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 ____.
Answer & explanation
Correct answer: option 1
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