A man has rs.1900. He lent some of it at 5% pa and rest at 9% pa. The total amount of interest he got after 4 yrs was rs.580.What was the sum?

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Answer 1 · 2018-07-31T13:07:30

Amount lent @ 9% Interest = Rs 1250 and amount lent at 5% Interest = Rs 650.

Taking it as simple Interest:

#I =( P N R) / 100#

Let x be the amount lent @ 9% Interest.

Then 1900 - x is the amount lent at 5% Interest.

#I = Rs 580, N = 4 years#

#(x * 4 * 9)/ 100 + ((1900-x) * 4 * 5)/100 = 580#

#36 x + 38000 - 20x = 58000#

#16 x = 58000 - 38000 = 20000#

#x = 20000/16 = Rs 1250#

#1900 - x = 1900 - 1250 = Rs 650#

Answer 2 · 2018-07-31T14:51:33

Amount lent @ 9% Interest = Rs 869.71 and amount lent @ 5% is = Rs 1030.29

Taking it as compound interest.

#A = P (1 + R/100)^ #

Let x be the amount lent at 9% Interest.

Then 1900 - x is the amount lent @ 5% Interest.

#P = 1900, I = 580, N = 4 years#

#1900 + 580 = x (1 + 9/100)^4 + (1900-x) (1 + 5/100)^4#

#x 1.09^4 + 1900 * 1.05^4 - x 1.05^4 = 2480#

#1.4116 x - 1.2155x = 2480 - 1900* 1.2155 = 170.55#

#x = 170.55 / (1.4116 - 1.2155) = 869.71#

#1900 - x = 1900 - 869.71 = 1030.29#