IBA ফ্যাকাল্টি ভিত্তিক প্রস্তুতি

Question: If the price of the commodity is increased by 50% by what fraction must its consumption be reduced so as to keep the same expenditure on its consumption?

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

After a 50% increase in price, It will become, 100, and a 50% increase will be 150.
Now, we have to reduce the consumption to keep expenditure 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 watch 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 watch 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 the simple interest rate. If the rate is increased by 3% p.a., what will the sum amount be in the same period?

Solution:
Here , Principal = Tk 800 , Amount = Tk 920
S.I. = 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
S.I. = (800 × 8 × 3)/(800 × 3)
= Tk 192

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

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

Question: A fruit seller buys lemons at 2 for one tk and sells then at 5 for three tk. His gain percentage is

Solution:
2 lemons cost 1 tk
So 1 lemon costs 1/2 tk
For comparing, let's calculate CP for 10 lemons
CP of 10 lemons = 10 × (1/2) = 5 tk

Now let's find selling price (SP) of lemons:
5 lemons cost 3 tk
So 10 lemons will cost = (10/5) × 3 = 6 tk

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

Question: Find the compound interest on Tk. 8500 at 4 % per annum for 2 years, compounded annually.

Solution:
Principal = Tk. 8500, Rate = 4 % per annum, Time = 2 years
Amount = 8500 {1 + (4/100)}²
= Tk. 9193.6

Compound Interest = Total amount - Principal
= 9193.6 - 8500
= 693.6

Question: Which number is 40% less than 90?

Solution:
Required number = 60% of 90 
= (90 × 60)/100
= 54

Question: An article is listed at Tk. 920. A customer pays Tk. 742.90 for it after getting two successive discounts. If the rate of first discount is 15%, the rate of 2nd discount is:

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: 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: 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

Question: The ratio of cost price and selling price is 4 : 5. The profit percent 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 7% per annum is Tk. 4347. The period (in years) is:

Solution;
Amount = 30000 + 4347 = 34347 tk

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

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: At simple interest, a sum doubles after 20 years. The rate of interest per annum is?

Solution:
Let,
sum = P,
then SI = P
and Time = 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: A television is priced at Tk. 15,600. A customer pays Tk. 12,150 for it after getting two successive discounts. If the rate of first discount is 10%, the rate of 2nd discount is:

Solution:
MP = 15,600
After first discount Marked Price (MP) becomes,
= 15,600 - 10% of 15,600
= 15,600 - 1,560
= 14,040

The Selling Price (SP) = 12,150
Let second discount be x% on 14,040
14,040 - x% of 14,040 = 12,150
14,040 - 14,040x/100 = 12,150
14,040 - 140.4x = 12,150
-140.4x = 12,150 - 14,040
-140.4x = -1,890
x = 1,890/140.4
x = 13.46%

Question: A finance company declares that, at a certain compound interest rate, a sum of money deposited by anyone will become 8 times in 3 years. If the same amount is deposited at the same compound rate of interest, then in how many years will it become 16 times?

Solution:

Question: The length, breadth and height of a room in the shape of a cuboid are increased by 10%, 20% and 50% respectively. Find 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.
% increase in volume = (980/1000) × 100 = 98%

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%