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Question

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

CAT 2021

A
200, 400, 600, 800
CORRECT ANSWER WRONG ANSWER
B
875, 625, 375, 125
CORRECT ANSWER WRONG ANSWER
C
125, 375, 625, 875
CORRECT ANSWER WRONG ANSWER
D
50, 350, 650, 950
CORRECT ANSWER WRONG ANSWER
Solution

Correct option is

(A)

Explanatory Answer :

take the numbers as

(a-3d),(a-d),(a+d),(a+3d)

So, Let the investment made by Ram in these years be (a-3d),(a-d),(a+d),(a+3d)

Then,

(a-3d) + (a-d) + (a+d) +(a+3d) = 2000

=> 4a = 2000

=> a = 500

Now, again AQ

 (a-3d)^{2} + (a-d)^{2} + (a+d)^{2}+(a+3d)^{2} = 1200000

=> 4(a^{2}+5d^{2}) = 1200000

=> (a^{2}+5d^{2}) = 300000

=> 250000+5d^{2} = 300000

=> 5d^{2} = 50000

=> d^{2} = 10000

=> d = pm 100