A sum is invested at simple interest at x% per annum for 3\(\frac{1}{2}\) years. Had it been invested at (x + 4)% per annum at simple interest, it gives Rs. 4452 more as interest. Find the sum.

31800

An increase in the rate of 4% leads to an increase of Rs. 4452 in 3\(\frac{1}{2}\) years.

⇒ Total interest in 3\(\frac{1}{2}\) yr at x%= \(\frac{7}{2}\)x%

⇒ Total interest in 3\(\frac{1}{2}\) yr at (x + 4)% = \(\frac{7}{2}\)(x + 4)%

⇒Extra interest received = \(\frac{7}{2}\)(4) = 14%

ATQ,

⇒ P × 14% = 4452

⇒ P = 31800