Question

a certain sum of money lent at 5% for 3 years and double the sum was lent at 4% for 9/2 if the total interest collected was rupees 510 find the sum lent at 5%​

Answer 1

Answer:

• The sum of money lent at 5% is ₹1000.

Step-by-step explanation:

Given that:

• A certain sum of money was lent at 5% for 3 years.
• Double the sum of money was lent at 4% for 9/2 years.
• Total interest collected was ₹510.

To Find:

• The sum of money lent at 5%.

Let us assume:

• The sum of money lent at 5% be x.

Then,

• The sum of money lent at 4% will be 2x.

As we know that:

$\sf{\circ\;SI=\dfrac{P\times R\times T}{100}}$

Where,

• SI = Simple Interest
• P = Principal
• R = Rate
• T = Time

Calculating interest when P = x, R = 5% and T = 3 years:

$\rm{SI=\dfrac{x\times 5\times 3}{100}}$

Multiplying,

$\rm{=\dfrac{15x}{100}}$

Calculating interest when P = 2x, R = 4% and T = 9/2 years:

$\rm{SI=\dfrac{2x\times 4\times 9}{2\times100}}$

Reducing the numbers,

$\rm{=\dfrac{2x\times 2\times 9}{1\times100}}$

Multiplying,

$\rm{=\dfrac{36x}{100}}$

According to the question:

$\rm{\longmapsto\dfrac{15x}{100}+\dfrac{36x}{100}=510}$

Adding LHS,

$\rm{\longmapsto\dfrac{15x+36x}{100}=510}$

$\rm{\longmapsto\dfrac{51x}{100}=510}$

Transposing 100 from LHS to RHS and changing its sign,

$\rm{\longmapsto51x=510\times100}$

Multiplying RHS,

$\rm{\longmapsto51x=51000}$

Transposing 51 from LHS to RHS and changing its sign,

$\rm{\longmapsto x=\dfrac{51000}{51}}$

Dividing RHS,

$\bf{\longmapsto x=1000}$

Hence,

• x = 1000

Therefore,

• The sum of money lent at 5% = x = ₹1000