Verified answer

Given :-

Rs.5000 at 5% simple interest and Rs.4500 at 6% simple interest per annum were given as loan in the same time.

To find :-

In how many years the amounts of both the principal's will be same .

Solution :-

Given that

Principal (P) = Rs. 5000

Rate of Interest (R) = 5%

Let the time be T years

We know that

Simple Interest = PTR/100

=> S.I. = (5000×T×5)/100

=> S.I. = 25000T/100

=> S.I. = 250T

Therefore, Simple Interest = Rs. 250T

We know that

Amount = principal + Interest

=> A = Rs. 5000+250T ---------(1)

and

Principal (P) = Rs. 4500

Rate of Interest (R) = 6%

Let the time be T years

We know that

Simple Interest = PTR/100

=> S.I. = (4500×T×6)/100

=> S.I. = 27000T/100

=> S.I. = 270T

Therefore, Simple Interest = Rs. 270T

We know that

Amount = principal + Interest

=> A = Rs. 4500+270T ---------(2)

According to the given problem

Amounts will be same for the same period of time

=> 5000+250T = 4500+270T

=> 5000-4500 = 270T-250T

=> 500 = 20T

=> 20T = 500

=> T = 500/20

=> T = 25

Therefore, Time = 25 years

Answer :-

In 25 years the amounts of the both principals will be same.

Check :-

We have,

P = Rs. 5000

T = 25 Years

R = 5%

We know that

Amount = P[ 1+(TR/100)]

=> A = 5000[1+(25×5/100)]

=> A = 5000[1+(125/100)]

=> A = 5000[1+(5/4)]

=> A = 5000(9/4)

=> A = 45000/4

=> A = 11,250--------(1)

And

P = Rs. 4500

T = 25 years

R = 6%

We know that

Amount = P[ 1+(TR/100)]

=> A = 4500[1+(25×6/100)]

=> A = 4500[1+(150/100)]

=> A = 4500[1+(3/2)]

=> A = 4500(5/2)

=> A = 22500/2

=> A = 11,250--------(2)

From (1) and (2)

We notice that The amounts of both loans are same for 25 years

Used formulae:-

→ S.I. = PTR/100

→ A = P+I

→ A = P[1+(TR/100)]

• P = Principal
• T = Time
• R = Rate of Interest
• S.I. = Simple Interest
• A = Amount

[tex]\bold{ANSWER≈}[/tex]

Given :

Rs.5000 at 5% simple interest and Rs.

4500 at 6% simple interest per annum

were given as loan in the same time.

To find :

In how many years the amounts of both

the principal's will be same.

Solution :

Given that

Principal (P) = Rs. 5000

Rate of Interest (R) = 5%

Let the time be T years

We know that

Simple Interest = PTR/100

=> S.I. = (5000xTx5)/100

=> S.I. = 25000T/100

=> S.I. = 250T

Therefore, Simple Interest = Rs. 250T

We know that

Amount = principal + Interest

=> A= Rs. 5000+250T ---------

and

-(1)

Principal (P) = Rs. 4500

Rate of Interest (R) = 6%

Let the time be T years

We know that

Simple Interest - PTR/100

=> S.I. = (4500xTx6)/100

=> S.I. = 27000T/100

=> S.I. = 270T

Therefore, Simple Interest = Rs. 270T

We know that

Amount = principal + Interest

=> A = Rs.

4500+270T ---------(2)

According to the given problem

Amounts will be same for the same

period of time

=> 5000+250T = 4500+270T

=> 5000-4500 270T-250T

=> 500 20T

=> 20T = 500

=> T = 500/20

=> T = 25

Therefore, Time = 25 years

Amount = P[ 1+(TR/100)]

=> A = 5000[1+(25x5/100)]

=> A = 5000[1+(125/100)]

=> A = 5000[1+(5/4)]

=> A = 5000(9/4)

=> A = 45000/4

=> A = 11,250--------(1)

And

P = Rs. 4500

T = 25 years

R = 6%

We know that

Amount = P[ 1+(TR/100)]

=> A = 4500[1+(25x6/100)]

=> A=4500[1+(150/100)]

=> A = 4500[1+(3/2)]

=> A = 4500(5/2)

=> A = 22500/2

=> A = 11,250--------(2)

From (1) and (2)

We notice that The amounts of both

loans are same for 25 years

Used formulae:

→ S.I. = PTR/100

→ A = P+I

- A = P[1+(TR/100)]

. P = Principal

. T = Time

• R = Rate of Interest

.

. S.I. = Simple Interest

.

A = Amount