Question

2. Calculate the time required for the simple
interest earned on 3,000 at the rate of
4% per annum to be equal to the simple
interest on * 8,000 at the rate of 8% per
annum for 3 years.​

Answer 1

GiveN:-

• Principal = Rs. 3000
• Rate = 4% per annum
• Principal = Rs. 8000
• Rate = 8% per annum
• Time = 3 years

To FinD:-

The time.

SolutioN:-

• First let's find the interest on Rs.8000

We know that,

$\large{\green{\underline{\boxed{\bf{Simple\:Interest=\dfrac{P\times\:R\times\:T}{100}}}}}}$

where,

• P is principal = Rs.8000
• R is rate = 8%
• T is time = 3 years

Putting the values,

$\large\implies{\sf{Simple\:Interest=\dfrac{8000\times8\times3}{100}}}$

$\large\implies{\sf{Simple\:Interest=\dfrac{80\cancel{00}\times8\times3}{1\cancel{00}}}}$

$\large\implies{\sf{Simple\:Interest=80\times8\times3}}$

$\large\therefore\boxed{\bf{Simple\:Interest=Rs.1920.}}$

Now,

• It is said that simple interest earned on 3,000 at the rate of 4% per annum to be equal to the simple interest on * 8,000 at the rate of 8% per annum for 3 years.
• So interest on Rs.3000 is 1920.

We know that,

$\large{\green{\underline{\boxed{\bf{Time=\dfrac{100\times\:I}{P\times\:R}}}}}}$

where,

• I is interest = Rs.1920
• P is principal = Rs.3000
• Rate = 4% per annum

Putting the values,

$\large\implies{\sf{Time=\dfrac{100\times\:1920}{3000\times\:4}}}$

$\large\implies{\sf{Time=\dfrac{1\cancel{00}\times\:1920}{30\cancel{00}\times\:4}}}$

$\large\implies{\sf{Time=\dfrac{1\times\:192\cancel{0}}{3\cancel{0}\times\:4}}}$

$\large\implies{\sf{Time=\dfrac{1\times\:\cancel{192}}{3\times\:\cancel{4}}}}$

$\large\implies{\sf{Time=\dfrac{48}{3}}}$

$\large\implies{\sf{Time=\dfrac{\cancel{48}}{\cancel{3}}}}$

$\large\therefore\boxed{\bf{Time=16\:years.}}$

VerificatioN:-

$\large\implies{\sf{Simple\:Interest=\dfrac{P\times\:R\times\:T}{100}}}$

$\large\implies{\sf{1920=\dfrac{3000\times4\times16}{100}}}$

$\large\implies{\sf{1920=\dfrac{30\cancel{00}\times4\times16}{1\cancel{00}}}}$

$\large\implies{\sf{1920=30\times4\times16}}$

$\large\implies{\sf{Rs.1920=Rs.1920.}}$

$\large\therefore\boxed{\bf{LHS=RHS.}}$

• Hence verified.

The time required for the simple interest earned on 3,000 at the rate of 4% per annum is 16 years.