IBA ফ্যাকাল্টি ভিত্তিক প্রস্তুতি

Question: If the price of a commodity increases by 50%, by what fraction should the quantity consumed be decreased to maintain the same total expenditure?

Solution:
Let the initial price of the commodity be 100.

After a 50% increase in price,
The increased price will be 150.
Now, we have to reduce the consumption to keep expenditure at 100.

Increase in price = 150 - 100 = 50

∴ We have to reduce the consumption
= (50/150) × 100
= 33.33% or 1/3

Question: If a shopkeeper sells a bat for Tk. 600, he incurs a loss of 20%. At what price should he sell it to make a profit of 20%?

Solution:
Let the cost price (CP) of the bat be x.
Selling price = x - 20% of x
⇒ 600 = x - (20x/100)
⇒ 600 = 80x/100
⇒ 80x = 60000
⇒ x = 750 (This is the CP)

To gain,
20% = 750 + 20% of 750
= 750 + (20 × 750)/100
= 750 + 150
= Tk. 900

Question: A sum of Tk. 800 amounts to Tk. 920 in 3 years at a certain simple interest rate. If the rate of interest is increased by 3% per annum, what will be the total amount after 3 years?

Solution:
Here, 
Sum = Tk 800, 
Amount = Tk 920,

∴ Simple interest = Amount - Principal 
= 920 - 800
= Tk 120

∴ Rate = (Interest × 100)/(Principal × Time)
= (120 × 100)/(800 × 3)
= 5% per annum

If the rate is increased by 3%, 
∴ Rate = 8% per annum

∴ simple interest = (800 × 8 × 3)/(800 × 3)
= Tk 192

∴ Amount = Principal + S.I.
= (800 + 192)
= Tk 992

Question: If one number is 20% smaller than another number, and that second number is 10% greater than 150, what is the value of the first number?

Solution:
Let,
First number x
Second number y

ATQ,
y is 10% more than 150
⇒ y = 150 + [(150 × 10)/100]
= 165 

and x is 20% less than y
⇒ x = 165 - [(165 × 20)/100]
= 165 - 33
= 132

∴ First number 132

Question: A fruit seller purchases guavas at the rate of 2 guavas for 1 taka and sells them at the rate of 5 guavas for 3 taka. What is his gain percentage?

Solution:
2 guavas cost 1 tk
So 1 lemon costs 1/2 tk

For comparing,
let's calculate CP (Cost Price) for 10 guavas
∴ CP of 10 guavas = 10 × (1/2) = 5 tk

Now,
Let's find the selling price (SP) of guavas:
5 guavas cost 3 tk
∴ 10 guavas will cost = (10/5) × 3 = 6 tk

∴ Gain = SP - CP = 6 - 5 = 1 tk
∴ Gain percentage = (Gain/CP) × 100
= (1/5) × 100
= 20%

Question: A book is listed at Tk. 920. A customer pays Tk. 742.90 for it after receiving two successive discounts. If the first discount is 15%, what is the rate of the second discount?

Solution:
MP = 920
After first discount Marked Price (MP) become,
= 920 - 15% of 920 = 782

The Selling Price (SP) = 742.90

Let,
second discount was x% on 782
⇒ 782 - x% of 782 = 742.90
⇒ 782x/100 = 39.1
⇒ 782x = 3910
⇒ x = 5%

∴ Second Discount = 5%

Question: Find the compound interest after 2 years on Tk. 14000 at the rate of interest 5% per annum.

Solution:
Let the sum P = 14000.
Rate of interest = 5%
Period = 2 years

Hence, compound interest = 14000(1 + 5/100)² - 14000
= 14000(1.05)² - 14000
= 14000 × 1.05 × 1.05 - 14000
= 15435 - 14000
= 1435

Question: A person who pays income tax at the rate of 4 paise per tk finds that a fall in the interest rate from 4% to 3.75% diminishes his net yearly income by tk 48. What is his capital?

Solution:
If the capital after tax deduction be p, then
p × (4 - 3.75) % = 48
⇒ (p × 0.25)/100 = 48
⇒ (p × 25)/10000 = 48
⇒ p/400 = 48
⇒ p = 48 × 400 = tk 19200

∴ Required capital = (19200 × 100)/96
= 20000 tk

Question: The population of a city grows by 10% every year. If the current population is 50,000, what will the population be 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

Question: The ratio of cost price and selling price is 4 : 5. The profit percentage is

Solution:
Given,
The ratio of cost price (C.P.) to selling price (S.P.) is 4:5.

Let,
The cost price be 4x and the selling price be 5x.

∴ Profit = S.P - C.P. = 5x - 4x = x
∴ Profit percent = (Profit/CP) × 100
= (x/4x) × 100
= (1/4) × 100
= 25%

Question: The compound interest on Tk. 30,000 at an annual rate of 7% amounts to Tk. 4,347. What is the time period (in years) for which the money was invested? 

Solution:
Amount = 30000 + 4347 = 34347 tk

Let, the time be n years,
Then,
30000{1 + (7/100)}ⁿ = 34347
⇒ (107/100)ⁿ = 34347/30000
⇒ (107/100)ⁿ = 11449/10000
⇒ (107/100)ⁿ = (107/100)²
∴ n = 2 years

Question: In an election between two candidates, the winner got 65% of the total votes cast and won the election by a majority of 2748 votes. What is the total number of votes cast if no vote is declared invalid?

Solution:
Winner gets 65% of valid votes and loser gets 35% of votes
Difference between this two = 2748
(65 - 35)% = 2748
⇒ 30% = 2748

Total number of voters, 100% = (2748 × 100)/30
= 9160

Question: A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Tk 22500. What is the reduced price per kg of tea?

Solution:
Let 10% of 22500 = 2250
Now,
25 kg = 2250
⇒ 1kg = 2250/25
∴ 1kg = 90

Question: A certain sum of money doubles in 20 years at simple interest. What is the annual rate of interest?

Solution:
Let,
sum = P,
then simple interest = P
and Time, T = 20 years

∴ Required rate = (100 × SI)/(P × T)
= (100 × P)/(P × 20)
= 5% per annum

Question: P is 6 times greater than Q then by what percent is Q smaller than P?

Solution:
Let Q = 10.
Then, P = 60.
Q is 50 less than P.
Q, % less than P = (50/60) × 100
= 83.33%

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

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

Question: A cuboidal room has its length, breadth, and height increased by 10%, 20%, and 50% respectively. Calculate the percentage change in the volume of the cuboid.

Solution:
Let,
Each side of the cuboid be 10 unit initially.
Initial Volume of the cuboid,
= length × breadth × height
= 10 × 10 × 10
= 1000 cubic unit.

After increment dimensions become,
Length = (10 + 10% of 10) = 11 unit.
Breadth = (10 + 20% of 10) = 12 unit.
Height = (10 + 50% of 10) = 15 unit.

Now, present volume = 11 × 12 × 15 = 1980 cubic unit.
Increase in volume = 1980 - 1000 = 980 cubic unit.
∴ percentage increase in volume = (980/1000) × 100 = 98%

Question: A merchant sells one table for Tk. 1200, making a profit of 25%, and another table for Tk. 1500, incurring a loss of 10%. What is his overall gain or loss percentage?

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%

Question: In an examination, 80% of the candidates passed algebra and 85% passed mechanics. If 73% of the candidates passed both subjects, what percentage of candidates failed in both algebra and mechanics?

Solution:
Students passed in algebra = 80%
Students passed in mechanics = 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%.

Question: 0.95 expressed as a percent of 1.9 is-

Solution:
Required Percentage = (0.95 ×100)/1.9
= (0.95 × 100 × 10)/(19 × 100)
= 50%