Question

Find the rate% if
P= ₹1600, T=4 years ,A =₹2000
a)7.25%
b) 6.5%
c) 6.25%​

Answer 1

Answer :-

• Option c is correct.
• The rate is 6.25%.

Given :-

• Principal = Rs 1600.
• Time = 4 years.
• Amount = Rs 2000.

To find :-

• The rate % per annum.

Step-by-step explanation :-

• In this question, the principal, time and amount has been given to us. We have to find the rate %, but for that we first have to find out the simple interest. Then we can find out our answer by forming an equation using the information given to us.

$\bf \underline{Calculations :-}$

We know that :-

$\underline{\boxed{\sf Simple \: Interest = Amount - Principal.}}$

Here,

• Amount = Rs 2000.
• Principal = Rs 1600.

Hence,

$\tt Simple \: Interest = Rs \: 2000 - Rs \: 1600.$

${\boxed{ \tt Simple \: Interest = Rs \: 400.}}$

• The simple interest is Rs 400.

Now, let's find the rate.

We know that :-

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

Here,

• Simple Interest = Rs 400.
• Principal = Rs 1600.
• Time = 4 years.

Let the rate be r.

Substituting these values in the given formula,

$\tt 400= \dfrac{1600 \times r \times 4}{100}$

Multiplying 1600 by 4,

$\tt 400 = \dfrac{6400 \times r}{100}$

Multiplying 6400 by r,

$\tt 400 = \dfrac{6400r}{100}$

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

$\tt400 \times 100 = 6400r$

Multiplying the numbers,

$\tt40000 = 6400r$

Transposing 6400 from RHS to LHS, changing it's sign,

$\tt \dfrac{40000}{6400} = r$

Dividing 40000 by 6400,

$\boxed{ \tt 6.25 = r.}$

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• Hence, the rate % is 6.25.