Question

Ramesh and Suresh both want to lend some money to make some profit. Ramesh has Rs. 5000 and Suresh has Rs.4000. the term for the interest paid on both the amounts is three years.
(i) Set the interest rates for both Ramesh and Suresh so that Suresh makes more profit than Ramesh.
(ii) Set the interest rates for both Ramesh and Suresh so that the total amount received by Suresh is more than Ramesh.

Answer 1

Given:

(i) Ramesh has Rs. 5000 and Suresh has Rs 4000 .

(ii) The term for the interest was 3 years.

To Find:

(i) The interest for both of them so that Suresh makes more profit than Ramesh.

(ii) Interest rates for both Ramesh and Suresh so that the total amount received by Suresh is more than Ramesh.

Solution:

Let x be the rate of interest for Suresh and y be the rate of interest for Ramesh.

Lets take Simple interest

We know that, Amount after 't' years is given as:

A = P ( 1 + rt )

A = amount

P = Principal money.

r = rate of interest

t = time in years

Therefore ,

Profit = A - P = P ( 1 + rt )- P = Prt

So, for the first condition for Suresh to have more profit than Ramesh,

Profit of Suresh > Profit of Ramesh

(4000 * x * 3) > (5000 * y * 3)

x > 5y/4

If the interest rate of Ramesh is 8% then, the rate of interest of Suresh should be

x > 5y *(8/4)

x > 10%

The interest rate for Suresh should be more than 10% when Ramesh's  interest is 8%.

Amount for Suresh > Amount for Ramesh

4000(1+3x) > 5000(1+3y)

4000+12000x > 5000+15000y

12000x >15000y+1000

12x>15y+1

So when x = 4%,

12(4)>15y+1

15y+1<48

y<47/15

y<3.13%

(i) The interest rate for Suresh should be more than 10% when Ramesh's  interest is 8%.

(ii) So, when the interest of Suresh is 4%, Ramesh's interest should be less than 3.13%