Question

the simple interest on a certain sum for 3 1/2 years ar7%per annum is rs.225 more than the simple interest on the same sum for 4 years at 5% per annum.find the sum​

Answer 1

Question :-

the simple interest on a certain sum for 3 1/2 years are 7%per annum is rs.225 more than the simple interest on the same sum for 4 years at 5% per annum.find the sum.

Solution :-

Let, the sum is x.

Case I :

Given that,

$\bullet \: \rm{Principal = x}$

$\bullet \: \rm{Rate =7\%}$

$\bullet \: \rm{Time =3\frac{1}{2} = 3.5 \: years }$

Now,

$\rm\hookrightarrow{Interest = \frac{PTR}{100}}$

On substituting all values,

$\rm:\longmapsto{ \frac{x \times 3.5 \times 7}{100} } \\ \\ \bf:\longmapsto \red{ \frac{24.5x}{100} } \: \: \: \: \: \: \: \:$

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Case II :

Given that,

$\bullet \: \rm{Principal = x}$

$\bullet \: \rm{Rate = 5\%}$

$\bullet \: \rm{Time = 4 \: years}$

On substituting all values in interest formula,

$\rm:\longmapsto{ \frac{x \times 5 \times 4}{100} } \\ \\ \bf:\longmapsto \red{ \frac{20x}{100} } \: \: \: \: \: \: \: \:$

In the question this also given that,

• The simple interest for case I is $225 more than the simple interest for case II.

Now,

$\rm:\longmapsto{ \frac{24.5x}{100} - \frac{20x}{100} = 225} \\ \\ \rm:\longmapsto{ \frac{24.5x - 20x}{100} = 225} \: \\ \\ \rm:\longmapsto{ 4.5x = 225 \times 100} \: \: \: \: \\ \\ \rm:\longmapsto{4.5x = 22500} \: \: \: \: \: \: \: \: \: \: \\ \\ \rm:\longmapsto{x = \frac{22500}{4.5} } \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf:\longmapsto \red{x = 5000} \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence,

• x = 5000

Then,

• Sum is Rs5000.

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