Question

the simple interest on a certain sum of money for 2.5 years at 12%per annum is rs.40 less than the simple interest on the same sum for 3.5 years at 10% per annum.find the sum​

Answer 1

The sum​ of money invested is Rs. 800.

• Let the sum be P.

• According to the first condition,

Sum = P

Time (T) = 2.5 years

Rate of interest (R) = 12 % p.a.

• Therefore, simple interest (S.I.) = (P × R × T) / 100

=> S.I. = (P × 12 × 2.5) / 100

Or, S.I. = 0.3 P

• According to the second condition,

Sum = P

Time (T') = 3.5 years

Rate (R') = 10 % p.a.

• Therefore, simple interest (S.I.') = (P × R' × T') / 100

=> S.I.' = ( P × 10 × 3.5 ) / 100

=> S.I.' = 0.35 P

• According to the question,

S.I.' - S.I. = 40

=> 0.35 P - 0.3 P = 40

=> 0.05 P = 40

=> P = 40 / 0.05

=> P = 800

• Therefore, sum = P = Rs. 800