Question

6. At what rate per cent per annum simple interest will 400 amount to ? 460 in 3 yr?

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Answer 1

➤ Given :-

Principle :- ₹ 400

Total amount :- ₹ 460

Time :- 3 years

➤ To Find :-

Rate of interest for the given sum.............

➤ Formula required :-

${\large \tt \dashrightarrow \orange{\boxed{\tt \gray{\dfrac{SI \times 100}{P \times T}}}}}$

➤ Solution :-

First, we should find the simple interest by subtracting the amount and principle of the given sum.............

Simple Interest :-

${\tt \longrightarrow 460 - 400}$

${\tt \longrightarrow Rs \: \: 60}$

Now,

Rate of interest :-

${\tt \longrightarrow \dfrac{60 \times 100}{400 \times 3}}$

${\tt \longrightarrow \dfrac{60 \times \cancel{100}}{ \cancel{400} \times 3} = \dfrac{60 \times 1}{4 \times 3}}$

${\tt \longrightarrow \dfrac{ \cancel{60} \times 1}{4 \times \cancel{3}} = \dfrac{20 \times 1}{4 \times 1} = \dfrac{20}{4}}$

${ \tt \longrightarrow \cancel \dfrac{20}{4} = \boxed{\tt 5 \bf\%}}$

$\Huge\therefore$ The rate of interest to be paid at end is 5 ${\bf\%}$.

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$\dashrightarrow$ Some related formulas :-

Simple Interest :- ${\boxed{\tt\dfrac{P \times R \times T}{100}}}$

Principle :- ${\boxed{\tt\dfrac{SI \times 100}{R \times T}}}$

Time :- ${\boxed{\tt\dfrac{SI \times 100}{P \times R}}}$

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More to know..................

• Simple Interest is the extra amount to be given when a person borrows some money from a person or a bank. The person who gives money is called lender. The person who takes money is called borrower.
• Principal is the amount given at first from lender to borrower.
• Rate of interest is the extra amount to be given from borrower to lender. It is always written in percentage format.
• Time is given for the borrower to return back the given money with the given interest.

Answer 2

GiveN:

• P (Principle) = ₹400
• A (Amount) = ₹460
• T (Time) = 3 years

To FinD:

• Rate of interest

Case 1 :

• First we have to find the Simple Interest (S.I)

Formula:

• Amount – Principle = Simple Interest

So, ₹460 – ₹400 = ₹60

• Hence, Simple Interest (S.I) is ₹ 60

Case 2 :

• Now, with the help of the given formula, we have to find the rate of interest.

Formula:

• $\bf \: \dfrac{SI × 100 }{P × T}$

Required Solution:

$\\ ➟ \: \sf \dfrac{ \cancel{60} \times {100}}{ {400 }\times \cancel{ 3}} \\ \\ \sf➟ \: \frac{20 \: \times \: \cancel{100 }}{ \cancel{400} } \\ \\ \sf \: ➟ \: \: \frac{20 \times 1}{4} \: \: \: \: \\ \\ \sf \: ➟ \: { \boxed{ \underline{ \bigstar{ \bold{ \pink{5}}}}}} \: \: \: \: \: \: \: \:$

• Hence, Rate of interest is 5 %

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Verification:

• For verification, we have to find the Total amount.
• But before finding the total amount, first we have to find the Simple Interest again.

Required Formula:

• $\bf \: \dfrac{P×R×T}{100}$

So,

$➟ \: \: \: \: \: \: \sf \: \dfrac{400 \times 5 \times 3}{100} \\ \\ \sf \: ➟ \: \: \: \: \: \: \frac{ \cancel{400 }\times 5 \times 3}{ \cancel{100} } \: \: \\ \\ \: \: \: \: \: ➟ \sf \: \: \: \: \: \: \: \: 4 \times 5 \times 3 = 60$

• Hence, Simple Interest (S.I) is ₹60

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Now, Let's find the Total amount.

Formula:

• Principle (P) + Simple Interest (S.I) = Total Amount

So, ₹400 + ₹60 = ₹460

⠀⠀⠀⠀⠀⠀⠀Hence Verified!