# A certain sum is lent 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 inter

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A certain sum is lent 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 Rs. 27,600, then the sum is (in Rs):
1. 27,000
2. 30,000
3. 25,000
4. 32,000

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Correct Answer - Option 2 : 30,000

Given:

Simple Interest = Rs. 27,600

Rate of interest for 3 years = 4% p.a.

Rate of interest for next 4 years = 8% p.a.

Rate of interest beyond 7 years = 12% p.a.

Total time period = 11 years

Formula Used:

S.I. = (P × R × T)/100

where, P → Principal, R → Rate of Interest, T → Time period, S.I. → Simple Interest

Calculations:

Let the sum lent be Rs. x.

Simple Interest = Rs. 27,600

Now, S.I. = (P × R × T)/100

For 11 years,

27,600 = (x × 4 × 3)/100 + (x × 8 × 4)/100 + (x × 12 × (11 – 7))/100

⇒ 27,600 = x × (12 + 32 + 48)/100

⇒ 27,600 = x ×( 92/100)

⇒ x = Rs. (27,600 × 100)/92

⇒ x = Rs. 30,000

∴ The sum is Rs. 30,000.