Page 187 - Math_Genius_V1.0_C8_Flipbook

E:\Working\Focus_Learning\Math_Genius-8\Open_Files\09_Chapter_7\Chapter_7
\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

Rate of growth (R) = 2% p.a., Time (T) = 2 years

 R  T  2  2  1  2
So, population after 2 years = P 1 + 100  = 1,20,000 1 + 100  = 1,20,000 1 + 50 






 51 2 51 51
= 1,20,000   50  = 1,20,000 × 50 × 50 = 1,24,848
Thus, the population of the town after 2 years will be 1,24,848.
Example 31: In a laboratory, the count of bacteria in a certain experiment was increasing at the
rate of 2.5% per hour. Find the bacteria at the end of 2 hours if the count was initially 5,06,000.
Solution: Initial count of bacteria (P) = 5,06,000

Rate of growth in the count of bacteria (R) = 2.5% per hour; Time (T) = 2 hours
.
 R  n  25  2  1025 2
So, the final count of bacteria (A) = P1 + 100 = 5,06,000 1 + 100  = 5,06,000   1000






41 41
= 5,06,000 × × = 531616.25 ≈ 531616
40 40
Example 32: A scooter was bought for `42,000. Its value depreciated at the rate of 8% per annum.
Find its value after 2 years.
Solution: Cost of the scooter = `42,000; Rate of depreciation = 8% per annum
 8  2  23  23
Therefore, value of the scooter after 2 years = `42,000 1 − 100 = `42,000  25  25  = `35,548.80.

 



Example 33: Girish bought a shop for `4,60,000 in 2013. In 2014, its value increased by 4%. In
2015, the value decreased by 5%. In 2016, it again increased by 10%. What will be the value of the
shop in 2017?
Solution: Let the value of the shop in 2017 be P. Given, initial value (P ) in 2013 = `4,60,000
1
Increase in value in 2014 (R ) = 4%, Decrease in value in 2015 (R ) = 5%
1
2
Increase in value in 2016 (R ) = 10%
3
∴ Value of the shop in 2017,
5  
10 
4  
R 

R  

R  
P = P 1 + 100  1 − 100  1 + 100  = 4,60,000 1 + 100  1 − 100  1 + 100
3
1
2

 
 

1 
 
 


1 
1  
1  

11
= 4,60,000 1 + 25  1 − 20  1 + 10  = 4,60,000 × 26 × 19 × 10 = 4,99,928
 
 


20
25
Thus, the value of shop in 2017 will be `4,99,928.
Practice Time 7E
1. Calculate the amount and compound interest on
(a) `5,000 for 2 years at 8% per annum, compounded annually.
1
(b) `10,000 for 1 years at 10% per annum, compounded half yearly.
2
(c) `18,000 for 1 year at 8% per annum, compounded quarterly.
2. Neelam borrowed `50,000 from a bank to buy a computer at a rate of 15% p.a. compounded yearly.
What amount will she pay at the end of 2 years and 4 months to clear the loan?
185 Comparing Quantities