A borrows an amount ₹3,600 from B at a rate of 20% simple interest for 2 years and lends 75% of this amount to C at 20% compound interest for 2 years. A uses the remaining amount for his personal purpose. Find the total loss incurred by A.
Answer & explanation
Correct answer: option 3
Simple interest on sum borrowed by A = \(\frac{P × R × T }{100}\)
= \(\frac{3600 × 20 × 2 }{100}\)
= 1440
Sum lent to C = 75% of 3600 = \(\frac{3 }{4}\) × 3600 = 2700
Compound interest on sum lent to C ,
C.I = P(1+$\frac{R}{100})^t$– P
= 2700 [ 1 + \(\frac{20 }{100}\) ]² - 2700
= 2700 × \(\frac{6 }{5}\) × \(\frac{6 }{5}\) - 2700
= 2700 [ \(\frac{11 }{25}\) ]
= Rs. 1188
Total loss of A
= 1440 - 1188 + 25% of 3600
= 252 + \(\frac{1 }{4}\) × 900
= Rs. 1152