Question

a sum of money invested at 6% per annum simple interest for a certain period of time yields 960 as interest.if this sum has been invested for 5 years more, it would have yielded 2160 as interest.find the sum​

Answer 1

Answer:

960 * 6 * 5 / 100

=288

288 add 2160

=2448

Answer 2

The sum of money invested is Rs. 4000 .

• Let the sum of money invested be Rs. P .

Let the time for which the money is invested be T years.

Given,

Rate of interest per annum (R) = 6

• According to the first condition,

Simple Interest (S.I.) yielded in time T = Rs. 960

The simple interest for a certain sum of money is given by the formula,

S.I. = ( P × R × T ) / 100

=> Rs. 960 = ( P × 6 × T ) / 100

Or, 960 × 100 = 6PT

Or, P = (960 × 100 ) / 6T

Or, P = 16,000 / T  -(i)

• According to the second condition,

Time for which the sum is invested = T + 5

Simple interested yielded (S.I.) in time (T + 5) = Rs. 2160

• Now, using the formula for simple interest, we get,

Rs. 2160 = { P × 6 × (T + 5) } / 100

Or, 2160 × 100 = 6P (T + 5)

Or, P = 216,000 / { 6 (T + 5) }  -(ii)

• Since the sum invested is same, equation (i) and (ii) are equal.

Therefore, equating (i) and (ii), we get,

16,000 / T = 216,000 / { 6 (T + 5) }

Or, 16000 { 6 ( T + 5 ) } = 216000 × T

Or, 96000 (T + 5 ) = 216000 T

Or, 96000 T + 480000 = 216000 T

Or, 216000 T - 96000 T = 480000

Or, 120000 T = 480000

Or, T = 480000 / 120000

Or, T = 4

∴   Time for which the money is invested is 5 years.

• Putting T = 4 in equation (i), we get,

P = 16000 / 4 = 4000

Therefore, the sum of money invested is Rs. 4000.