Question

a person lent out rs.16000 on simple intrest and the same sum on compound intrest for 2 years at 12 1/2percent per annum. find the ratio of the amounts recieved by him as intrest after 2 year.


please solve in paper with clear steps.​

Answer 1

★Given:-

• A person lent out Rs.16000 on simple interest.
• And,the same sum on compound interest for 2 years at 12 1/2percent per annum.

★To find:-

• Find the ratio of the amounts received by him as interest after 2 years.

★Solution:-

(1) Simple interest

We have,

• Principle= Rs.16000
• Rate = 12.5%
• Time = 2 years

And,

$\leadsto \underline{\boxed{\sf Interest = \frac{PRT}{100} }}$

Here,

$:\implies \sf Interest = \frac{16000\times 25\times 2}{100\times 2} \\\\:\implies \sf 160\times 25\\\\:\implies \underline{\sf Rs.4000}}$

And,

$\leadsto \underline{\boxed{\sf Amount =P+I}}$

$:\implies \sf A_1 = 16000+4000 \\\\\implies \underline{\bold{Rs.20000}}$

--------------------------

(2)Compound Interest

We have,

• Principle= Rs.16000
• Rate = 12.5%
• Time = 2 years

And,

$\leadsto \underline{\boxed{\sf C.I. = P(1+\dfrac{R}{100})^2}}}$

Therefore,

$:\implies \sf A_2 = 16000(1+\frac{25}{200} )^2\\\\:\implies \sf 1600 (1+\frac{1}{8} )^2\\\\:\implies \sf 16000(\frac{9}{8} )^2\\\\:\implies \underline{\bold{A_2 =Rs.20250}}$

Now,

Ratio of amounts :-

$:\implies \sf \dfrac{A_1}{A_2} =\dfrac{20000}{20250} \\\\\\:\implies \sf \dfrac{A_1}{A_2} =\dfrac{80}{81} \\\\\\:\implies \boxed{\boxed{\sf A_1:A_2=80:81}}$

Hence,

Ratio of the amounts received by him as interest after 2 years is 80:81

________________

Answer 2

★Given:-

A person lent out Rs.16000 on simple interest.

And,the same sum on compound interest for 2 years at 12 1/2percent per annum.

★To find:-

Find the ratio of the amounts received by him as interest after 2 years.

★Solution:-

(1) Simple interest

We have,

Principle= Rs.16000

Rate = 12.5%

Time = 2 years

And,

$\leadsto \underline{\boxed{\sf Interest = \frac{PRT}{100} }}$

Here,

$:\implies \sf Interest = \frac{16000\times 25\times 2}{100\times 2} \\\\:\implies \sf 160\times 25\\\\:\implies \underline{\sf Rs.4000}}$

And,

$\leadsto \underline{\boxed{\sf Amount =P+I}}$

$:\implies \sf A_1 = 16000+4000 \\\\\implies \underline{\bold{Rs.20000}}$

--------------------------

(2)Compound Interest

We have,

Principle= Rs.16000

Rate = 12.5%

Time = 2 years

And,

$\leadsto \underline{\boxed{\sf C.I. = P(1+\dfrac{R}{100})^2}}}$

Therefore,

$:\implies \sf A_2 = 16000(1+\frac{25}{200} )^2\\\\:\implies \sf 1600 (1+\frac{1}{8} )^2\\\\:\implies \sf 16000(\frac{9}{8} )^2\\\\:\implies \underline{\bold{A_2 =Rs.20250}}$

Now,

Ratio of amounts :-

$:\implies \sf \dfrac{A_1}{A_2} =\dfrac{20000}{20250} \\\\\\:\implies \sf \dfrac{A_1}{A_2} =\dfrac{80}{81} \\\\\\:\implies \boxed{\boxed{\sf A_1:A_2=80:81}}$

Hence,

Ratio of the amounts received by him as interest after 2 years is 80:81

________________