# Simple interest for 3 years on a sum is Rs. 480 and compound interest for 2 years on the same principle is Rs. 336. Find the value of the principle in

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Simple interest for 3 years on a sum is Rs. 480 and compound interest for 2 years on the same principle is Rs. 336. Find the value of the principle in rupees.
1. 1000
2. 1200
3. 1400
4. 1600

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Correct Answer - Option 4 : 1600

Given :

Simple interest on sum for 3 years is rupees 480

Compound interest on the same sum for 2 years is Rs. 336

Calculations :

Let the sum be 'P'

Simple interest per year = 480/3 = 160 rupees

Compound interest for 1st year = 160 rupees   (Compound interest is equal to simple interest for 1st year)

Compound interest for 2nd year = 336 - 160 = 176 rupees (Compound interest for 2nd year = Interest for 1st year + Interest on 1st year's interest)

Rate of interest(R) = (16/160) × 100    (Interest on 1st year's interest)

⇒ 10%

Now we know

Interest = (P × R × T)/100

160 = (P × 10 × 1)/100            (where R = 10 and T = 1 year)

P = 1600 rupees

∴ The value of the principle is Rs. 1600