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

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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

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