Question

3
5. If A lends 3500 to B at 10% per annum and B lends the same sum to Cat 11.5% per annum
then the gain of B in a period of 3 years is?​

Answer 1

Given:

• If A lends 3500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum

To Find:

• the gain of B in a period of 3 years is?

Understanding the question:

Now, here A person ( B ) took loan from the person ( A) at the rate 10%P.A and lended the same amount to another person ( c ) at 11.5% P.A and, now we have said to find the profit ( gain ) earned by the person (B) so, now we have to calculate the amount which B has to give to the person A and then the amount B gets from ,then subtract them to find the profit earned

Solution:

We Know,

$\: \: \: \: \: \star{ \blue{ \boxed{ \tt{simple \: intrest = \frac{p \times t \times r}{100} }}}}$

Where,

• ➪ P Stands for ${ \pink{ \bf{ principal}}}$

• ➪ T stands for ${ \gray{ \bf{time}}}$

• ➪ R stands for ${ \orange{ \bf{rate}}}$

Now, substituting the values for the loan taken from person A by B we get,

$\longrightarrow \tt \: s.i = \frac{p \times t \times r}{100} \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt s.i = \frac{35\cancel0\cancel0 \times 10 \times 3}{ 1\cancel0\cancel0} \\ \\ \\\longrightarrow \tt s.i = 35 \times 10 \times 3 \: \: \: \: \: \\ \\ \\ \longrightarrow{ \boxed{ \tt {s.i = r.s1050 }}} \: \: \: \: \: \: \: \: \:$

We know,

$\: \: \: \: \: \: { \star{ \pink{ \boxed{ \tt{amount = principal + intrest}}}}}$

So ,

→ Amount = 3500 + 1050

→ Amount = 4550

Therefore,

$\: \: \: \: \: \: \: \: { \underline{ \rm{the \: amount \: to \: be \: paid\: = rupees \: 4550}}}$

Now,

• Let's find the amount person( C ) gives to ( B )

Applying the formula

$\: \: \: \: \: \star{ \orange{ \boxed{ \tt{simple \: intrest = \frac{p \times t \times r}{100} }}}}$

We get,

$\longrightarrow \tt s.i = \frac{p \times t \times r}{100} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt s.i = \frac{35{ \cancel{00}} \times 11.5 \times 3}{1 \cancel{00}} \\ \\ \\ \longrightarrow \tt s.i = 35 \times 11.5 \times 3 \: \: \: \: \\ \\ \\ \longrightarrow { \boxed{\tt {s.i = rs.1207.5}}} \: \: \: \: \: \: \:$

Now,

→Amount = 3500+1207.5

→Amount = 4707.5

Therefore,

$\: \: \: \: \: \: \: \: { \underline{ \rm{the \: amount \: to \:be \: paid \: = rupees \: 4707.5}}}$

Now,

$\longrightarrow \sf \: profit \: earned = 4707.5 - 4550 \\ \\ \\ \longrightarrow \sf \: profit \: earned = \orange{157.5 \bigstar} \: \: \: \: \: \: \: \: \: \: \: \:$

Hence:

• B earned a profit of rupees 157.5

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

${ \boxed{ \bf{\overline{ \underline{ \mid{more \: to \: know \mid}}}}}}$

Additional information :

$\begin{gathered}\small\boxed{\begin{array}{cc}\large\sf\dag \: {\underline{More \: Formulae}} \\ \\ \bigstar \: \sf{Principle :- \dfrac{SI \times 100}{R \times T}} \\ \\\bigstar \: \sf{Rate \: of \: Interest :- \dfrac{SI \times 100}{P \times T}} \\ \\ \bigstar \: \sf{Time :- \dfrac{SI \times 100}{P \times R}}\end{array}}\end{gathered}$

Answer 2

Given:

• If A lends 3500 to B at 10% per annum and B lends the same sum to Cat 11.5% per annum

To Find:

• the gain of B in a period of 3 years is?

Solution:

We know,

• Simple interest = PTR/100

◕Let's find the amount A has to pay B in return first!

→ Simple Interest = principal × time × rate /100

→ Simple interest = 3500 × 3 × 10 /100

→ Simple interest = rupees 1,050

Now,

→ Amount = principal + Simple Interest

→ Amount = 3500 + 1050

→ Amount = Rupees 4,550

• Henceforth B has to pay Rupees 4,550 To A

◕ Now , let's find the Amount C has to pay to B

Using the same formula!

→ Simple interest = principal × rate × time /100

→ Simple Interest = 3500 × 11.5 × 3 / 100

→ Simple Interest = Rupees1,207.5

So,

→ Amount = 3500 + 1207.5

→Amount = Rupees 4707.5

Now,

→ Profit ( gain ) = 4707.5 - 4550

→ Profit ( gain ) = Rupees 175.5

Hence:

• The profit earned = Rupees 175.5 Rupees