এনএসআই [NSI] নিয়োগ প্রস্তুতি [Archived]

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

Solution:
 120% of 45 + 45% of 120
= {(120/100) × 45} + {(45/100) × 120}
= 54 + 54
= 108

Question: An agent sells goods worth Tk. 18,000. If his commission rate was 12.5​%, what was the amount of his commission?

Solution:

Commission = 12.5% of 18000
= (125/10) × (1/100) × 18000
= (125/1000) × 18000
= 2250

Question: By selling a laptop for Tk. 4,500, a shopkeeper gains 20%. If the profit is reduced to 10%, then the selling price will be?

Solution:
Let the cost price be x

According to the question,
x + 20% of x = 4500
⇒ x + 20x/100= 4500
⇒ x + 0.20x = 4500
⇒ 1.20x = 4500
⇒ x = 4500/1.20
∴ x = 3750

So, cost price = Tk. 3750

Now, Selling price when profit is 10%,
SP = 3750 + 10% of 3750
= 3750 + 375
= 4125
∴ The new selling price will be Tk. 4,125.

Question: What is the interest for 2 years on Tk. 600 at a simple interest rate of 9.5%?

Solution: 
Interest rate, R = 9.5% 
Principal amount, P = 600 tk
Time, T = 2 years

We Know, SI = PRT/100
= (600 × 2 × 9.5)/100
= 114 Tk.

∴ The interest for 2 years is Tk. 114.

Question: What percent of 10 kg is 50 grams?

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

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.

Question: Three partners A, B, and 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. 16500 at the end of a year. Find out B's share in it.

Solution: 
Suppose C's capital = x
then, B's capital = 4x (Since B's Capital is four times C's capital)
A's capital,
2 × A's capital = 3 × B's capital (Since twice A's capital is equal to thrice B's capital)
⇒ 2 × A = 3 × 4x 
∴ A = 6x

Now,
A : B : C
= 6x : 4x : x
= 6 : 4 : 1

B's share = 16500 × (4/11)
= 1500 × 4
= 6000

Question: A candidate has to obtain a minimum of 40% of the total marks to pass. He got 30% of the total marks and failed by 50 marks. What are the maximum marks?

Solution: 
Let the maximum marks be x.

Then,
40% of x - 30% of x = 50
⇒ 10% of x = 50
⇒ 10x/100 = 50
⇒ x= (50 × 100)/10
∴  x = 500

Question: A farmer borrowed Tk. 3600 at 15% simple interest per annum. At the end of 4 years, he cleared this account by paying Tk. 4000 and a cow. The cost of the cow is:

Solution:
P = 3600 tk, R = 15%, T = 4 yrs

S.I = PRT/100
= (3600 × 15 × 4)/100
= 2160 Tk.

Hence,
amount after 4 years = (3600 + 2160) = 5760 Tk.
∴ Cost of the cow = (5760 – 4000) = 1760 Tk.

Question: Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months, and 7 months respectively. What was the ratio of their investment?

Solution:
Let their investments be
x Tk for 14 months,
y Tk for 8 months and
z Tk for 7 months respectively.

Then,
14x : 8y : 7z = 5 : 7 : 8

Now, 
14x/8y = 5/7
⇒ 98x = 40y
⇒ y = 49x/20

And,
14x/7z = 5/8
⇒ 112x = 35z
⇒ z = 16x/5

∴ x : y : z
= x : 49x/20 : 16x/5
= 20 : 49 : 64

Question: The population of a town increases every year by 5%. If its present population is 60,000, then after 2 years, what will be the population?

Solution: 
We know, Population after n years = P × [1 + (r/100)]ⁿ

∴ Population after 2 years = 60000 × [1 + (5/100)]²  
= 60000 × (1 + 0.05)² 
= 60000 × 1.1025
= 66150

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

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

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

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

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

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

Question: A person pays Tk. 8000 as an amount on the sum of Tk. 6000 that he had borrowed for 3 years. What will be the rate of interest?

Solution:
Amount, A = Tk. 8000
Principal, P= Tk. 6000
Time, T = 3 years
Interest Rate, R =?

Amount = Principal  + Simple Interest
SI = A – P
= 8000 – 6000
= Tk. 2000

SI = (P × R ×T)/100
⇒ R = (SI × 100)/(P × T)
= (2000 × 100)/(6000 × 3) 
= 11.11 %
∴ The rate of interest is 11.11 %.

Question: 'A' began a business with Tk. 85000. He was joined afterwards by 'B' with Tk. 42500. For how much period does 'B' join, if the profits at the end of the year are divided in the ratio of 3 : 1 ?

Solution: 
Suppose 'B' joined for x months.

Now,
A's capital = Tk. 85000, time = 12 months
B's capital = Tk. 42500, time = x months

According to the question,
A's share : B's Share = 3 : 1
⇒ (85000 × 12)/(42500 × x) = 3/1
⇒ x = (85000 × 12)/(42500 × 3)
⇒ x = 8
∴ 'B' joined for 8 months.

Question: A merchant has 1200 kg of rice, part of which he sells at 10% profit and the rest at 20% profit. If his overall gain is 16%, find the quantity of rice he sold at 20% profit.

Solution: 
Let the cost price per kg = Tk. x
∴ Total cost price = 1200x
Again,
Let the rice sold at 10% profit = y kg
Then the rice sold at 20% profit = (1200 - y) kg

Now,
Selling price of y kg at 10% profit,
SP₁ = (y × x) × (110/100)
= 110xy/100

Selling price of (1200 - y) kg at 20% profit,
SP₂ = (1200 - y) × (x) × (120/100)
= 120x(1200 - y)/100

Total Selling Price, SP = SP₁ + SP₂ 
= (110xy/100) + 120x(1200 - y)/100
= {110xy + 120x(1200 - y)}/100

Now,
Overall profit is 16%,
So, total SP =1200x × (116/100)
= 139200x/100

Now equating both total selling prices:
{110xy + 120x(1200 - y)}/100 = 139200x/100
⇒ 110xy + 120x(1200 - y) = 139200x
⇒ 110xy + 144000x - 120xy = 139200x
⇒ - 10xy = - 4800x
⇒ y = 4800x/10x
∴ y = 480 

So, rice sold at 20% profit = 1200 - y
= 1200 - 480 = 720 kg

Question: A man buys a chair and table for Tk. 6000. He sells the chair at a loss of 10% and the table at gain of 10%. He still gains Tk. 100 on the whole. Cost price of chair is:

Solution:
Given,
Total cost price (CP) of chair and table = Tk. 6000
Total profit = Tk. 100

Let, the Cost Price (CP) of the chair be x Tk.
So, the Cost Price of the table is = (6000 - x) Tk.

At 10% loss,
Selling Price of chair = x - 10% of x
= x - (10x/100)
= 90x/100

At 10% gain,
Selling Price of table = (6000 - x) + 10%  of (6000 - x)
= (6000 - x) + {(10/100) × (6000 - x)}
= 110(6000 - x)/100

So, Total Selling Price of chair and table,
= 90x/100 + {110(6000 - x)/100}
= {90x + 110(6000 - x)}/100

Now,
Total SP = Total CP + Profit
⇒ {90x + 110(6000 - x)}/100 = 6000 + 100
⇒ 90x + 110(6000 - x) = 100 × 6100
⇒ 90x + 660000 - 110x = 610000
⇒ - 20x = - 50000
⇒ x = 2500
∴ Cost price of the chair = Tk. 2500

Question: The true discount on Tk. 2562 due 4 months hence is Tk. 122. What is the rate percent?

Solution: 
Given,
Amount (A) = 2562 Tk
True Discount (TD) = 122 Tk
Time (T) = 4 months = 1/3 of a year

Present Worth, P.W. = (2562−122) Tk
= 2440 Tk

True Discount (TD) = Simple Interest (SI) on the Present Worth (PW) for the given time period.
∴ S.I. on 2440 Tk for 4 months is 122 Tk.

We know, SI = PRT/100
∴ R = (SI × 100)/(P × T)
= [(100 × 122)/(2440 × (1/3)]
= 15

∴ Rate is 15%

Question: Find the compound interest on TK. 30000 at 7% interest compounded annually for two years.

Solution: 
Principal, P = Rs 30000
Rate, R = 7%
Time, T = 2 year

By formula:
A = P(1 + R/100)^T 
= 30000 (1 + 7/100)²
= 30000 (107/100)²
= 30000 × (11449/10000)
= 34347

Compound Interest = A - P = 34347 - 30000
= 4347

Question: Find the compound interest on Tk. 2000 at the rate of 20% per annum for 1.5 years. When interest is compounded half-yearly.

Solution: 
Principal P = 2000
Rate, R = 20%
Time, T = 1.5 years

Now,
Compound interest for half-yearly:
A = P{1 + R/(2×100)}^2T
= 2000{1 + (20/200)}^2×1.5
= 2000 × {1 + (1/10)}³
= 2000 × (11/10)³ 
= 2000 × (1331/1000)
= 2662

Compound Interest = A – P
= 2662 – 2000 = 662 Tk

Questjion: A man buys an article for 20% less than its value and sells it for 20% more than its value. What is his gain or loss percentage?

Solution: 
Let, the value of article is x Tk.

Buying price at 20% less,
= x - 20% of x
= x - (20x/100)
= x - 0.2x
= 0.8x Tk.

Selling Price at 20% more, 
= x + 20% of x
= x + 0.2x
= 1.2x Tk.

Profit = 1.2x - 0.8x
= 0.4x Tk.

∴ Profit Percentage = (0.4x/0.8x) × 100%
= (40/0.8)%
= 50%

∴ The gain percentage is 50%.

Question: A shopkeeper offers two successive discounts of 10% and 20% on an item marked at Tk. 1,200. What is the final selling price?

Solution: 
New Price after First Discount : 
1200 - 10% of 1200
= 1200 - 120
= 1080 Taka

Final Selling Price after Second Discount:
1080 - 20% of 1080
= 1080 - 216
= 864

So, Final Selling Price = Tk. 864

সঠিক উত্তর: 16%
অপশনে সঠিক উত্তর না থাকায় প্রশ্নটি বাতিল করা হলো। 
---------------------------- 

Question: The marked price of an item is twice the cost price, discount 20% of market price and profit is 10% of selling price. Find profit percentage to cost.

Solution:
Let Cost Price = x
So, Marked price = 2x
∴ Discount = 20% of Marked Price
= 20% of 2x
= 2x/5

∴ Selling Price = Marked Price - Discount
= 2x - (2x/5)
= (10x - 2x)/5
= 8x/5

Profit = 10% of Selling Price
= 10% of 8x/5
= 4x/25

∴ Profit Percentage = (Profit/Cost Price) × 100%
= (4x/25)/x × 100%
= (4/25) × 100%
= 16%

Question: What is the total interest on Tk. 1,200 at 10% per annum for 9 months?

Solution: 
Given,
Principal (P) = Tk. 1200
Rate (R) = 10%
Time (T) = 9 months
= 9/12 year
= 3/4 year

By Formula,
SI = PRT/100
= {1200 × 10 × (3/4)}/100
= (1200 × 10 × 3)/400
= 90 Tk

Question: : On a 12% discount sale, an article costs Tk. 704. What was the original price of the article?

Solution:
Let the original price be Tk. x.

According to the question,
x - 12% of x = 704
⇒ x - (12x/100) = 704
⇒ (100x - 12x)/100 = 704
⇒ 88x = 70400
∴ x = 800

So, the original price of the article was Tk. 800.