ

60500

উত্তর

সঠিক উত্তর: খ

60500

খ

ব্যাখ্যা

Question: A city's population increases by 10% each year. If its present population is 50,000, what will be the population after 2 years?

Solution:
Here we can use the compound interest based formula,
Population after n years
= P × [1 + (r/100)]n
∴ Population after 2 years = 50000 × [1 + (10/100)]²
= 50000 × (110/100)²
= 50000 × 1.21
= 60,500

৬২৯.

A dealer buys dry fruits at Tk. 100, Tk. 80, and Tk. 60 per kilogram. He mixes them in the ratio 3 : 4 : 5 by weight and sells at a profit of 50%. At what price per kilogram does he sell the dry fruits?

ক
80
খ
100
গ
95
ঘ
115

সঠিক উত্তর: ঘ

115

উত্তর

সঠিক উত্তর: ঘ

115

ঘ

ব্যাখ্যা

Question: A dealer buys dry fruits at Tk. 100, Tk. 80, and Tk. 60 per kilogram. He mixes them in the ratio 3 : 4 : 5 by weight and sells at a profit of 50%. At what price per kilogram does he sell the dry fruits?

Solution:
Let the dealer buy 3 kg, 4 kg and 5 kg.
∴ Price of total dry fruits = (3 × 100) + (4 × 80) + (5 × 60) = Tk. 920

At 50% Profit,
Selling Price, SP = 920 + 50% of 920
= 920 + (50/100) × 920
= 1380

Hence,
Price of dry fruits per kg = 1380/12 = 115 Tk.

৬৩০.

If a number x is 10% less than another number y and y is 10% more than 125, then x is equal to:

ক
133
খ
123.75
গ
152
ঘ
140.55

সঠিক উত্তর: খ

123.75

উত্তর

সঠিক উত্তর: খ

123.75

খ

ব্যাখ্যা

Question: If a number x is 10% less than another number y and y is 10% more than 125, then x is equal to:

Solution:
y is 10% more than 125
y = 125 × (110/100)
= 137.5

and x is 10% less than y
x = (90/100) × y
= (90/100) × 137.5
= 123.75

৬৩১.

Strawberries are bought at 5 for Tk 10 and sold at 6 for Tk 15. The gain percent is-

ক
20%
খ
22.5%
গ
25%
ঘ
27.5%

সঠিক উত্তর: গ

25%

উত্তর

সঠিক উত্তর: গ

25%

গ

ব্যাখ্যা

Question: Strawberries are bought at 5 for Tk 10 and sold at 6 for Tk 15. The gain percent is-

Solution:
Cost per strawberry = 10/5 Tk
= 2 Tk

Sell per strawberry = 15/6 Tk
= 2.5 Tk

So, gain percentage = {(2.5 - 2)/2} × 100
= 25 Tk or 25%

৬৩২.

একটি কোম্পানির ৪৬% কর্মচারি পুরুষ। যদি ৬০% কর্মচারি ইউনিয়ন করে এবং এর মধ্যে ৭০% কর্মচারি পুরুষ হয়, তাহলে শতকরা কতজন মহিলা কর্মচারি ইউনিয়ন করে না?

ক
ক) ৯০%
খ
খ) ৮৭.৫%
গ
গ) ৫০%
ঘ
ঘ) ৩৬%

সঠিক উত্তর: ঘ

ঘ) ৩৬%

উত্তর

সঠিক উত্তর: ঘ

ঘ) ৩৬%

ঘ

ব্যাখ্যা

প্রশ্ন: একটি কোম্পানির ৪৬% কর্মচারি পুরুষ। যদি ৬০% কর্মচারি ইউনিয়ন করে এবং এর মধ্যে ৭০% কর্মচারি পুরুষ হয়, তাহলে শতকরা কতজন মহিলা কর্মচারি ইউনিয়ন করে না?

সমাধান:
ধরি,
কোম্পানির কর্মচারির সংখ্যা ১০০ জন।
∴ কোম্পানির পুরুষ কর্মচারি ৪৬ জন।
কোম্পানির মহিলা কর্মচারি (১০০ - ৪৬) জন = ৫৪ জন

ইউনিয়ন করে ৬০ জন।
ইউনিয়নে মহিলা কর্মচারির সংখ্যা ৬০ × (৩০/১০০) জন
= ১৮ জন

ইউনিয়ন না করা মহিলা কর্মচারির সংখ্যা (৫৪ - ১৮) জন
= ৩৬ জন

∴ শতকরা ৩৬ জন মহিলা কর্মচারি ইউনিয়ন করে না।

৬৩৩.

ক
ক) Tk. 75
খ
খ) Tk. 80
গ
গ) Tk. 125
ঘ
ঘ) Tk. 210

সঠিক উত্তর: ঘ

ঘ) Tk. 210

উত্তর

সঠিক উত্তর: ঘ

ঘ) Tk. 210

ঘ

ব্যাখ্যা

(61 -63): Answer the questions on the basis of the information given below

61.Your income for a year is Tk. 26,000. You receive a raise so that next year's income will be Tk. 29,000. How much more will will be Tk. 29,000. you pay in taxes next year if the tax rate remains the same?

Solution:
২৬০০০ টাকা বেতন থাকাকালীন টেক্স দিতে হত = ১০৭০ + (২৫০০০ এর বেশি ইনকামের ৭%)
= ১০৭০ + (২৬০০০ - ২৫০০০) এর ৭%
= ১০৭০ + (১০০০ এর ৭%)
= ১০৭০ + ৭০
= ১১৪০ টাকা

নতুন বেতন ২৯০০০ এর জন্য টেক্স দিতে হবে = ১০৭০ + (২৯০০০ - ২৫০০০) এর ৭%
= ১০৭০ + (৪০০০ এর ৭%)
= ১০৭০ + ২৮০ টাকা
= ১৩৫০ টাকা

∴ অতিরিক্ত টেক্স দিতে হবে = (১৩৫০ - ১১৪০) = ২১০ টাকা

৬৩৪.

A fruit seller had some oranges. He sells 40% oranges and still has 420 oranges. How many oranges did he have originally?

ক
500
খ
700
গ
850
ঘ
675
ঙ
600

সঠিক উত্তর: খ

700

উত্তর

সঠিক উত্তর: খ

700

খ

ব্যাখ্যা

He sells 40% of oranges and still there are 420 oranges remaining.
=> 60% of oranges = 420
=> Total oranges × 60 /100 = 420
=> Total oranges = 420 × 100/ 60 = 700

৬৩৫.

Rahman spends 40% of his monthly income on household items, 25% of his monthly income on buying clothes, 10% of his monthly income on medicines and saves the remaining Tk. 9,000. What is Rahman’s monthly income?

ক
Tk. 32,000
খ
Tk. 30,000
গ
Tk. 35,000
ঘ
Tk. 36,000

সঠিক উত্তর: ঘ

Tk. 36,000

উত্তর

সঠিক উত্তর: ঘ

Tk. 36,000

ঘ

ব্যাখ্যা

Question: Rahman spends 40% of his monthly income on household items, 25% of his monthly income on buying clothes, 10% of his monthly income on medicines and saves the remaining Tk. 9,000. What is Rahman’s monthly income?

Solution:
Total spends = (40 + 25 + 10) = 75%

∴ Saves = (100 - 75) = 25%

Let total income of Rahman be x. Then,
⇒ x × 25% = 9000
⇒ 25x/100 = 9000
⇒ x/4 = 9000
⇒ x = 9000 × 4
∴ x = 36000

∴ Rahman’s monthly income is Tk. 36,000

৬৩৬.

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

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

সঠিক উত্তর: গ

গ) BDT 200

উত্তর

সঠিক উত্তর: গ

গ) BDT 200

গ

ব্যাখ্যা

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

৬৩৭.

If the radius of a circle is increased by 100%, by what percent is the area of the circle increased?

ক
ক) 500%
খ
খ) 400%
গ
গ) 300%
ঘ
ঘ) 200%

সঠিক উত্তর: গ

গ) 300%

উত্তর

সঠিক উত্তর: গ

গ) 300%

গ

ব্যাখ্যা

মনে করি,
radius = 10
সুতরাং area = πr²
= 100π
radius 100% বাড়ল।
নতুন radius = 20
area = πr²
= 400π
area বাড়ল 300%

৬৩৮.

A candidate scoring 30% marks in an examination fails by 24 marks while another candidate who score 60% marks gets 36 marks more than the minimum pass marks. What is the minimum pass mark?

ক
75
খ
80
গ
84
ঘ
86

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: A candidate scoring 30% marks in an examination fails by 24 marks while another candidate who score 60% marks gets 36 marks more than the minimum pass marks. What is the minimum pass mark?

Solution:
Let,
the total marks of the exam be x.

∴ 30% of x = 3x/10
60% of x = 3x/5

ATQ,
3x/10 + 24 = 3x/5 - 36
⇒ (3x + 240)/10 = (3x - 180)/5
⇒ 5(3x + 240) = 10(3x - 180)
⇒ 15x + 1200 = 30x - 1800
⇒ 1200 + 1800 = 30x - 15x
⇒ 15x = 3000
∴ x = 200

∴ the minimum pass mark = (3 × 200)/10 + 24
= 600/10 + 24
= 84

৬৩৯.

Alam sold an item for Tk. 6,384 and incurred a loss of 30%. At what price should he have sold the item to have gained a profit of 30% ?

ক
ক) Tk. 14,656
খ
খ) Tk. 11,856
গ
গ) Tk. 13,544
ঘ
ঘ) None of these

সঠিক উত্তর: খ

খ) Tk. 11,856

উত্তর

সঠিক উত্তর: খ

খ) Tk. 11,856

খ

ব্যাখ্যা

30% ক্ষতিতে দাম, 70% = 6384
30% লাভে দাম, 130% = (6384×130) / 70 = 11856

৬৪০.

Jabed spends 60% of her salary and donates 20% of her salary to charity. If he is left with Tk. 2000, what is her monthly salary?

ক
10000 tk
খ
11000 tk
গ
12000 tk
ঘ
12600 tk

সঠিক উত্তর: ক

10000 tk

উত্তর

সঠিক উত্তর: ক

10000 tk

ক

ব্যাখ্যা

Question: Jabed spends 60% of her salary and donates 20% of her salary to charity. If he is left with Tk. 2000, what is her monthly salary?

Solution:
Let Jabed's salary be x

ATQ,
x - (60% of x + 20% of x) = 2000
⇒ x - 80% of x = 2000
⇒ 20% of x = 2000
⇒ 20x/100 = 2000
⇒ 20x = 200000
⇒ x = 200000/20
⇒ x = 10000

Therefore, Jabed's monthly salary is Tk. 10,000.

৬৪১.

If a bucket is 80% full, then it contains 4 liters more water than when it is 200/3% full, What is the capacity of the bucket?

ক
ক) 15 liters
খ
খ) 30 liters
গ
গ) 25 liters
ঘ
ঘ) 7.5 liters

সঠিক উত্তর: খ

খ) 30 liters

উত্তর

সঠিক উত্তর: খ

খ) 30 liters

খ

ব্যাখ্যা

Question : If a bucket is 80% full, then it contains 4 liters more water than when it is 200/3% full, What is the capacity of the bucke?

Solution:
Let the capacity of the bucket be x.
(80 - 200/3)% of x =4 litres.
⇒ 40/3 % of x = 4 litres
⇒ 40x/(3 × 100)= 4
⇒40x = 3 × 4 × 100
x = (3 × 4 × 100)/40
x = 30

৬৪২.

A cloth merchant bought 35 shirts, each at a price of Tk. 280. He sold each of them for Tk. 308. Find his percentage profit.

ক
5%
খ
10%
গ
12%
ঘ
15%

সঠিক উত্তর: খ

10%

উত্তর

সঠিক উত্তর: খ

10%

খ

ব্যাখ্যা

Question: A cloth merchant bought 35 shirts, each at a price of Tk. 280. He sold each of them for Tk. 308. Find his percentage profit.

Solution:
The profit percentage remains same for one unit as well for all the units. Thus the calculations should be done for one unit only.
CP = Tk. 280
SP = Tk. 308
Profit = 308 - 280 = 28.

Profit percentage = (28/280) × 100 = 10%

৬৪৩.

A shopkeeper buys 100 mangoes at Tk. 12 each. He sells 60 mangoes at Tk. 17.40 each and x mangoes at Tk. 11.31 each. The shopkeeper makes a profit of at least 10%. Find the least possible value of x.

ক
ক) 24
খ
খ) 25
গ
গ) 27
ঘ
ঘ) 28

সঠিক উত্তর: খ

খ) 25

উত্তর

সঠিক উত্তর: খ

খ) 25

খ

ব্যাখ্যা

Question: A shopkeeper buys 100 mangoes at Tk. 12 each. He sells 60 mangoes at Tk. 17.40 each and x mangoes at Tk. 11.31 each. The shopkeeper makes a profit of at least 10%. Find the least possible value of x.

Solution:
1টি আমের ক্রয়মূল্য =12 টাকা
100টি আমের ক্রয়মূল্য = (12 × 100) টাকা
= 1200

প্রশ্নমতে
60 × 17.40 + x × 11.31 = 1200 এর 110%
1044 + 11.31x = 1200 এর 110/100
1044 + 11.31x = 1320
11.31x = 1320 - 1044
11.31x = 276
x = 276/11.31
x = 24.40
x ≈ 25

৬৪৪.

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

সঠিক উত্তর: ক

loss 6.25%

উত্তর

সঠিক উত্তর: ক

loss 6.25%

ক

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 same. C.P. = 2400 × (100/125) = 1920.
New selling price = 1800
Loss = 1920 - 1800 = 120
∴ Loss percentage = 100 × (120/1920) = 6.25%.

৬৪৫.

As the price of mango has reduced 20%, it is now possible to buy 2 more mangoes at Tk.12. What is the current price of 50 mangoes?

ক
ক) Tk. 50
খ
খ) Tk. 40
গ
গ) Tk. 30
ঘ
ঘ) Tk. 60

সঠিক উত্তর: ঘ

ঘ) Tk. 60

উত্তর

সঠিক উত্তর: ঘ

ঘ) Tk. 60

ঘ

ব্যাখ্যা

Question: As the price of mango has reduced 20%, it is now possible to buy 2 more mangoes at Tk.12. What is the current price of 50 mangoes?

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

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

1টি আমের বর্তমানমূল্য = 1.5 × 0.8 = 1.2 টাকা
50টি আমের বর্তমানমূল্য = 1.2 × 50 টাকা
= 60 টাকা

৬৪৬.

Mr. X's salary is Tk. 20000 and he gets 10% commission of his salary. If his salary increased by 10%, by what percent his commission will increase?

ক
5%
খ
10%
গ
12%
ঘ
15%

সঠিক উত্তর: খ

10%

উত্তর

সঠিক উত্তর: খ

10%

খ

ব্যাখ্যা

Question: Mr. X's salary is Tk. 20000 and he gets 10% commission of his salary. If his salary increased by 10%, by what percent his commission will increase?

Solution:
পূর্বের কমিশন,
= 20000 এর 10% টাকা
= 20000 এর 10/100
= 2000 টাকা

10% বৃদ্ধিতে,
বর্তমান বেতন = 20000 + 20000 এর 10%
= 20000 + 2000
= 22000 টাকা

নতুন কমিশন = 22000 এর 10%
= 22000 এর 10/100
= 2200 টাকা

কমিশন বৃদ্ধি পায় = 2200 - 2000 = 200 টাকা

শতকরা কমিশন বৃদ্ধি পায় = {(200/2000) × 100}%
= 10%

৬৪৭.

The morning greets us with fresh air, _______?

ক
didn't it
খ
do we
গ
does it
ঘ
doesn’t it

সঠিক উত্তর: ঘ

doesn’t it

উত্তর

সঠিক উত্তর: ঘ

doesn’t it

ঘ

ব্যাখ্যা

• Noun যদি subject হিসেবে ব্যবহার করা হয় tag question করার নিয়ম:
- কখনো কখনো common noun ব্যবহার করে abstract noun বুঝানো হয়।
- The morning এখানে abstarct noun হিসেবে ব্যবহার করা হয়েছে।
- তাই The Morning এর অর্থ ধরে এর পরিবর্তে it- pronoun বসাতে হবে।
- Statement টি positive হলে tag question টি negative হবে।

• Complete Sentence: The morning greets us with fresh air, doesn't it?

Source: A Passage to the English Language S. M. Zakir Hussain, Live MCQ English Wizard.

৬৪৮.

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

ক
ক) 7.8
খ
খ) 6.5
গ
গ) 8.8
ঘ
ঘ) 8.5

সঠিক উত্তর: গ

গ) 8.8

উত্তর

সঠিক উত্তর: গ

গ) 8.8

গ

ব্যাখ্যা

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

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

44% of 20
= 44 × (20/100)
= 8.8

৬৪৯.

A trader marks his goods 40% above cost price and allows a discount of 25%. The profit he makes is:

ক
ক) 15%
খ
খ) 10%
গ
গ) 5%
ঘ
ঘ) 2%
ঙ
ঙ) 7%

সঠিক উত্তর: গ

গ) 5%

উত্তর

সঠিক উত্তর: গ

গ) 5%

গ

ব্যাখ্যা

Let original CP = Rs. 100
Then, the Marked Price = 40% of 100 + 100 = 140
SP = 140 - 25% of 140 = 105
%Profit = (5×100)/100 = 5%

Net Graphic Change Method:
100 == 40% UP ⇒ 140 == 25% discount ⇒ 105 So, % Profit = 5%

৬৫০.

If 20% of A = 30% of B, and B = 400, find A.

ক
400
খ
500
গ
600
ঘ
700

সঠিক উত্তর: গ

600

উত্তর

সঠিক উত্তর: গ

600

গ

ব্যাখ্যা

Question: If 20% of A = 30% of B, and B = 400, find A.

Solution:
the equation;
20% of A = 30% of B
⇒ (20/100) × A = (30/100) × B
⇒ 0.2A = 0.3 × 400 [Substitute B = 400]
⇒ 0.2A = 120
⇒ A = 120/0.2
⇒ A = 600

∴ A = 600

৬৫১.

Milon purchased two articles at the same price and sold one at a profit of 20% and the other at a profit of 25%. If the difference between the two selling price is Tk. 75, what is the cost price of each of the articles?

ক
2500
খ
1500
গ
2000
ঘ
2400

সঠিক উত্তর: খ

1500

উত্তর

সঠিক উত্তর: খ

1500

খ

ব্যাখ্যা

Question:
Milon purchased two articles at the same price and sold one at a profit of 20% and the other at a profit of 25%. If the difference between the two selling price is Tk. 75, 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 = 125
The difference in the selling price = 125 - 120 = 5

The difference in the selling price = 5 if the cost price = 100
If the difference in selling price = 75, then the cost price = (75 × 100)/5 = 1500

৬৫২.

By selling 45 chocolates for Tk. 40, a man loses 20%. How many should he sell for Tk. 24 to gain 20% in the transaction?

ক
10
খ
12
গ
15
ঘ
18

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: By selling 45 chocolates for Tk. 40, a man loses 20%. How many should he sell for Tk. 24 to gain 20% in the transaction?

Solution:
cost price 45 chocolates = 40/0.8 = 50 taka

selling price after 20% gain = 50 + 50 × .2 = 60 taka

he should he sell for Tk. 24 = (24 × 45)/60 = 18 chocolates

৬৫৩.

The selling price of a an article after giving two successive discounts of 10% and 5% on the marked price is Tk. 171. What is the marked price?

ক
Tk. 240
খ
Tk. 220
গ
Tk. 200
ঘ
Tk. 250

সঠিক উত্তর: গ

Tk. 200

উত্তর

সঠিক উত্তর: গ

Tk. 200

গ

ব্যাখ্যা

Question: The selling price of a an article after giving two successive discounts of 10% and 5% on the marked price is Tk. 171. What is the marked price?

Solution:
If the marked price Tk.100, then after giving discounts of 10%,
selling price of the article = (100 - 10) = Tk. 90

If discounts of 5% on Tk. 90,
selling price of the article = (90 - 90 × 5%) = 90 - 4.5 = Tk. 85.5.

If the selling price Tk. 85.5, marked price is Tk. 100
If the selling price Tk. 171, marked price is Tk. 100 × 171/85.5 = Tk. 200

৬৫৪.

By selling 45 lemons for tk 40, a man loses 20%. How many should he sell for tk 24 to gain 20% in the transaction?

ক
16
খ
17
গ
18
ঘ
19

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: By selling 45 lemons for tk 40, a man loses 20%. How many should he sell for tk 24 to gain 20% in the transaction?

Solution:
The cost price of 45 lemons = (40 × 100)/80
= 50

Selling price of 45 lemons to gain 20% profit = (50 × 120)/100
= 60 tk

No. of lemons he should sell for tk 24 to gain 20% profit = (45 × 24)/60
= 18

৬৫৫.

Mr. Shane buys 10 kg of sugar at Taka 40 per kg and 40 kg rice at Taka 50 per kg. At what price approximately in Taka per kg should he sell to make a profit of 2% on cost?

ক
Tk. 114.4
খ
Tk. 87.4
গ
Tk. 47.4
ঘ
Tk. 48.96

সঠিক উত্তর: ঘ

Tk. 48.96

উত্তর

সঠিক উত্তর: ঘ

Tk. 48.96

ঘ

ব্যাখ্যা

মোট খরচ = (10 × 40 + 40 × 50) টাকা
= (400 + 2000) = 2400 টাকা
10% লাভে বিক্রয়মূল্য (2400 + 2400 × 2/100) = 2448 টাকা
∴ প্রতি কেজির বিক্রয়মূল্য (2448 ÷ 50) টাকা = 48.96 টাকা

৬৫৬.

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

ক
Tk. 200
খ
Tk. 220
গ
Tk. 250
ঘ
Tk. 300

সঠিক উত্তর: গ

Tk. 250

উত্তর

সঠিক উত্তর: গ

Tk. 250

গ

ব্যাখ্যা

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

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

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

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

∴ Total Profit (50+ 200) = Tk. 250

৬৫৭.

What percentage of the whole week does Sami spend in school except lunch time, if his school times are 8 am to 4 pm from Saturday to Thursday where as there is 1 hour to his lunch time?

ক
18%
খ
20%
গ
25%
ঘ
30%

সঠিক উত্তর: গ

25%

উত্তর

সঠিক উত্তর: গ

25%

গ

ব্যাখ্যা

Question: What percentage of the whole week does Sami spend in school except lunch time, if his school times are 8 am to 4 pm from Saturday to Thursday where as there is 1 hour to his lunch time?

Solution:
Time spend by Sami in a day = {(12 + 4) - 8} hours
= 8 hours

Except lunch time Sami spend in a day = (8 - 1) hours
= 7 hours

Percentage time spend in a week = {(7 × 6)/(7 × 24)} ×100%
= 25%

৬৫৮.

A shirt is sold for Tk. 1500 at a profit of 20%. What would have been the actual profit or loss percentage if it had been sold for Tk. 1200?

ক
4% loss
খ
5% profit
গ
5% loss
ঘ
4.5% profit

সঠিক উত্তর: ক

4% loss

উত্তর

সঠিক উত্তর: ক

4% loss

ক

ব্যাখ্যা

Question: A shirt is sold for Tk. 1500 at a profit of 20%. What would have been the actual profit or loss percentage if it had been sold for Tk. 1200?

সমাধান:
ধরি, শার্টের ক্রয়মূল্য = x টাকা

20% লাভে বিক্রয়মূল্য = x + x এর 20%
= x + (x × 20/100)
= x + x/5 = 6x/5

প্রশ্নমতে,
6x/5 = 1500
⇒ 6x = 1500 × 5
⇒ 6x = 7500
⇒ x = 7500/6
⇒ x = 1250

∴ শার্টের ক্রয়মূল্য = Tk. 1250

বিক্রয়মূল্য = Tk. 1200 ক্রয়মূল্য = Tk. 1250

যেহেতু বিক্রয়মূল্য < ক্রয়মূল্য, তাই ক্ষতি হবে।

ক্ষতি = ক্রয়মূল্য - বিক্রয়মূল্য
= 1250 - 1200 = 50 টাকা

শতকরা ক্ষতি = (ক্ষতি/ক্রয়মূল্য) × 100%
= (50/1250) × 100%
= 5000/1250
= 4%

∴ 4% ক্ষতি হবে

৬৫৯.

The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is-

ক
15
খ
16
গ
18
ঘ
25

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is-

Solution:

Let
C.P. of each article be Tk. 1
C.P. of x articles = Tk. x.

S.P. of x articles = Tk. 20.

Profit = Tk. (20 - x).

∴ {(20 - x)/x} × 100 = 25

⇒ 2000 - 100x = 25x
⇒ 125x = 2000
∴ x = 16.

৬৬০.

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
5.5%
খ
7.1%
গ
9.1%
ঘ
10%

সঠিক উত্তর: গ

9.1%

উত্তর

সঠিক উত্তর: গ

9.1%

গ

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%

৬৬১.

What percent of 8 is 10% of 5?

ক
7.5%
খ
6.5%
গ
6.25%
ঘ
5.76%

সঠিক উত্তর: গ

6.25%

উত্তর

সঠিক উত্তর: গ

6.25%

গ

ব্যাখ্যা

Question: What percent of 8 is 10% of 5?

Solution:
10% of 5 = 5 × (10/100) = 0.5

0.5 is, {(0.5/8) × 100} = 6.25 percent of 8

∴ 6.25 percent of 8 is 10% of 5

৬৬২.

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

ক
25%
খ
12%
গ
15%
ঘ
20%

সঠিক উত্তর: ঘ

20%

উত্তর

সঠিক উত্তর: ঘ

20%

ঘ

ব্যাখ্যা

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

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

And the profit is 8%.
C.P = {100/(100 + p %)} × S.P
⇒ C.P = (100/108) × 432
∴ C.P = 400

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

S.P = Marked price = 480, and C.P = 400
Profit = S.P - C.P = 480 - 400 = 80

P% = (Profit/C.P) × 100
= (80/400) × 100
= 80/4
= 20%

৬৬৩.

In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A?

ক
50%
খ
53%
গ
54%
ঘ
55%
ঙ
57%

সঠিক উত্তর: খ

53%

উত্তর

সঠিক উত্তর: খ

53%

খ

ব্যাখ্যা

Question: In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A?

Solution:
Say there are total of 100 registered voters in that city.
Thus 60 are Democrats and 40 are Republicans.

60 × 0.75 = 45 Democrats are expected to vote for Candidate A;
40 × 0.20 = 8 Republicans are expected to vote for Candidate A.

Thus total of 45 + 8 = 53 registered voters are expected to vote for Candidate A,
which is 53% of the total number of registered voters.

৬৬৪.

A total profit of Tk. 3,600 is to be distributed amongst A, B and C such that A : B = 5 : 4 and B : C = 8 : 9. The share of C in the profit is:

ক
ক) 1,200
খ
খ) 1,500
গ
গ) 1,650
ঘ
ঘ) 1,700

সঠিক উত্তর: ক

ক) 1,200

উত্তর

সঠিক উত্তর: ক

ক) 1,200

ক

ব্যাখ্যা

A Total Profit = Tk 3600
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 : 4 × 8
B : C = 8 × 4 : 9
So, ratio of
A : B : C = 40 : 32 : 36 = 10 : 8 : 9
Now,
C shares in profit = (3600×9)/27
= Tk 1200

৬৬৫.

Problem Solving, Analytical & Financial aptitude
The price of a certain television set is discounted by 10 percent, and the reduced price is then discounted by 10 percent. The series of successive discount is equivalent to a single discount of -

ক
20
খ
19
গ
18
ঘ
21
ঙ
None of these

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: The price of a certain television set is discounted by 10 percent, and the reduced price is then discounted by 10 percent. The series of successive discount is equivalent to a single discount of -

Solution:
Let,
The initial price is Tk. 100

After 1st 10% discount,
The price = 100 - 10% of 100 = 100 - 10 = 90

After 2nd 10% discount,
The price = 90 - 10% of 90 = 90 - 9 = 81

∴ equivalent single discount = 100 - 81 = 19

৬৬৬.

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) 20%
খ
খ) 25%
গ
গ) 35%
ঘ
ঘ) 15%

সঠিক উত্তর: ক

ক) 20%

উত্তর

সঠিক উত্তর: ক

ক) 20%

ক

ব্যাখ্যা

ধরি,
বই এর দাম = 100 টাকা
কলম এর দাম= 100 + 25 = 125 টাকা
কলম হোল্ডার এর দাম = 100 + 50 = 150 টাকা

কলম থেকে কলম হোল্ডার এর দাম বেশি = 150 -125 টাকা
= 25 টাকা

কলম থেকে কলম হোল্ডার শতকরা বেশি = (25 x 100)/125
= 20%

৬৬৭.

If each side of a rectangle is increased by 50%, its area will increase by -

ক
ক) 200%
খ
খ) 125%
গ
গ) 150%
ঘ
ঘ) 50%

সঠিক উত্তর: খ

খ) 125%

উত্তর

সঠিক উত্তর: খ

খ) 125%

খ

ব্যাখ্যা

ধরি, আয়তক্ষেত্রটির দৈর্ঘ্য x একক এবং প্রস্থ y একক
সুতরাং ক্ষেত্রফল = xy বর্গ একক
৫০% বৃদ্ধিতে নতুন দৈর্ঘ্য = x + (xএর৫০%) = x + x/2 = ৩x/2
৫০% বৃদ্ধিতে নতুন প্রস্থ = y + (yএর ৫০%) = y + y/2 = ৩y/2
নতুন ক্ষেত্রফল = (৩x/2) × (৩y/2) = ৯xy/৪
ক্ষেত্রফল বৃদ্ধি পেয়েছে = ৯xy/৪ - xy = ৫xy/৪
∴ ক্ষেত্রফল শতকরা বৃদ্ধি পেয়েছে = (৫xy × ১০০)/৪xy = ১২৫%

শর্টকাটঃ ক্ষেত্রফল বৃদ্ধি পাবে = [50 + 50 + (50×50 / 100)] % = 125%

৬৬৮.

If a man were to sell his chair for Tk. 675, he would lose 25%. To gain 25% he should sell it for:

ক
ক) Tk. 1125
খ
খ) Tk. 900
গ
গ) Tk. 1005
ঘ
ঘ) Tk. 1215

সঠিক উত্তর: ক

ক) Tk. 1125

উত্তর

সঠিক উত্তর: ক

ক) Tk. 1125

ক

ব্যাখ্যা

Question: If a man were to sell his chair for Tk. 675, he would lose 25%. To gain 25% he should sell it for:

Solution:
CP of chair = (100/75) × 675
= Tk. 900

To gain 25%, SP = (125/100) × 900
= Tk. 1125

৬৬৯.

On reducing the entry fee by 25% in a park, the number of people coming to the park increased by 20%, then the percent increase or decrease in the income from the entry fee is -

ক
ক) 8% increase
খ
খ) 7% decrease
গ
গ) 10% decrease
ঘ
ঘ) 9% increase

সঠিক উত্তর: গ

গ) 10% decrease

উত্তর

সঠিক উত্তর: গ

গ) 10% decrease

গ

ব্যাখ্যা

Let
The entry fee = Tk. 100 per head and number of people coming to the park = 100.
So income = Tk. (100 × 100) = Tk.10000.

Further entry fee is Tk.(100 - 25) = Tk. 75 and number of people coming to the park = 100 + 20 = Tk.120.
Hence income = Tk. (75 × 120) = Tk. 9000.

So decrease in income = Tk. (10000 - 9000) = Tk. 1000.

The percent decrease in the income = (1000/10000) ×100 = 10%

৬৭০.

A person incurs a loss of 5% by selling a watch for Tk.1330. At what price should the watch be sold to earn 5% profit ?

ক
ক) Tk.1450
খ
খ) Tk.1470
গ
গ) Tk.1460
ঘ
ঘ) Tk.1430

সঠিক উত্তর: খ

খ) Tk.1470

উত্তর

সঠিক উত্তর: খ

খ) Tk.1470

খ

ব্যাখ্যা

Question: A person incurs a loss of 5% by selling a watch for Tk.1330. At what price should the watch be sold to earn 5% profit ?

Solution:
5% ক্ষতিতে
বিক্রয়মূল্য 95 টাকা হলে ক্রয়মূল্য 100 টাকা
বিক্রয়মূল্য 1 টাকা হলে ক্রয়মূল্য 100/95 টাকা
বিক্রয়মূল্য 1330 টাকা হলে ক্রয়মূল্য (100 × 1330)/95 টাকা
= 1400 টাকা

5% লাভে
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য 105 টাকা
ক্রয়মূল্য 1 টাকা হলে বিক্রয়মূল্য 105/100 টাকা
ক্রয়মূল্য 1400 টাকা হলে বিক্রয়মূল্য (105 × 1400)/100 টাকা
= 1470 টাকা

৬৭১.

If x = 20%, by what percent is x larger than x²?

ক
25%
খ
400 %
গ
120%
ঘ
240%

সঠিক উত্তর: খ

400 %

উত্তর

সঠিক উত্তর: খ

400 %

খ

ব্যাখ্যা

x = 20%
⇒ x
= 20/100
= 1/5

⇒ x²
= 1/25
= 1/25 × 100%
= 4%

x is larger than x² (in percentage)
= (20% - 4%)
= 16%

x is larger than x² (in percentage)
= 16/4 ×100%
= 400%

৬৭২.

A worker union contract specifies a 6% salary increase plus a Tk. 450 bonus for each worker. For a worker, this is equivalent to an 8% salary increase. What was this worker's salary before the new contract?

ক
Tk. 22500
খ
Tk. 23400
গ
Tk. 25000
ঘ
Tk. 21650

সঠিক উত্তর: ক

Tk. 22500

উত্তর

সঠিক উত্তর: ক

Tk. 22500

ক

ব্যাখ্যা

Question: A worker union contract specifies a 6% salary increase plus a Tk. 450 bonus for each worker. For a worker, this is equivalent to an 8% salary increase. What was this worker's salary before the new contract?

Solution:
ধরি, কর্মীর পূর্বের বেতন = x টাকা।

6% বৃদ্ধিতে বেতন = x + x এর 6%
= x + (6x/100) = 106x/100

বোনাস হিসেবে 450 টাকা যোগ করলে মোট বেতন = (106x/100) + 450

8% বৃদ্ধিতে বেতন = x + x এর 8%
= x + (8x/100) = (108x/100)

প্রশ্নমতে,
(106x/100) + 450 = (108x/100)
⇒ 450 = (108x/100) - (106x/100)
⇒ 450 = (2x/100)
⇒ x = (450 × 100)/2
∴ x = 22500

অর্থাৎ, কর্মীর পূর্ববর্তী বেতন ছিল 22500 টাকা।

৬৭৩.

If the ratio of cost price and selling price is of an article be 20 : 21, the percentage of profit is-

ক
ক) 3%
খ
খ) 4%
গ
গ) 5%
ঘ
ঘ) 6%

সঠিক উত্তর: গ

গ) 5%

উত্তর

সঠিক উত্তর: গ

গ) 5%

গ

ব্যাখ্যা

Let cost price 20x
selling price 21x
profit = 21x - 20x = x
Percentage of profit is ={(x/20x)× 100}%
= 5%

৬৭৪.

If 61% of Bangladeshi people like coffee and 74% like tea, how many like both?

ক
ক) 13%
খ
খ) 16%
গ
গ) 26%
ঘ
ঘ) 35%

সঠিক উত্তর: ঘ

ঘ) 35%

উত্তর

সঠিক উত্তর: ঘ

ঘ) 35%

ঘ

ব্যাখ্যা

n(C ∩ T) = 61% + 74% - 100% = 35%

৬৭৫.

An association of mathematics teachers has 1260 members. Only 525 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast?

ক
75%
খ
58%
গ
42%
ঘ
34%
ঙ
25%

সঠিক উত্তর: ঙ

25%

উত্তর

সঠিক উত্তর: ঙ

25%

ঙ

ব্যাখ্যা

Question: An association of mathematics teachers has 1260 members. Only 525 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast?

Solution:
Total number of members = 1260
Number of members that cast votes = 525
Since , winning candidate received 60 percent of the votes cast
Number of votes for winning candidate = (60/100) × 525 = 315

Percent of total membership that voted for winning candidate = (315/1260) × 100 = 25%

৬৭৬.

Mr. Masum usually makes 45% profit on every Mobile phone he sells. During a sale, he reduces his margin of profit to 40%, while his sales increase by 10%, What is the ratio of his new profit to his usual profit?

ক
44 : 47
খ
11 : 35
গ
34 : 45
ঘ
44 : 45

সঠিক উত্তর: ঘ

44 : 45

উত্তর

সঠিক উত্তর: ঘ

44 : 45

ঘ

ব্যাখ্যা

Question: Mr. Masum usually makes 45% profit on every Mobile phone he sells. During a sale, he reduces his margin of profit to 40%, while his sales increase by 10%, What is the ratio of his new profit to his usual profit?

Solution:
প্রথমে Mobile বিক্রয় করেন = x টি

45% লাভে মোট লাভ = 45x/100
10% বিক্রি বৃদ্ধিতে নতুন বিক্রির পরিমাণ = x + x এর 10%
= x + 10x/100
= 1.1x

নতুন লাভ = 1.1x × 40/100
= 44x/100

নতুন লাভ : পুরাতন লাভ = 44x/100 : 45x/100
= 44 : 45

৬৭৭.

A seller sold his articles in two types such that three fourth at a profit of 10% and the remaining at loss of 2%. If the total profit was Tk. 1500, what was the total value of the articles?

ক
Tk. 20409.25
খ
Tk. 21009.48
গ
Tk. 21428.57
ঘ
Tk. 21400

সঠিক উত্তর: গ

Tk. 21428.57

উত্তর

সঠিক উত্তর: গ

Tk. 21428.57

গ

ব্যাখ্যা

Let the total value be Tk. X.
The value of 3/4 th = Tk. 3X/4 then the value of 1/4 th = Tk. X/4
Since he made a profit of 10% on 3X/4 and loss 2% on X/4
Selling price = Tk. [110% of 3X/4] + [98% of X/4]
= Tk. 330X/400 + 98X/400
= Tk. 428X/400
Since the total cost price is Tk. X and the total profit is Tk. 1500 then
Tk. {(428X /400) - X} = Tk. 1500
⇒ {(428X - 400X)/400} = 1500
⇒ 28X = 1500 x 400
⇒ 28X = Tk. 6,00,000
⇒ X = 6,00,000/28 = Tk. 21428.57
= Tk. 21428.57
Hence the answer is Tk. 21428.57

৬৭৮.

A machine is sold at a profit of 10%. Had it been sold for Tk. 40 less, there would have been a loss of 10%. What was the cost price?

ক
Tk.175
খ
Tk. 200
গ
Tk. 225
ঘ
Tk. 250

সঠিক উত্তর: খ

Tk. 200

উত্তর

সঠিক উত্তর: খ

Tk. 200

খ

ব্যাখ্যা

Question: A machine is sold at a profit of 10%. Had it been sold for Tk. 40 less, there would have been a loss of 10%. What was the cost price?

Solution:
Let, cost price of the machine is x taka

Selling price = 1.1x taka

ATQ,
1.1x - 40 = 0.9x
⇒ 1.1x - 0.9x = 40
⇒ 0.2x = 40
⇒ x = 40/.2
= Tk. 200

৬৭৯.

Altaf saved Tk. 2.50 in buying an item on sale. If he spent Tk. 25 for the item, approximately how much percent he save in the transaction?

ক
(120/11)%
খ
(100/11)%
গ
(91/11)%
ঘ
10%

সঠিক উত্তর: খ

(100/11)%

উত্তর

সঠিক উত্তর: খ

(100/11)%

খ

ব্যাখ্যা

Question: Altaf saved Tk. 2.50 in buying an item on sale. If he spent Tk. 25 for the item, approximately how much percent he save in the transaction?

Solution:
cost price = 25 + 2.5 = 27.5 taka

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

৬৮০.

A bike originally cost Tk. 1000 and was discounted 10%. After three months it was sold after being discounted another 15%. How much was the bike sold for?

ক
Tk. 820
খ
Tk. 805
গ
Tk. 790
ঘ
Tk. 765

সঠিক উত্তর: ঘ

Tk. 765

উত্তর

সঠিক উত্তর: ঘ

Tk. 765

ঘ

ব্যাখ্যা

Question: A bike originally cost Tk. 1000 and was discounted 10%. After three months it was sold after being discounted another 15%. How much was the bike sold for?

Solution:
Given
Original price = Tk. 1000
10% discounted price = 1000 - (10% of 1000)
= 1000 - (10/100 of 1000)
= Tk. 900

The bike was sold after another 15% discount.
∴ 15% of Tk. 900 = Tk. (15/100 of 900)
= Tk. 135

∴ Selling price= Tk. (900 - 135)
= Tk. 765

৬৮১.

A dishonest shopkeeper pretends to sell his goods at cost price but uses false weights and gains 11.11%. Find the false weight he is using instead of 1kg weight.

ক
900 gm
খ
950 gm
গ
850 gm
ঘ
800 gm

সঠিক উত্তর: ক

900 gm

উত্তর

সঠিক উত্তর: ক

900 gm

ক

ব্যাখ্যা

Question: A dishonest shopkeeper pretends to sell his goods at cost price but uses false weights and gains 11.11%. Find the false weight he is using instead of 1kg weight.

Solution:

Let the false weight be x gm.

Gain % = [(True weight - False weight)/ False weight] × 100

⇒ 11.11 = 100/9 = [(1000 - x)/x] × 100

⇒ 9000 - 9x = x
⇒ 10x = 9000

⇒ x = 900

∴ the shopkeeper is using weights of 900 gm instead of 1kg.

৬৮২.

1.14 expressed as a percent of 1.9 is-

ক
6%
খ
10%
গ
60%
ঘ
90%
ঙ
None of these

সঠিক উত্তর: গ

60%

উত্তর

সঠিক উত্তর: গ

60%

গ

ব্যাখ্যা

Question: 1.14 expressed as a percent of 1.9 is-

Solution:
Required Percentage = (1.14 ×100)/1.9
= (114 × 100 × 10)/(19 × 100)
= 60%

৬৮৩.

Rokeya bought 30 kg of wheat at the rate of Tk. 9.50 per kg and 40 kg of wheat at the rate of Tk. 8.50 per kg and mixed them. She sold the mixture at the rate of Tk. 8.90 per kg. Her total profit or loss in the transaction was -

ক
ক) Tk. 2 loss
খ
খ) Tk. 2 profit
গ
গ) Tk. 7 loss
ঘ
ঘ) Tk. 7 profit

সঠিক উত্তর: ক

ক) Tk. 2 loss

উত্তর

সঠিক উত্তর: ক

ক) Tk. 2 loss

ক

ব্যাখ্যা

C.P. of 70 kg wheat
= Tk. (30 × 9.50 + 40 × 8.50)
= Tk. (285 + 340)
= Tk. 625
S.P. of 70 kg wheat
= Tk. (70 × 8.90)
= Tk. 623
∴ Loss = Tk. (625 - 623) = Tk. 2

৬৮৪.

To gain 10% on selling sample of milk at the cost price of pure milk, the quantity of water to be mixed with 50 kg. of pure milk is -

ক
ক) 2.5 kg
খ
খ) 5 kg
গ
গ) 7.5 kg
ঘ
ঘ) 10 kg

সঠিক উত্তর: খ

খ) 5 kg

উত্তর

সঠিক উত্তর: খ

খ) 5 kg

খ

ব্যাখ্যা

Question: To gain 10% on selling sample of milk at the cost price of pure milk, the quantity of water to be mixed with 50 kg of pure milk is -

Solution:
Let the quantity of water mixed be x kg.
Let CP of 1 kg of pure milk = Tk 1

Hence,
% gain = x × (100/50)
⇒ 10 = 100x/50
⇒ 100x = 500
⇒ x = 5

৬৮৫.

In an examination 36% are pass marks. If an examine gets 17 marks and fails by 10 marks, what are the maximum marks?

ক
ক) 90
খ
খ) 75
গ
গ) 60
ঘ
ঘ) 55

সঠিক উত্তর: খ

খ) 75

উত্তর

সঠিক উত্তর: খ

খ) 75

খ

ব্যাখ্যা

Pass mark = (17 + 10) = 27
Let maximum marks be x
Then 36% of x = 27
Or, 36x/100 = 27
Or, 36x = 2700
Hence, x = 75

৬৮৬.

A wholesaler bought 1200 radios for Tk. 18 each. The wholesaler sold 60 percent of the radios for Tk. 30 each and the rest for Tk. 15 each. What is the wholesaler's average (arithmetic mean) profit per radio?

ক
ক) Tk. 6
খ
খ) Tk. 5
গ
গ) Tk. 4
ঘ
ঘ) Tk. 3

সঠিক উত্তর: ক

ক) Tk. 6

উত্তর

সঠিক উত্তর: ক

ক) Tk. 6

ক

ব্যাখ্যা

Question: A wholesaler bought 1200 radios for Tk. 18 each. The wholesaler sold 60 percent of the radios for Tk. 30 each and the rest for Tk. 15 each. What is the wholesaler's average (arithmetic mean) profit per radio?

Solution:
৬০% রেডিও বিক্রি করে ৩০ টাকায় এবং ৪০% বিক্রি হয় ১৫ টাকায়

মোট বিক্রয়মূল্য = {১২০০ × (৬০/১০০) × ৩০} + {১২০০ × (৪০/১০০) × ১৫}
= ২১৬০০ + ৭২০০ টাকা
= ২৮৮০০ টাকা

গড় বিক্রয়মূল্য = ২৮৮০০/১২০০ টাকা
= ২৪ টাকা

গড় ক্রয়মূল্য ১৮ টাকা

গড় লাভ = (২৪ - ১৮) টাকা
= ৬ টাকা

৬৮৭.

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

ক
4%
খ
5%
গ
6%
ঘ
8%

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

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

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

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

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

৬৮৮.

400 students took a mock test: 60% of the boys and 80% of the girls cleared the cut off in the test. If the total percentage of students clearing the cut off in the test is 65%, then how many girls appeared in the test?

ক
100
খ
120
গ
150
ঘ
300

সঠিক উত্তর: ক

100

উত্তর

সঠিক উত্তর: ক

100

ক

ব্যাখ্যা

Question: 400 students took a mock test: 60% of the boys and 80% of the girls cleared the cut off in the test. If the total percentage of students clearing the cut off in the test is 65%, then how many girls appeared in the test?

Solution:
400 students took a mock test:
60% of the boys and 80% of the girls cleared the cut off in the test.
the total percentage of students clearing the cut off in the test is 65%

Let's assume there were b boys and g girls in the test.

According To question:
the total number of students who cleared the cut off = (60/100)b + (80/100)g = 0.65 × 400 .........(1)
the total number of students who took the test = b + g = 400
⇒ b = 400 - g

Substituting this value of b in the first equation: (60/100)(400 - g) + (80/100)g = 0.65 × 400
⇒ (24000 - 60g)/100 + 80g/100 = 260
⇒ 24000 - 60g + 80g = 26000
⇒ 20g = 2000
∴ g = 100
So, 100 girls appeared in the test.

৬৮৯.

After paying 10% tax on all income over 2000. Rahman had a net income of Tk 20000. Rahman's income before tax was?

ক
Tk 25000
খ
Tk 22450
গ
Tk 22000
ঘ
Tk 21990

সঠিক উত্তর: গ

Tk 22000

উত্তর

সঠিক উত্তর: গ

Tk 22000

গ

ব্যাখ্যা

Question: After paying 10% tax on all income over 2000. Rahman had a net income of Tk 20000. Rahman's income before tax was?

Solution:
Let, Rahim’s income was = x
Taxable Income = x - 2000
Tax paid = 10% × (x - 2000)

According to the question,
⇒ x - 10% × (x - 2000) = 20000
⇒ x - {10 × (x - 2000)}/100 = 20000
⇒ x - (x - 2000)/10 = 20000
⇒ 10x - (x - 2000) = 200000
⇒ 10x - x + 2000 = 200000
⇒ 9x = 200000 - 2000
⇒ x = 198000/9
⇒ x = 22000

∴ Rahim's income before tax was Tk 22,000

৬৯০.

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

ক
Tk. 90
খ
Tk. 130
গ
Tk. 100
ঘ
Tk. 120
ঙ
None of the above

সঠিক উত্তর: ঙ

None of the above

উত্তর

সঠিক উত্তর: ঙ

None of the above

ঙ

ব্যাখ্যা

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

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

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

Now, the selling price of the remaining 5 pens = 1000 - 450 = Tk. 550

Hence, the selling price of 1 pen = Tk. 110

৬৯১.

A person sells an item for Tk. 7,600 and incurs a 5% loss. At what price should the item be sold to gain a 15% profit?

ক
Tk. 9200
খ
Tk. 8740
গ
Tk. 9600
ঘ
Tk. 9100

সঠিক উত্তর: ক

Tk. 9200

উত্তর

সঠিক উত্তর: ক

Tk. 9200

ক

ব্যাখ্যা

Question: A person sells an item for Tk. 7,600 and incurs a 5% loss. At what price should the item be sold to gain a 15% profit?

Solution:
5% ক্ষতিতে বিক্রয়মূল্য = 100 - 5 = 95 টাকা।

বিক্রয়মূল্য 95 টাকা হলে ক্রয়মূল্য 100 টাকা।
∴ বিক্রয়মূল্য 1 টাকা হলে ক্রয়মূল্য 100/95 টাকা।
∴ বিক্রয়মূল্য 7,600 টাকা হলে ক্রয়মূল্য (100/95) × 7,600 টাকা
= 8,000 টাকা।

আবার, 15% লাভে বিক্রয়মূল্য = 100 + 15 = 115 টাকা।

ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য 115 টাকা।
∴ ক্রয়মূল্য 1 টাকা হলে বিক্রয়মূল্য 115/100 টাকা।
∴ ক্রয়মূল্য 8,000 টাকা হলে বিক্রয়মূল্য (115/100) × 8,000 টাকা
= 9,200 টাকা।

∴ জিনিসটি 9,200 টাকায় বিক্রি করতে হবে।

৬৯২.

A person makes a profit of 20% on 25% of the quantity, and a loss of 20% on the rest. What is the percentage gain or loss on the whole?

ক
12.5%
খ
7.5%
গ
9%
ঘ
10%
ঙ
8%

সঠিক উত্তর: ঘ

10%

উত্তর

সঠিক উত্তর: ঘ

10%

ঘ

ব্যাখ্যা

Let Cost Price = 100
Profit = 25 x 20% = 5
Loss = 75 x 20% = 15
Net loss = 10
Net Loss as % = 10/100 x 100 = 10%

৬৯৩.

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

ক
ক) 8
খ
খ) 15
গ
গ) 27
ঘ
ঘ) 35

সঠিক উত্তর: ক

ক) 8

উত্তর

সঠিক উত্তর: ক

ক) 8

ক

ব্যাখ্যা

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%

৬৯৪.

Akmal multiplied a number by 2/5 instead of 5/2. What is the percentage error in the calculation?

ক
54%
খ
80%
গ
44%
ঘ
84%

সঠিক উত্তর: ঘ

84%

উত্তর

সঠিক উত্তর: ঘ

84%

ঘ

ব্যাখ্যা

Question: Akmal multiplied a number by 2/5 instead of 5/2. What is the percentage error in the calculation?

Solution:
Let the number be x

∴ Error = (5x/2) - (2x/5)
= (25x - 4x)/10
= 21x/10

∴ percentage Error = {(21x/10)/(5x/2) × 100}%
= 84%

৬৯৫.

The sum of principal and simple interest of a certain amount of money would be Tk. 460 after 3 years from now and Tk. 500 after 5 years from now. What is the total interest rate?

ক
ক) 5%
খ
খ) 12%
গ
গ) 15%
ঘ
ঘ) 20%

সঠিক উত্তর: ক

ক) 5%

উত্তর

সঠিক উত্তর: ক

ক) 5%

ক

ব্যাখ্যা

Question: The sum of principal and simple interest of a certain amount of money would be Tk. 460 after 3 years from now and Tk. 500 after 5 years from now. What is the total interest rate?

Solution:
ধরি,
মুনাফার হার = r
মূলধন = P

দেওয়া আছে,
৩ বছরে মুনাফা আসলে হয় = ৪৬০ টাকা
৫ বছরে মুনাফা আসলে হয় = ৫০০ টাকা

∴ ২ বছরে সরল মুনাফা = ৫০০ - ৪৬০ = ৪০ টাকা
তাহলে, ৩ বছরের সরল মুনাফা = (৪০/২)৩ = ৬০ টাকা

∴ মূলধন, P = ৪৬০ - ৬০ = ৪০০ টাকা

আমরা জানি,
I = Pnr
r = I/Pn
= 60/(400 × 3)
= 0.05 × 100%
= 5%

৬৯৬.

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) 500cm
খ
খ) 5cm
গ
গ) 0.97cm
ঘ
ঘ) 1.97cm
ঙ
ঙ) 0.95cm

সঠিক উত্তর: ক

ক) 500cm

উত্তর

সঠিক উত্তর: ক

ক) 500cm

ক

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:
Let
the original length of the bar = L cm

Increase in length 0.2% of L = (0.2L)/100 cm
ATQ,
(0.2L)/100 = 1
⇒ 0.2L = 100
⇒ L = 100/0.2
⇒ L = 500

∴ The original length is 500 cm.

৬৯৭.

The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is:

ক
8%
খ
3%
গ
5%
ঘ
10%

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is-

Solution:
জনসংখ্যা বৃদ্ধি পায় ২৬২৫০০ - ১৭৫০০০ জন
= ৮৭৫০০ জন

১৭৫০০০ জনে ১০ বছরে বৃদ্ধি পায় ৮৭৫০০ জন
∴ ১৭৫০০০ জনে ১ বছরে বৃদ্ধি পায় ৮৭৫০০/১০ জন = ৮৭৫০ জন
∴ ১ জনে ১ বছরে বৃদ্ধি পায় = ৮৭৫০/১৭৫০০০ জন
∴ ১০০ জনে ১ বছরে বৃদ্ধি পায় = (৮৭৫০ × ১০০)/১৭৫০০০ জন
= ৫ জন

৬৯৮.

What percent of 700 is 2.1?

ক
ক) 0.003
খ
খ) 0.3
গ
গ) 0.03
ঘ
ঘ) 3

সঠিক উত্তর: খ

খ) 0.3

উত্তর

সঠিক উত্তর: খ

খ) 0.3

খ

ব্যাখ্যা

Question: What percent of 700 is 2.1?

Solution:
Let,
the percent is x.

ATQ,
x% of 700 = 2.1
⇒ (x/100) × 700 = 2.1
⇒ 7x = 2.1
⇒ x = 2.1/7
∴ x = 0.3

৬৯৯.

If each side of a rectangle is increased by 10% the increase in the area of a rectangle will be ____ .

ক
ক) 11%
খ
খ) 21%
গ
গ) 25%
ঘ
ঘ) 44%

সঠিক উত্তর: খ

খ) 21%

উত্তর

সঠিক উত্তর: খ

খ) 21%

খ

ব্যাখ্যা

ধরি,
আয়তকারক্ষেত্রের দৈর্ঘ্য = x
আয়তকার ক্ষেত্রের প্রস্থ = y
∴ ক্ষেত্রফল = xy বর্গএকক

10% বৃদ্ধিতে নতুন দৈর্ঘ্য = x + x এর 10%
= x + x এর 10/100
= x + x/10
= 11x/10

10% বৃদ্ধিতে নতুন প্রস্থ = y + y এর 10%
= y + y এর 10/100
= y + y/10
= 11y/10
∴ নতুন ক্ষেত্রফল = (11x/10) × (11y/10) বর্গএকক
= 121xy/100 বর্গএকক

ক্ষেত্রফল বৃদ্ধি = {(121xy/100) - xy} বর্গএকক
= 21xy/100 বর্গএকক

∴ ক্ষেত্রফল বৃদ্ধির হার = {(21xy × 100)/100 × xy}%
= 21%

৭০০.

By Selling 45 lemons for Tk. 40, a man loses 20%. How many should he sell for Tk..24, to gain 20% in the transaction?

ক
16
খ
18
গ
20
ঘ
21

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: By Selling 45 lemons for Tk. 40, a man loses 20%. How many should he sell for Tk..24, to gain 20% in the transaction?

Solution:
SP per Lemons = 40/45 = Tk. 0.88.
Let, CP was Tk. X per Lemons.
SP = CP - 20% of CP
⇒ 0.88 = 0.8X
⇒ X = Tk. 1.11

To get 20% profit,
SP = 1.11 + 20% of 1.11 = Tk.1.33

Thus, he can sell = 24/1.33
= 18 Lemons in Tk. 24.