Question

a) A person borrowed Rs.8,000 at a certain rate of interest for 2 years and then Rs.10,000 at

1% lower than the first. In all he paid Rs.2500 as interest in 3 years. Find the two rates at

which he borrowed the amount.

b) In what time will a sum of money double itself at 5% C.I. payable half-yearly ?​

Answer 1

Answer:

R = 7.35 %

R - 1 = 6.35 %

14 Years

Step-by-step explanation:

Considering Simple Interest :

person borrowed Rs.8,000

=> Principle = Rs 8000

Let say Interest Rate = R % Per anuum

Interest for 3 Years = 8000 * R * 3 /100 = 240R

Principle = 10000

Interest rate = R - 1 % Per annum

Interest for 1 year = 10000 * (R - 1)/100 = 100R - 100

240R + 100R - 100 = 2400

=> 340R = 2500

=> R = 7.35 %

R - 1 = 6.35 %

b) In what time will a sum of money double itself at 5% C.I. payable half-yearly ?​

Let Say  Principle = P

Rate of interest = 5 %  Per Annum

Compounded half Yearly

Let say in n Years it got doubled then

2P = P ( 1  + 5/200)²ⁿ

=> 2 = (1.025)²ⁿ

=> 2n = 28  ( approx)

=> n = 14

in 14 Years