Question

A sum of money invested at 6 percent per annum simple interest for a certain period of time yields ₹960 as interest. If this sum had been invested for 5 years more , it would have yielded ₹9160 as interest. Find the sum.​

Answer 1

Question

A sum of money invested at 6 percent per annum simple interest for a certain period of time yields ₹960 as interest. If this sum had been invested for 5 years more , it would have yielded ₹9160 as interest. Find the sum.​

Answer

We have ,

• Rate of Interest = 6% per annum

• SI after certain period = Rs. 960

• SI after 5 more years = Rs. 2160

Now we need : Principal Amount

We know that Simple Interest Increase with constant rate and that's Equal Every Year.

↠ SI of 5 years = After 5 yr – Certain Period

↠ SI of 5 years = Rs. 2160 – Rs. 960

↠ SI of 5 years = Rs. 1200

↠ SI of 1 years =  $\frac{rs. 1200}{5}$

↠ SI of 1 years = Rs. 240

So we Get that Simple Interest of 1 year is Rs. 240

____________________________________

⊕Time Period⊕

  ⇒ Time = Period of SI / SI of 1 year

 ⇒  Time =  $\frac{Rs. 960}{Rs. 240}$

 ⇒ Time = 4 years

_____________________________________

We have,

• Simple Interest = Rs. 960
• Rate = 6% per annum
• Time = 4 Years

______________________________________

We need principle amount now . so,

⇒ Simple interest = Principle × Rate × Time / 100

⇒ 960 = Principle amount × 6× 4 / 100

⇒ 960 × $\frac{100}{24}$ = Principle amount

⇒ Principle amount = 40 × 100

⇒  Principle amount = Rs. 4000

So the principle amount is 4000 Rupees

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