NCTB Class 8 Math Chapter Two Exercise 2.2 Solution by Math Expert. Bangladesh Board Class 8 Math Solution Chapter 2 Profits Exercise 2.2 Solution.
Board |
NCTB |
Class |
8 |
Subject |
Mathematics |
Chapter |
2 |
Chapter Name |
Profits |
Exercise |
2.2 Solution |
Math
Exercise (2.2)
(1) Which one of the following is 8% of TK. 1050?
(a) Tk. 80
(b) Tk. 82
(c) Tk. 84
(d) Tk.86
Solution:
(1050X8/100) Tk
= (c) 84 Tk.
(2) What is the simple profit of Tk. 1,200 in 4 years at the rate of simple profit of 10% per annum?
(a) Tk. 120
(b) Tk. 240
(c) Tk. 360
(d) Tk. 480
Solution:
Profit = 1200X4X10/100
= (d) 480 Tk.
(3) The cost price of something is 5 pieces at Tk. 1 and selling price is 4 pieces at Tk. 1. What will be the percentage of profit or loss?
(a) Profit 25%
(b) Loss 25%
(c) Profit 20%
(d) Loss 20%
Solution:
CP of 5pc = 1Tk.
SP of 4pc = 1Tk.
Therefore, (1/5X100)
= (c) Loss 20%.
(4) Counting Profit:
(i) Profit = profit-principal-principal.
(ii) Profit = Principal X Profit X Principal/2
(iii) Compound Profit = Compound principal-principal
According to the above information, which one of the following is correct?
(a) (i) and (ii)
(b) (i) and (iii)
(c) (ii) and (iii)
(d) (i), (ii) and (iii)
Solution:
(b) (i) & (iii) are correct.
(5) At 10% simple profit for principal Tk. 2000
(i) Profit 1 year is Tk. 200
(ii) Amount in 5 years is 1 ½ times of principal.
(iii) In 6 years the profit will be equal to principal.
Which one of the following is correct?
(a) (i) and (ii)
(b) (i) and (iii)
(c) (ii) and (iii)
(d) (i), (ii) and (iii)
Solution:
Profit = (2000 X 10/100 X1)
= 200 Tk.
6 year profit = (2000 X 10/100 X 6)
= 1200 Tk.
Amount in 5 year = 2000+ (2000 X 10/100 X 5)
= 3000 Tk.
P X 1~2/3 = 2000 X 5/3
= 1000/3 Tk.
= (a) (i) & (iii) are correct.
(6) Mr. Jamil deposited Tk. 2,000 in a bank at the rate of profit 10% per annum:
(1) What will be the profit-principal at the end of the year?
(a) Tk. 2,050
(b) Tk. 2,100
(c) Tk. 1,200
(d) Tk. 2,250
Solution:
Profit principal = 2000+ (2000 X 10/100 X 1)
= 2200 Tk.
(2) In simple profit, what will be the profit-principal at the end of 2^{nd} year?
(a) Tk. 2,400
(b) Tk. 2,420
(c) Tk. 2,440
(d) Tk. 2,450
Solution:
End of 2^{nd} year profit principal
= 2000+ (2000 X 10/100 X 2)
= 2000+400
= (a) Tk. 2,400.
(3) What will be the compound principal at the end of 1^{st} year?
(a) Tk. 2,050
(b) Tk. 2,100
(c) Tk. 21,500
(d) Tk. 2,200
Solution:
Compound principal = 2000 (1 + 10/100)^{1}
= 2000 X 110/100
= (d) 2200 Tk.
(7) If the rate of profit is 10% per annum, find the compound principal of Tk. 8000 in 3 years.
Solution:
Compound principal = 8000 (1 + 10/100)^{3}
= 8000 X 110/100 X 110/100 X 110/100
= 10648 Tk. (Answer)
(8) What will be the difference of simple profit and compound profit of Tk. 5,000 in 3 years if the rate of profit is Tk. 10 percent per annum?
Solution:
Simple profit = (5000 X 3 X 10/100) + 5000
= 1500 Tk. + 5000
= 6500 Tk.
Compound profit = 5000 (1 + 10/100)^{3}
= 5000 X 110/100 X 110/100 X 110/100
= 6655
Difference = (6655 – 6500) Tk. = 155 Tk. (Answer)
(9) What was the principal if the compound principal of any amount of principal at the end of one year is Tk. 6,500 and at the end of two years is Tk. 6,760 at the same rate of profit?
Solution:
Compound principal end of 2 year 6760 Tk.
Compound principal end of 1 year 6500 Tk.
(-)
——————————————————————–
1 year compound principal = 260 Tk.
(10) If the rate of compound profit is Tk. 8.50 percent per annum, find the compound principal and compound profit of Tk. 10000 in 2 years.
Solution:
P = 10,000 Tk; N = 2 year. R = 8.5%
Therefore, compound profit = P (1 + 8.5/100)^{2}
= 10,000 (1 + 8.5/100)^{2}
= 10000 X 108.5/100 X 108.5/100
= 1772.25 Tk.
Compound principal = (10,000+1772.25)
= 11772.25 Tk. (Answer)
(11) Present population of a city is 64 Lac. What will be the population of the city after 2 years if growth rate of population of the city is 25 per thousand?
Solution:
Here, P = 6400000 (Total population)
Growth rate of population = 25/1000 X 100%
= 2.5%
N = 2 year.
Therefore, after two years total population
C = p (1+n)^{n}
= 6400000 (1 + 2.5/100)^{2}
= 6400000 X 102.5/100 X 102.5/100
= 6724000 (Answer).
(12) A person borrows Tk. 5,000 from a lending organization at the rate of 8% compound profit. At the end of every year he paid off Tk. 2,000. How much more money will he have as loan after paying off the 2^{nd} installment?
Solution:
After 1 year amount of C.I
= 5000 (1 + 8/100)^{1}
= 5000 (1 + 2/25)^{1}
= 5000 (25+2/25)^{1}
= 5400 Tk.
After paid 2000 Tk. Rest = (5400-2000) Tk.
= 3400 Tk.
Therefore, Amount = 3400 (1 + 8/100)
= 3400 (1 + 2/25)
= 3400 X 27/25
= 13672 Tk.
After 2^{nd} Installment, remaining amount = (3672 – 2000) Tk.
= 1672 (Answer).
(13) At the same rate of compound profit a principal will amount to Tk. 19,500 after 1 year and Tk. 20,280 after 2 years.
(A) Write down the formula for profit.
(B) Find out the principal.
(C) Find the difference between simple profit and compound profit after 3 years at the same rate for the principal.
Solution:
(a) We know that, formula for profit
C – P = P (1+r)^{n} – p.
Where, P = Principal
R = rate of interest
N = time.
(b) 1^{st} time, 1 year, amount = 19500 Tk.
2 year amount = 20280 Tk.
P (1+r)^{1} = 19500 —– (1)
P (1+r)^{2} = 20280 —– (2)
(2) ÷ (1)
1+r = 20280/19500
= 19500+19500r = 20280
= r = 780/19500
= r = 1/25.
Putting the value in (1)
P (1 + 1/25) = 19500
= P (26/25) = 19500.
= P = 19500X25/26
= 18750 Tk (Answer)
(c) In C.I amount (c) = P (1+r)^{n}
= 18750 (1 + 1/25)^{3} Tk.
= 18750 (26/25)^{3}
= 21091.2
Interest profit = C – P
= (21091.2 – 18750) Tk.
= 2341.2 Tk.
Therefore, in just profit interest (I) = Prn
= 18750 X 1/25 X 3
= 2250 Tk.
Therefore, Difference with SI & C.I
= (23412.2 – 2250.00) Tk.
= 91.2 Tk. (Answer)
(14) Shipra Barua deposited Tk. 3,000 in a bank and got Tk. 3,600 together with the profit 2 years.
(a) Find the percentage of simple profit.
(b) What will be the profit-principal after another 3 years?
(c) What would be the compound principal after 2 years if Tk. 3,000 was deposited at the same percentage of compound profit?
Solution:
(a) Interest = A – P
= (3600 – 300)
= 600 Tk.
Therefore, 3000 Tk, 2 year interest 600 Tk.
Therefore, 1 Tk, 1 year interest 600/3000X2 Tk
Therefore, 100 Tk, 1 year interest 600X100/3000X2 Tk
= 10 Tk.
Therefore, rate 10% (Answer)
(b) 100 Tk, 1 year interest 10 Tk.
1 Tk 1 year interest 10/100 Tk
3000 Tk 3 year interest 10X3000X3/100
= 900 Tk.
The profit principle after another 3 years
= (3600+900) Tk.
= 4500 Tk. (Answer)
(c) Here, P= 3000 Tk.
N= 2 year.
R= 10%
Therefore, amount on C.I (C) = P(1+r)^{n}
= C= 3000X (1+ 10/100)^{2}
= 3000 (100+10/100)^{2}
= 3000X (110/100)^{2}
= 3000X (11/10)^{2}
= 3000X 121/100
= 3630 Tk (Answer).