1.

Prema invests a certain sum at the rate of 10% per annum of interest and anothersum at the rate of 8% per annum to get a yield of Rs. 1640 in one year's time. Nextyear she interchanges the rates and gets a yield of Rs. 40 less than the previous year.How much did she invest in each type in the first year?

Answer»

Let amount Prema invests = P1 and P2

We know, SI = P*R*T/100

For R=10%, T = 1, P = P1SI1 = P1*10*1/100 = P1/10

For R=8%, T = 1, P = P2SI2= P2*8*1/100 = 2P2/25

SI1 + SI2 = 1640P1/10 + 2P2/25 = 16405P1 + 4P2 = 1640*50....(1)

Next year

For R=8%, T = 1, P = P1SI1 = P1*8*1/100 = 2P1/25

For R=10%, T = 1, P = P2SI2= P2*10*1/100 = P2/10

SI1 + SI2 = 16402P1/25 + P2/10 = 16004P1 + 5P2 = 1600*50......(2)

Multiply eq(1) by 4 and eq(2) by 5. Subtract eq(2) from eq(1)

20P1 + 16P2 = 1640*20020P1 + 25P2 = 1600*250

-9P2 = 328000 - 4000009P2 = 72000P2 = 72000/9 = 8000

Put value of P2 = 8000 in eq(1)

5*P1 + 4*8000 = 820005P1 = 82000 - 32000P1 = 50000/5 = 10000

Amounts Prema deposited are Rs 10000 and Rs 8000


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