Answer:

Step-by-step explanation:

p= rs. 200

r%=10%

let the time period be "x"

I= P*n{n+1}*r% /  2*12*100

= 200 * X {X+1}*10 /  2*12*100

= X{X+1}*5 / 6

= 5X^2+5X / 6

M.V = P*n + I

6775   = 200*X + 5X^2 + 5X / 6

6775   = 6*200X +5X^2 + 5X / 6

6775   = 1200X +5X + 5X^2  / 6

6775*6= 1205X + 5X^2

40650 = 1205X + 5X^2

divide on both the sides by 5 since it is divisible and do so until it is not divisible by any number

8130 = 241X + X^2

X^2 + 241X - 8130=0

factorize 8130 to get 241 as the answer { see the pic if you don't know }

x^2 - 30x + 271x - 8130

x { x - 30} + 271 { x - 30}

{ x-30 } { x + 271}

neglect negative periods

x= 30 months

P=200,r=10%,MV=6775

MV=p*n+p*n(n+1)/2*12*r/100

substitute and simplify