Question

A farmer takes a loan of Rs. 8400 at the simple interest rate of 7 ½ % per

annum. After what time will he have to pay Rs. 10920 to clear the dept?​

Answer 1

Step-by-step explanation:

Given

Principal, P= ₹8400

Rate, R = 7 ½% =7.5

Total Amount A= ₹10920

Find Time T

T will be in years bcz interest rate is annually

Simple Interest = Total amount- Principal amount

S.I = 10920-8400 = 2520

we know

S.I = PRT/100

T= (S.I×100)/PR

T = (2520×100)/(8400×7.5) =4

Time T is 4 years.

Answer 2

Correct Question :-

• A farmer takes a loan of Rs. 8400 at the rate of 7 ½ % per annum. After what time will he have to pay Rs. 10920 to clear the debt?

Answer :-

• The farmer will have to pay Rs 10920 after 4 years to clear his debt.

Given :-

• A farmer takes a loan of Rs 8400 at the rate of 7 ½% per annum.

To find :-

• The time after which he will have to pay Rs 10920 to clear his debt.

Step-by-step explanation :-

• Here, the loan taken by the farmer, that is, Rs 10000 is the principal, 7 ½ % is the rate and Rs 10920 is the amount. We have to find the time. First let's find the simple interest using the principal and amount, then we can use it to find the time.

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We know that :-

$\underline{\boxed{\sf SI = Amount - Principal}}$

Here,

• Amount = Rs 10920.
• Principal = Rs 8400.

Hence,

$\boxed{\bf SI = 10920 - 8400}$

$\overline{\boxed{\bf SI = Rs \: 2520}}$

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Now let's find the time as we know the simple interest!

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

Here,

• Principal = Rs 8400.
• Rate = 7 ½ % = 15/2%
• Simple interest = Rs 2520.

• Let the time be t.

Hence,

$\tt 2520 = \dfrac{8400 \times 15 \times t}{100 \times 2}$

Cutting off the zeroes,

$\tt 2520 = \dfrac{84 \times 15 \times t}{1 \times 2}$

Reducing the numbers,

$\tt 2520 = \dfrac{42 \times 15 \times t}{1\times1}$

Multiplying the numbers,

$\tt 2520 = \dfrac{630 \times t}{1}$

Now let's multiply the remaining numbers since we can't reduce them anymore.

$\tt 2520 = 630\times t$

Multiplying 630 with t,

$\tt 2520 = 630t$

Transposing 630 from LHS to RHS, changing it's sign,

$\tt \dfrac{2520}{630} = t$

Dividing 2520 by 630,

$\overline{\boxed{\tt 4 = t}}$

• Hence, the time is 4 years.

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Abbreviations used :-

SI = Simple Interest.