NCTB Class 8 Math Chapter Two Exercise 2.1 Solution

NCTB Class 8 Math Chapter Two Exercise 2.1 Solution by Math Expert. Bangladesh Board Class 8 Math Solution Chapter 2 Profits Exercise 2.1 Solution.

Board	NCTB
Class	8
Subject	Mathematics
Chapter	2
Chapter Name	Profits
Exercise	2.1 Solution

Exercise 2.1 Solution

(1) With profit 20% selling price = (100+20)

= 120 Rs.

Let, CP = 100 Rs.

Therefore, Here, SP 120 Rs then CP = 100 Rs.

Therefore, SP 1 Rs. Then CP = 100/120 Rs.

Therefore, 576 Rs. Then CP = 100×576/120

= 480 TK.

Therefore, SP of Retailer = 480 TK.

Now, 20% profit, SP = (100+20)

= 120 TK.

If SP 120 TK Then CP = 100 TK.

Therefore, If SP 120 TK then CP = 100/120 TK.

Therefore, If SP 480 TK then C P = 100×480/120 TK.

= 400 TK.

Therefore, Cost price of whole seller = 400 TK.

(2) Let, cost price = 100 TK.

5% loss, SP = (1000-5)

= 95 Tk.

Therefore, If SP 95 TK; then CP = 100 TK.

Therefore, 1 TK; then CP = 100/95 TK.

Therefore, 2375 TK; then C P = 100×2375/95 TK.

= 2500 TK.

Again, 6% profit, SP = (100+6) = 106 TK.

Therefore, If C P 100 TK, then SP = 106 TK.

Therefore, If CP 2500 TK, then S P = 106×2500/100

= 2650 TK.

Therefore, Selling price = 2650 TK.

(3) Taking L.C.M 10, 15, 12 —–

= 60.

Therefore, 10 bananas, CP = 30 TK.

Therefore, 1 bananas, C P = 30/10 TK.

Therefore, 60 bananas, C P 30 x 60/10 TK.

= 180 TK.

Now, 15 bananas CP = 30 TK.

1 bananas CP = 30/15 TK.

60 bananas C P = 30×60/15

= 120 TK.

Therefore, Total (60+60) 120 bananas cost price = (180+120) TK = 30 TK.

Therefore, 12 bananas SP = 30 TK.

1 bananas SP 30/12 TK.

Therefore, 120 bananas S P = 30×120/12 TK.

= 300 TK.

Therefore, C P = S P = 300 TK.

Therefore, No profit & No loss.

(4) Here, r = 10.50 %

P = 2000 Tk.

n = 5 yr.

∴ Profit = 2000 x 10.50/100 x 5

= 1050 TK.

(6) Here, P = 13000 TK.

I = (18850-13000) TK.

= 5850 TK.

N = 5yr.

R =?

Therefore, We know that,

I = p .r . n/100 (P mean Principal; r means rate percentage and n means number of times)

=> r = I/p . n

= 5850/13000×5

= 9/100

= 9%

(7) Let, P = 100 TK.

8 year later, amount = (100×2) TK.

= 200 TK.

Therefore, Interest = (200-100) = 100 Tk.

Therefore, Here P = 100 TK.

I = 100 TK.

n = 8 year.

R =?

We know, I = p .n .r

=> 100 = 100 x 8 x r

=> r = 100/100×8

= 12.50%

(8) 1^st, P = 6500 TK.

n = 4 year

A = 8840 TK.

I = A- P

= (8840-6500) TK.

= 2340 TK.

R =?

We know, I = P n r.

=> 2340 = 6500x 4 x r

=> r = 2340/ 6500×4

= 9%

2^nd, A = 10200 TK.

n = 4 year

P =?

And, r = 9%

We know, A = P + I

= P+ P n r

=> 10200 = P (1+n r)

= P (1+ 4 x 9/100)

=> 10200 = P (1 + 9/25)

=> 10200 = P (34/25)

=> P = 25x 10200/34

= 7500 TK.

(9) Here, n = 4 year

I = 4760 TK.

r = 8.50%

p =?

We know, I = p n r

=> 4760 = P x 4 x 8.50/100

=> P = 4760 x 100 x 100/4 x 850

= 14000 TK.

Therefore, Amount deposit in the bank 14000 TK.

(10) Let, P = 100 TK.

In 6 year, Amount = (100×2) = 200 TK.

6 year, Interest = (200-100) = 100 TK.

In 100 TK, 6 year Interest 100 TK.

Therefore, 100 TK, 1 year Interest 100/6 TK.

Therefore, 100 TK, 4 year Interest 100 x 4/6 TK.

= 200/3 TK.

Therefore, Amount = (100+ 200/3) = 500/3 TK.

Therefore, when amount 500/3, P = 100 TK.

Therefore, amount 1, P = 3x 100/500 TK.

Therefore, Amount 2050, P = 3x 100x 2050/500

= 1230 TK.

(11) 1^st, r = 6% ; n = 4 year

P = 500 TK; I =?

We know, I = p n r

= 500 x 4 x 6/100

= 120 TK.

2^nd, r = 5% ; n = 2 year 6 month

= (2 + 6/12)

= 2 ½ year

Therefore, I = 120 TK;

We know, I =  P n r

=> 120 = P x 2.5 x 5/100

=> P = 120 x 100/ 2.5 x 5

= 960 TK.

(12) Rate of interest increase = (100-8) = 2%

Therefore, In 100 TK. 1 year Interest 2 TK.

Therefore 100 TK, 4 year Interest (2 x 4) TK.

= 8 TK.

If, increasing 8 TK, P = 100 TK.

Therefore, increasing 2 TK, P = 100/8 TK.

Therefore, Increasing 128 TK, P = 100x 128/8

= 1600 TK.

(13) Let, principal = P

Therefore, P + 5 year interest = 1830 TK.

P + 3 year Interest = 1578 TK.

(-)________________________________________

2 year interest = 252 TK.

Therefore, 1 year interest = 252/2 TK.

Therefore, 3 year interest = 252x 3/2

= 378 TK.

Principal = Amount – Interest

= (1578-378) TK.

= 1200 TK.

Therefore, 1200 TK, 3 year interest is 378 TK.

Therefore, 1 TK, 1 year interest is 378/1200 x3 Tk.

Therefore, 100 TK, 1 year Interest 378 x100/1200 x 3 TK.

= 10.50 TK.

Therefore, Interest rate 10.50%.