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:
Answer & explanation
Correct answer: option 2
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