Question

The difference between SI and CI of a certain sum of money is ₹250 at 10% p.a. for 3 years. find the principal.​

Answer 1

Given:-

• Difference between SI and CI of a certain sum of money is ₹250
• Rate = 10% p.a.
• Time = 3 years

To Find:-

• The principal

Assumption:-

• Let the sum of money be P

Solution:-

For SI,

We know,

• $\sf{SI = \dfrac{P \times R\times T}{100}}$

Putting the values here,

= $\sf{SI = \dfrac{P\times 10\times 3}{100}}$

= $\sf{SI = \dfrac{30P}{100}}$

∴ The SI on a certain sum of money is $\sf{\dfrac{30P}{100}}$

For CI,

We know,

• $\sf{CI = P\bigg(1+\dfrac{r}{100}\bigg)^n - P}$

Putting the values here,

= $\sf{CI = P\bigg(1+\dfrac{10}{100}\bigg)^3 - P}$

= $\sf{CI = P\bigg(1+\dfrac{1}{10}\bigg)^3 - P}$

= $\sf{CI = P\bigg(\dfrac{10+1}{10}\bigg)^3 - P}$

= $\sf{CI = P\bigg(\dfrac{11}{10}\bigg)^3 - P}$

= $\sf{CI = \dfrac{1331P}{1000} - P}$

= $\sf{CI = \dfrac{1331P - 1000P}{1000}}$

= $\sf{CI = \dfrac{331P}{1000}}$

∴ CI on a certain sum of money is $\sf{\dfrac{331P}{1000}}$

Now,

According To The Problem,

CI - SI = 250

Hence,

$\sf{\dfrac{331P}{1000} - \dfrac{3P}{10} = 250}$

= $\sf{\dfrac{331P - 300P}{1000} = 250}$

= $\sf{31P = 250\times 1000}$

= $\sf{31P = 250000}$

= $\sf{P = \dfrac{250000}{31}}$

= $\sf{P = 8064.5}$

∴ The sum of money is ₹8064.5

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