Question

A sum of money was put at simple interest at a certain rate for 2 years. If this sum had been put
at 3% higher rate, it would have earned 720 more as interest. Find the sum.
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Answer 1

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✺Answer:

♦️GiveN:

• Sum of money was put with simple Interest.
• At a certain rate and time is 2 years.
• If it would have put 3% higher rate, then earned 720 more as simple Interest.

♦️To FinD:

• The sum i.e. Principal money.

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✺Explanation of Q.

The question is based on Simple Interest concept, and also we will use linear eqaution in solving this. Not much concepts not needed, just apply formula, from the equation and find the solution.

Concept to be used:

Formula for finding Simple Interest:

$\large{ \ddag \: \: { \boxed{ \rm{ \pink{(SI)= \frac{ P \times T \times R}{100}}}}}}$

♠️ Note.....

Symbols have their usual meanings.

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Now applying this formula and forming equations will solve this question.

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✺Solution:

Let the principal = P

Rate of Interest = r

Time given = 2 years

And, simple Interest = SI

By applying formula,

$\large{ \rm{ \rightarrow \: SI = \large{ \frac{P \times 2 \times r}{100}..........(1)}}}$

Now, It is given that

If New rate = r+3

Then New SI = SI + 720

Time taken is 2 years and principal is P

By applying Formula,

$\large{ \rm{ \rightarrow \: new \: SI \: = \large{\frac{P\times 2 \times (r + 3)}{100}}}} \\ \\ \large{\rm{\rightarrow \: SI \:+\: 720\: = \large{\frac{P\times 2 \times (r + 3)}{100}........(2)}}}$

Subtracting equation (1) from (2),

$\large{ \rm{ \rightarrow \: \frac{P \times 2 \times (r + 3)}{100} - \frac{P \times 2 \times r }{100} = \: Rs. 720 }} \\ \\ \large{ \rm{ \rightarrow \: \frac{2P(r + 3) - 2Pr }{100} = 720}}$

Taking 2p common,

$\large{ \rm{ \rightarrow \: \frac{2P( \cancel{r} + 3 - \cancel{ r})}{100} = 720}} \\ \\ \large{ \rm{ \rightarrow \: \frac{2P \times 3}{100} = 720}} \\ \\ \large{ \rm{ \rightarrow \: P = \cancel{ \frac{720 \times 100}{2 \times 3}}}} \\ \\ \large{ \rm{ \rightarrow \: \boxed{ \red{ \rm{ \: P= \: Rs. 12000}}}}}$

Thus, the Sum of initial money:

$\large{ \rm{ \therefore{ \underline{ \purple{Principal = Rs.12000}}}}}$

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Answer 2

Answer:

P = Rs. 12000.

Thank You