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.
Answer & explanation
Correct answer: option 1
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