Two equal sums(in ₹) are lent at 8% and 4% simple interest p.a, respectively at the same time.The first sum is received 2 years earlier than the other and the amount received in each case is ₹14,500. Each sum is:

₹12,500

By using formula ,

Amount = Principal + simple interest

= Principal + \(\frac{Principal ×Rate × Time }{100}\)

Amount received in both cases are equal . So ,

P + \(\frac{P ×8 × T }{100}\) = P + \(\frac{P ×4× (T +2)}{100}\)

 \(\frac{P ×8 × T }{100}\) = \(\frac{P ×4× (T +2)}{100}\)

8T = 4T + 8

4T = 8

T = 2 years

To find out the initial sum ,

14500 = P + \(\frac{P ×8 × T }{100}\)

14500 = P + \(\frac{P ×8 × 2 }{100}\)

P = 14500 × \(\frac{100 }{116}\) = 12500