Sudeep invested $\frac{1}{8}$ of a certain sum at 5% p.a. for two years and $\frac{3}{5}$ of the sum at 6% p.a. for two years and the remaining at 10% p.a. for two years. If the total interest received is ₹1,674, then the total sum invested is:
Answer & explanation
Correct answer: option 3
Let Principal (P) = 100
Principal for Part 1 at 5% for 2 years= \(\frac{1}{8}\) × 100= 12.5
Principal for Part 2 at 6% for 2 years= \(\frac{3}{5}\) × 100= 60
Remaining Principal for Part 3 at 5% for 2 years= 100- 12.5- 60= 27.5
Interest = \(\frac{Principal ×Rate × Time }{100}\)
⇒ Total Interest = \(\frac{ 12.5 × 8 × 2 }{100}\) + \(\frac{ 60× 6 × 2 }{100}\) + \(\frac{ 27.5 × 10 × 2 }{100}\)
⇒ Total Interest = 1.25 + 7.2+ 5.5 = 12.85
ATQ
13.95 part = Rs 1674
⇒ 1 part = Rs 120
⇒ 100 part = Rs 12000