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:

₹12,000

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