Correct Answer - Option 3 : T = 50 years; P = Rs. 200/3
If time = T, r = 10%
As we know,
A = P + Prt/100
⇒ 400 = P + (P × 10 × T)/100
400 = P + 10PT/100 ----(i)
Again,
If time = T, r = 4%
⇒ 200 = P + (P × 4 × T)/100
200 = P + 4PT/100 ----(ii)
Multiply by 2 in equation (ii)
400 = 2P + 8PT/100 ----(iii)
From equation (i) and equation (iii)
P + 10PT/100 = 2P + 8PT/100
⇒ 2P - P = 10PT/100 - 8PT/100
⇒ P = 2PT/100
∴ T = 50 years.
From equation (ii),
200 = P + (4 × P × 50)/100
⇒ 200 = P + 2P
⇒ 3P = 200
∴ P = Rs. 200/3