A certain sum at simple interest amount to ₹ 1350 in 5 yr and to ₹ 1620 in 8 yr what is the sum?

Given, A₁ = ₹ 1350, A₂ =₹ 1620
T₁ = 5 yr and T₂ = 8 yr
Let principal amount be ₹ P.
∴ In time = 8 - 5 = 3 yr
Simple interest will be
1620 - 1350 = ₹ 270
∴ R = [(A₂ - A₁ ) x 100] / [A₁ T₂ - A₂ T₁]
= [(1620 - 1350) x 100] / [(1350 x 8) - (1620 X 5)]
= (270 x 100)/[10800 - 8100]
= 27000/2700
⇒ R = 10%
∴ P = (SI x 100) / (R x T)
= (270 x 100) / (10 x 3)
= ₹ 900