Question

A certain sum is invested for t years. It amounts to rs. 400 at 10% per annum. But when invested at 4% per annum, it amounts to rs. 200. Find the time (t). (1) 45 years (2) 60 years (3) 40 years (4) 50 years (

Answer 1

answer : option (4) 50 years

Let principal = x Rs.

we know, S.I = P × r × t/100

case 1 : S.I = A - P = 400 - x , r = 10%

so, (400 - x) = x × 10 × t/100

or, (400 - x) = xt/10......(1)

case 2 : S.I = A - P = 200 - x , r = 4%

so, (200 - x) = x × 4 × t/100

or, (200 - x) = xt/25 .....(2)

from equations (1) and (2),

(400 - x)/(200 - x) = 25/10 = 5/2

or, 2(400 - x) = 5(200 - x)

or, 800 - 2x = 1000 - 5x

or, 3x = 200

or, x = 200/3

now, putting x = 200/3 in equation (1),

(400 - 200/3) = 200t/30

or, 1000/3 = 20t/3

or, t = 50

hence, time = 50 years , option (4) is correct choice.

Answer 2

Answer:

50 years

option d

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