Question

If a certain sum of money invested for a certain time it amount to rs. 350 at 5% per annum and it amount to rs. 250 at 3% per annum. Find the time and principal

Answer 1

But is this, simple or compound

Answer 2

Dear Student,

◆ Answer -

Sum of money invested = 100 Rs

Time for investing = 50 years

◆ Explanation -

Let P be sum of money invested for time t.

From given conditions,

Total = P (100 + r×t) / 100

For 5% interest rate,

350 = P (100 + 5×t) / 100

P (100 + 5t) = 350 × 100

P (100 + 5t) = 35000

P = 35000 / (100 + 5t) ...(1)

For 3% interest rate,

250 = P (100 + 3×t) / 100

P (100 + 3t) = 250 × 100

P (100 + 3t) = 25000

P = 25000 / (100 + 3t) ...(2)

From (1) by (2),

35000 / (100 + 5t) = 25000 / (100 + 3t)

35000 × (100 + 3t) = 25000 × (100 + 5t)

7 × (100 + 3t) = 5 × (100 + 5t)

700 + 21t = 500 + 25t

25t - 21t = 700 - 500

4t = 200

t = 200 / 4

t = 50 years

And total sum invested is -

P = 35000 / (100 + 5t)

P = 35000 / (100 + 5×50)

P = 35000 / 350

P = 100 Rs

Hence, 100 Rs was invested for 50 years at consecutive interest rates.

Thanks dear. Hope this helps you...