Question

An a certain sum simple interest for 5/2 years at an annual rate 12% is rs 50 less than the interest on the same sum for 7/2 years at an annual rate of 10% . Find the sum​

Answer 1

Step-by-step explanation:

Given :-

On a certain sum simple interest for 5/2 years at an annual rate 12% is rs 50 less than the interest on the same sum for 7/2 years at an annual rate of 10% .

To find:-

Find the sum ?

Solution:-

Let the sum be Rs. X

Principle = Rs. X

Given Time = 5/2 years

Rate of Interest = 12%

We know that

Simple Interest (I) = PTR/100

=> I = (X×5×12)/(100×2)

=> I = 60X/200

=> I = 3X/10

Simple Interest = Rs. 3X/10 ----------(1)

and Given that

Given time = 7/2 years

Rate of interest = 10%

We know that

Simple Interest (I) = PTR/100

=> I = (X×7×10)/(100×2)

=> I = 70X/200

=> I = 7X/20

Simple Interest = Rs. 7X/20-------(2)

On a certain sum simple interest for 5/2 years at an annual rate 12% is rs 50 less than the interest on the same sum for 7/2 years at an annual rate of 10% .

=> 3X/10 = (7X/20)-50

=> (3X/10)-(7X/20) = -50

=> (6X-7X)/20 = -50

=> (-X/20) = -50

=>X /20 = 50

=> X = 50×20

=> X = 1000

The Sum = Rs. 1000

Answer:-

The required sum for the given problem is

Rs. 1000

Check:-

P = 1000

T= 5/2 years

R = 12%

I = (1000×5×12)/(2×100)

I = 60000/200

I = 300

And

P = 1000

T = 7/2 years

R = 10%

I = (1000×7×10)/(2×100)

I = 70000/200

I = 700/2

I = 350

Given that

350-300 = 50

On a certain sum simple interest for 5/2 years at an annual rate 12% is rs 50 less than the interest on the same sum for 7/2 years at an annual rate of 10%.

Verified the given relations in the problem.

Used formulae:-

• Simple Interest (I) = PTR/100
• P = Principle
• T = Time
• R = Rate of Interest