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Suresh took a loan of Rs. 40,000 from a bank at simple interest of 25% p.a. interest for 2 years. He invested for two years compounded annually and earned an interest of Rs. 7999.2 He invested remaining amount in scheme Q which offers 10% p.a. more rate of compounded interest than scheme P for two years compounded annually. Then, find the total profit made by Suresh after paying the interest to bank?

Suresh took a loan of Rs. 40,000 from a bank at simple interest of 25% p.a. interest for 2 years. He invested for two years compounded annually and earned an interest of Rs. 7999.2 He invested remaining amount in scheme Q which offers 10% p.a. more rate of compounded interest than scheme P for two years compounded annually. Then, find the total profit made by Suresh after paying the interest to bank? Correct Answer Rs. 3055

Calculation:

Amount to be paid to bank = (PTR) / 100 = (40,000 × 2 × 25) / 100 = Rs. 20,000

Amount invested in scheme P = 45.45% of 40,000 = Rs. 18,180

Amount invested in scheme Q = 40,000 - 18,180 = Rs. 21, 820

Suppose the rate of interest provided in scheme P be r% per annum.

⇒ 18180 × = Rs. 7999.2

⇒ (1 + (r / 100))2 - 1 = 7999.2 / 18180

⇒ (1 + (r / 100))2 - 1 = 11 / 25

⇒ (1 + (r / 100))2 = 11 / 25 + 1

⇒ (1 + (r / 100))2 = 36 / 25

⇒ 1 + (r / 100) = √(36 / 25)

⇒ r / 100 = 6 / 5 - 1

⇒ r / 100 = 1 / 5

⇒ r = 100 / 5

⇒ r = 20%

So, the rate in for scheme Q = 20% + 10% = 30%

Compound interest from Scheme B = 21,820 × (1 + (30 / 100))2 - 21,820

⇒ 21,820 × (1.69 - 1)

⇒ 21,820 × 0.69

⇒ Rs. 15055.8

Total interest received from both schemes = Rs. 7999.2 + Rs. 15055.8 = Rs. 23055

∴ Profit earned by Suresh = Rs. (23,055 - 20,000) = Rs. 3055

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