Question

A invests ₹8,000 and B invests 11000 at the same rate of interest per annum. It at the end of 3 years, B gets ₹720 more Interest than A find the rate of interest.
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Answer 1

Question:

A invests ₹8,000 and B invests ₹ 11000 at the same rate of interest per annum. It at the end of 3 years, B gets ₹720 more Interest than A find the rate of interest.

To find:

• Rate percent

Answer:

There are two methods to this question:

Method 1:

Let:

• Rate % = x%
• Simple interest for A = SI 1
• Simple interest for B = SI 2

To find Simple interest for A:

• P = ₹8,000
• R = x%
• T = 3 years

We know:

$\pink{ \underline{ \boxed{ \sf{}Simple \: Interest = \dfrac{P\times R\times T}{100}}}}$

Using this formula we can find value of Simple Interest for A.

$:\implies \sf SI 1 = \dfrac{8000 \times x \times 3}{100}$

$:\implies \sf SI 1 = \dfrac{80 \: \cancel{00} \times x \times 3}{ \cancel{100}}$

$:\implies \sf SI 1 = 80 \times x \times 3$

$:\implies \star \boxed{ \sf SI 1 = ₹ \: 240x} \star$

To find Simple interest for B:

• P = ₹8,000
• R = x%
• T = 3 years

We know:

$\blue{ \underline{ \boxed{ \sf{}Simple \: Interest = \dfrac{P\times R\times T}{100}}}}$

Using this formula we can find value of Simple Interest for B.

$:\implies \sf SI \: 2 = \dfrac{11000 \times x \times 3}{100}$

$:\implies \sf SI \: 2 = \dfrac{110 \: \cancel{00} \times x \times 3}{\cancel{100}}$

$:\implies \sf SI \: 2 = 110 \times x \times 3$

$:\implies \star \boxed{ \sf SI \: 2= ₹ \: 330x} \star$

According to question:

Simple interest of B - Simple interest of A = ₹720

So:

$: \implies \sf{}₹ \: 330x-₹ \: 240x = ₹ \: 720$

$: \implies \sf{}₹ \:90x = ₹ \: 720$

$: \implies \sf{}x = \dfrac{₹ \: 720}{₹ \:90}$

$: \implies \sf{}x = \dfrac{ \cancel{₹ \: 720}}{ \cancel{₹ \:9 0}}$

$:\implies \star \boxed{ \sf x = 8} \star$

As we have suppose Rate % as x%

.°. Rate = 8

Method 2:

Let:

• Rate % = x%

Given:

• A invests = ₹ 8,000
• B invests = ₹ 11000

Now:

$\text{B invests ? more rupees than A= B invests- A invests}$

$\text{B invests ? more rupees than A= ₹11000 - ₹8000}$

$\text{B invests ? more rupees than A= ₹3000}$

According to question:

Simple Interest on 3 year on ₹ 3000 = ₹720

So:

$:\implies\sf{} ₹\:720= \dfrac{3000\times x\times 3}{100}$

$:\implies\sf{} ₹\:720= \dfrac{30\cancel{00}\times x\times 3}{\cancel{100}}$

$:\implies\sf{} ₹\:720= 30 \times x\times 3$

$:\implies\sf{} ₹\:720= 90x$

$: \implies \sf{}x = \dfrac{ \cancel{₹ \: 720}}{ \cancel{₹ \:9 0}}$

$:\implies \star \boxed{ \sf x = 8} \star$

As we have suppose Rate % as x%

.°. Rate = 8

And all we are done!

Answer 2

8

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