Question

a man borrowed rupee 500 at 15% per annum at the end of 3 year 4 months and his radio for the balance amount find the cost of the radio​

Answer 1

» To Find :

The Cost Price of the Radio.

» Given :

• Principal = ₹ 500.

• Rate = 15% p.a.

• Time = 3 years 4 months .

» We Know :

Amount :

(When n years and x months are given)

$\purple{\sf{\underline{\boxed{A = P\left(1 + \dfrac{R}{100}\right)^{n}\left(1 + \dfrac{R \times \dfrac{x}{12}}{100}\right)}}}}$

Where ,

• A = Amount
• P = Principal
• R = Rate of interest
• n = Time period
• x = months

» Concept :

According to the question , the Man bought the radio for the Balance amount , so the total Amount will be cost price of the Radio

» Solution :

Given values :

• Principal = ₹ 500.

• Rate = 15% p.a.

• Time = 3 years 4 months .

Using the formula and substituting the values in it , we get :

$\green{\sf{\underline{\boxed{A = P\left(1 + \dfrac{R}{100}\right)^{n}\left(1 + \dfrac{R \times \dfrac{x}{12}}{100}\right)}}}}$

$\sf{\Rightarrow A = 500 \times \left(1 + \dfrac{15}{100}\right)^{3}\left(1 + \dfrac{15 \times \dfrac{4}{12}}{100}\right)}$

$\sf{\Rightarrow A = 500 \times \left(\dfrac{100 + 15}{100}\right)^{3}\left(1 + \dfrac{15 \times \dfrac{\cancel{4}}{\cancel{12}}}{100}\right)}$

$\sf{\Rightarrow A = 500 \times \left(\dfrac{115}{100}\right)^{3}\left(1 + \dfrac{15 \times \dfrac{1}{3}}{100}\right)}$

$\sf{\Rightarrow A = 500 \times \left(\dfrac{115}{100}\right)^{3}\left(1 + \dfrac{\cancel{15} \times \dfrac{1}{\cancel{3}}}{100}\right)}$

$\sf{\Rightarrow A = 500 \times \left(\dfrac{115}{100}\right)^{3}\left(1 + \dfrac{5}{100}\right)}$

$\sf{\Rightarrow A = 500 \times \left(\dfrac{115}{100}\right)^{3}\left(\dfrac{100 + 5}{100}\right)}$

$\sf{\Rightarrow A = 500 \times \left(\dfrac{115}{100}\right)^{3}\left(\dfrac{105}{100}\right)}$

$\sf{\Rightarrow A = 500 \times \dfrac{\cancel{115}}{100} \times \dfrac{\cancel{115}}{\cancel{100}} \times \dfrac{\cancel{115}}{\cancel{100}} \times \dfrac{105}{100}}$

$\sf{\Rightarrow A = 5\cancel{00} \times \dfrac{23}{2\cancel{0}} \times \dfrac{23}{2\cancel{0}} \times \dfrac{23}{20} \times \dfrac{21}{20}}$

$\sf{\Rightarrow A = \cancel{5} \times \dfrac{23}{2} \times \dfrac{23}{2} \times \dfrac{23}{\cancel{20}} \times \dfrac{21}{20}}$

$\sf{\Rightarrow A = \dfrac{23}{2} \times \dfrac{23}{2} \times \dfrac{23}{4} \times \dfrac{21}{20}}$

$\sf{\Rightarrow A = \dfrac{23 \times 23 \times 23 \times 21}{2 \times 2 \times 4 \times 20}}$

$\sf{\Rightarrow A = \dfrac{255507}{320}}$

$\sf{\Rightarrow A = \dfrac{255507}{320}}$

$\purple{\sf{\Rightarrow A = 798.46}}$

Hence ,the amount is ₹ 798.46.

So, the Cost Price of the Radio is ₹ 798.46.

» Additional information :

• Simple Interest = $\dfrac{P \times R \times t}{100}$

• Rate = $\dfrac{SI \times 100}{P \times T}$

• Time = $\dfrac{SI \times 100}{R \times P}$

• Principal = $\dfrac{SI \times 100}{R \times T}$