# P invested some money at rate of interest 30% at simple interest. At end of year, he removed 20% of total amount (interest + sum) for his savings and

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P invested some money at rate of interest 30% at simple interest. At end of year, he removed 20% of total amount (interest + sum) for his savings and again invest remaining sum in the same scheme for next year. At the end of second year, he kept Rs.1352 into his savings by doing the same process. Find the initial amount he invested in this scheme.
1. Rs.5000
2. Rs.5200
3. Rs.6000
4. Rs.4500

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Correct Answer - Option 1 : Rs.5000

Formula:

Let P = Principle, R = Rate of interest and N = time period

Simple interest = PNR/100

Calculation:

Let amount invested initially by P be Rs.a

Total amount he kept into savings at the end of second year = Rs.1352

Total amount he earned at the end of second year = 1352 × 100/20 = Rs.6760

Amount earned at the end of first year = a + a × 30 × 1/100 = Rs.13a/10

Amount invested for second year = 13a/10 × 80/100 = Rs.52a/50

Amount earned at the end of second year = 52a/50 + 52a/50 × 30 × 1/100 = Rs.(52a/50 × 13/10)

⇒ 52a/50 × 13/10 = 6760

⇒ a = 5000

∴ The amount invested by P initially is Rs.5000.

Amount kept in savings in a year = (Simple interest + sum invested)  × 20/100

Amount invested in second year = (Simple interest + sum invested)  × (100 - 20)/100