A farmer wants to divide rupee 390300 between his two daughters who are 16 year and 18 years old respectively in such a way that the sum invested at the rate of 4% per annum, compounded
annually will give the same amount to each, when they attain the age of 21 years. How should he divide the sum?
Answers
Given : A farmer wants to divide rupee 390300 between his two daughters who are 16 year and 18 years old respectively in such a way that the sum invested at the rate of 4% per annum, compounded
annually will give the same amount to each, when they attain the age of 21 years.
To Find : Amount received by each daughters
Solution:
Let say Younger daughter receiver = Rs X
then Elder Daughter will will receive = 390300 - X Rs
Younger daughter will receive interest for 21 - 16 = 5 years
Elder daughter will receive interest for 21 - 18 = 3 years
Hence Younger daughter will receive interest for 2 years extra
=> After 2 year younger daughters amount should be same as Elder Daughter
as after that both will be getting interest for 3 years
Formula is A = P (1 + R/100)ⁿ
X ( 1 + 4/100)² = 390300 - X
=> X (26/25)² = 390300 - X
=> X = 1,87,500
390300 - X = 2,02,800
Hence younger daughter receive = 1,87,500 Rs
and Elder daughter receive = 2,02,800
PS
X ( 1 + 4/100)² = 390300 - X
this can be understand this ways also
X ( 1 + 4/100)⁵ = (390300 - X) ( 1 + 4/100)³
=> X ( 1 + 4/100)² = 390300 - X
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Step-by-step explanation:
16years rs187500 18years rs202800