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Ram invests a total sum of 2000 rupees on government bonds in 4 years. If these investments are in A.P and the sum of squares of the investments is 1200000. Find the investment made by ram in each year respectively. It is also known that he always invest more than the previous year.
Asked by rushabhjain.av | 19 Nov, 2018, 10:54: PM
Let initial investment is Rs. a and every year increased by Rs.d  ;

Then total investment for 4 years :-  a +(a+d) +(a+2d) + (a+3d) =  4a+6d = 2000

By simplifying above equation, we get 2a + 3d = 1000 ..................(1)

Sum of squares of invested amount = a2 + (a+d)2 + (a+2d)2 + (a+3d)2  = 1200000  ....(2)

eqn.(2) is simplified to :-  4a2 + 12ad + 14d2 = 1200000   ...............(3)

By substituting for 2a, using eqn.(1), i.e., 2a = (1000-3d ) in eqn.(3)
we get an equation in one variable d and if we solve that equation, we get  d =  200 .

From knon value d=200, using equation (1), we get a = 200.

Hence initial investment is Rs.200 and every year investment is increased by Rs.200
Answered by Thiyagarajan K | 20 Nov, 2018, 03:27: AM

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