A certain sum is lent on simple interest at 4% p.a. for 3 years, 8% p.a. for the next 4 years, and 12% p.a. beyond 7 years. If for a period of 11 years, the simple interest obtained is ₹ 27,600 , the sum is (in ₹):

Correct option is C

Given:

Sum lent for first 3 years at 4%

Sum lent for next 4 years at  8%

Sum lent for beyond 7 years =12%

Time for money lent =11years

Simple interest earned =₹27,600

Formula Used:

​$$SI = \frac{P \times R \times t}{100}$$​​

Solution:

If  the money lent for 11 years then:

Time for money lent at 12% = 11-7 = 4 years

Total SI = SI for 3years at 4% + SI for 4 years at 8% + SI for 4 years at 12%

Let the sum lent be P

Then

​$$\frac{P \times 4 \times 3}{100}+ \frac{P \times 8 \times 4}{100}+ \frac{P \times 12 \times 4}{100} = 27600$$​​

​$$\frac{12P + 32P + 48P}{100} = 27600$$​​

​$$\frac{92P}{100} = 27600$$​​

​$$P= \frac{27600 \times 100}{92}$$​​

​$$P= ₹30000$$ 

Thud, the Principal is ₹30000