The simple interest on a certain sum for 8 months at 4%

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The simple interest on a certain sum for 8 months at 4% per annum is ₹129 less than thesimple interest on the same sum for 15 months at 5% per annum. The sum is :

Let the sum be p.
From the question ,

p × 5 × 15	-	p × 4 × 8	= 129
100 × 12		100 × 12

⇒	p	(75 - 32) = 129
	100 × 12

⇒ p =	129 × 1200	= ₹ 3600
	43

Second method to solve this question :
P₁ = P, R₁ = 4%,
T₁ = 8 months = 8/12 years
P₂ = P, R₂ = 5%,
T₂ = 15 month = 15/12 years
S.I. = ₹ 129

12900 =	75P - 32P
	12

12900 =	43P
	12

P = ₹ 3600