Two equal sums are lent at 10% and 8% simple interest p.a. respectively, at the same time. The first sum is received 2 years earlier than the second one and the amount received in each case was ₹36,900. Each sum was ____.

₹20,500

By using formula ,

Amount = Principal + simple interest

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

Amount received in both cases are equal . So ,

P + \(\frac{P ×10 × T }{100}\) = P + \(\frac{P ×8× (T +2)}{100}\)

 \(\frac{P ×10 × T }{100}\) = \(\frac{P ×8× (T +2)}{100}\)

10T = 8T + 16

2T = 16

T = 8 years

To find out the initial sum ,

36900 = P + \(\frac{P ×10 × 8 }{100}\)

36900 = P + \(\frac{P ×10× 8 }{100}\)

P = 36900 × \(\frac{100 }{180}\) = 20500