Question

14. P and Q invest 36,000 and 25,000 respectively at the same rate of interest per year. If at the end of 4 years, P gets 3,080 more interest than Q, find the rate of interest.​

Answer 1

Question:-

P and Q invest 36,000 and 25,000 respectively at the same rate of interest per year. If at the end of 4 years, P gets 3,080 more interest than Q, find the rate of interest.

Required Answer:-

Given:-

• P and Q invest 36,000 and 25,000 respectively at a same rate of interest. per year.
• At the end of 4 years, P gets 3,080 more interest than Q

To Find:-

• The rate of the interest.

Solution:-

Let,

• → P's invest p = Rs. 36000
• → Q's invest p' = Rs. 25000
• → Rate of the interest = R%
• → Time T = 4 years.

We know that:-

• I = PTR

Where,

• I = Simple Interest
• P = Principle Amount
• T = Time
• R = Rate of interest

Therefore,

☆P's interest = p x T x R%

• P's interest = Rs. (36000 x 4 x R)/100
• P's interest = Rs. 144000R/100
• P's interest = Rs. 1440R

Again,

☆Q's interest = p' x T x R%

• Q's interest = Rs. (25000 x 4 x R)/100
• Q's interest = Rs. 100000R/100
• Q's interest = Rs. 1000R

Difference in P's and Q's interest:-

☆P's interest - Q's Interest = Rs. (1440R - 1000R) = Rs. 440R

According to the Question:-

440R = 3080

• ⇒ R = (3080/440)%
• ⇒ R = 7%

★ Hence, rate of the interest is 7%

Some Important Informations:-

• Simple Interest:- Simple interest is a quick and easy method of calculating the interest charge on a loan.

• Compound Interest:- Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

• Simple Interest Formula:- I = PTR

• Compound Interest Formula:- C = A - P

• Final Amount Formula (During simple interest):- A = P(1 + TR)

• Final Amount Formula (During compound interest):- A = P(1 + R)^T