Question

a sum of ₹5000 deposited in a bank gives an interest of rupees 200in a 6 months what will be the interest on rupees 6400 for 9 months at the same rate of interest
​

Answer 1

Answer:

• Rate of interest = 8%
• Simple Interest = 384 rupees

Step-by-step explanation:

Given:

• Principal = 5000 rupees
• Simple Interest = 200 rupees
• Time = 6 months = 6/12 years = 1/2 years

To Find:

• Rate of interest

Solution:

we have,

• P = 5000 rupees
• S.I = 200 rupees
• T = 1/2 years

As we know

$\: \: \sf \: rate = \frac{si \times 100}{p \times t}$

Now put on formula

$\: \: \sf \: rate = \frac{200\times 100}{5000 \times \frac{1}{2} } \\ \\ \: \: \sf \: rate = \frac{200 \times 100 \times 2}{5000 } \\ \\ \: \: \sf \: rate = 8 \: percent$

Hence,Rate of interest is 8%.

we have,

• R = 8%
• P = 6400 rupees
• T = 9 months = 9/12 years = 3/4 years

As we know,

$\: \: \sf \: si = \frac{p \times r \times t}{100}$

Now put on formula

$\: \: \sf \: si = \frac{6400 \times 8 \times 3}{100 \times 4} \\ \\ \: \: \sf \: si = 384 \: rupees$

Hence, Simple Interest is 384 rupees.

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Answer 2

Given :

• Principal (P) = Rs 5000
• Simple Interest (SI) = Rs 200
• Time (T) = 6 months = 1/2 years

To Find :

• The Simple interest on rupees 6400 for 9 months at the same rate of interest .

Solution :

✰ In this question, Firstly we will find the Rate after that we will find the Simple Interest for the Second condition.

⠀

⟶⠀SI = P × R × T/100

⟶⠀Rate = SI × 100/P × T

⟶⠀Rate = 200 × 100/5000 × 1/2

⟶⠀Rate = 20/5 × 1/2

⟶⠀Rate = 20 × 2/5

⟶⠀Rate = 40/5

⟶⠀Rate = 8%

⠀

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✰ Now for the Second Condition, Principal is Rs 6400 , Time is 9 months = 3/4years, and Rate is 8% .

⠀

⟶⠀SI = P × R × T/100

⟶⠀SI = 6400 × 8 × 3/4/100

⟶⠀SI = 6400 × 8 × 3/100 × 4

⟶⠀SI = 64 × 8 × 3/4

⟶⠀SI = 64 × 24/4

⟶⠀SI = 1536/4

⟶⠀SI = Rs 384

⠀

So, Simple Interest is Rs 384

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★ Additional Info :

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