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A certain sum invested for T years at 10% per annum Simple Interest amounts to Rs. 400. The amount gets halved when the interest comes down to 4% per annum, the principal and time being the same. What is the principal and value of T?
1. T = 50 years; P = Rs. 200 
2. T = 25 years; P = Rs. 200/3
3. T = 50 years; P = Rs. 200/3 
4. T = 50 years; P = Rs. 100

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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

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