Question

On a certain sum the interest paid after 3 years is Rs 450 at 5% rate of interest per annum. Find the sum.​

Answer 1

Answer :-

• The sum is Rs 3000.

To find :-

• The sum.

Step-by-step explanation :-

• Here, the interest is Rs 450, the rate is 5% per annum and the time is 3 years. We have to find the simple interest.

We know that :-

$\underline{ \boxed{\sf SI = \dfrac{Principal \times Rate \times Time}{100}}}$

Here,

• Rate = 5% per annum.
• Time = 3 years.
• Interest = Rs 450.

• Let the principal be p.

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Substituting the given values in this formula,

$\hookrightarrow\rm450 = \dfrac{p \times 5 \times 3}{100}$

Multiplying 5 with 3,

$\hookrightarrow\rm450 = \dfrac{p \times 15}{100}$

Multiplying p with 15,

$\hookrightarrow\rm450 = \dfrac{15p}{100}$

Transposing 100 from RHS to LHS, changing it's sign,

$\hookrightarrow\rm450 \times 100 = 15p$

Multiplying 450 with 100,

$\hookrightarrow\rm45000 = 15p$

Transposing 15 from RHS to LHS, changing it's sign,

$\hookrightarrow\rm \dfrac{45000}{15} = p$

Dividing 45000 by 15,

$\hookrightarrow\overline{ \boxed{\rm Rs \: 3000 = p}}$

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• So, the sum is Rs 3000.

Answer 2

Given :

• Interest (I) = Rs 450
• Rate (R) = 5% p.a
• Time (T) = 3 years

To Find :

• Principal

Solution :

✰ As we know that, Interest is given by I = P × R × T/100 where I , P , R and T stands for Interest, Principal, Rate and Time respectively. Now from this formula we got to know that P = I × 100/R × T . Now in this question, Interest and Rate along with the Time are given, so simply we will put the given values in the formula to find the Principal.

⠀⠀⠀

⠀⠀⠀⟼⠀⠀⠀I = P × R × T/100

⠀⠀⠀⟼⠀⠀⠀P = I × 100/R × T

⠀⠀⠀⟼⠀⠀⠀P = 450 × 100/5 × 3

⠀⠀⠀⟼⠀⠀⠀P = 45000/15

⠀⠀⠀⟼⠀⠀⠀P = Rs 3000

Thus Principal is Rs 3000

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★ Additional Info :

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