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A man has deposited his money in a bank under two separate options for 8 years. First option gives an interest rate of 8% for first 2 years and 11% for the rest of the time the money is kept in the bank. The second option is a fixed deposit that cannot be withdrawn before 8 years and gives an interest of 10% throughout the entire term. If interest on the deposit under option 1 is less than Second option by 15,400 at the time the term of second option ends and the total money is 80000. What is the amount of money deposited in each option? (Assume all interests are simple.)

A man has deposited his money in a bank under two separate options for 8 years. First option gives an interest rate of 8% for first 2 years and 11% for the rest of the time the money is kept in the bank. The second option is a fixed deposit that cannot be withdrawn before 8 years and gives an interest of 10% throughout the entire term. If interest on the deposit under option 1 is less than Second option by 15,400 at the time the term of second option ends and the total money is 80000. What is the amount of money deposited in each option? (Assume all interests are simple.) Correct Answer option 1 = Rs. 30,000 and option 2 = Rs. 50,000, option 1 = Rs. 35,000 and option 2 = Rs. 45,000

Let the money deposited in option 1 is x and in option 2 is y

Total money is Rs. 80,000

x + y = 80,000       ----(1)

Now, the term of second option is 8 years

Therefore, for second option the total interest = (10/100) × 8 × y = 0.8 × y

For first option the interest for first 2 years = (8/100) × 2 × x = 0.16 × x

For the first option the interest for next 6 years = (11/100) × 6 × x = 0.66 × x

Total interest in first option = 0.16x + 0.66x = 0.82 × x

Interest earned on option 1 is less than second by 15,400:

0.8 × y - 0.82 × x = 15,400       ----(2)

Multiply eqn(1) by 0.8 we get:

0.8 × x + 0.8 × y = 64,000       ----(3)

Subtract eqn(2) from eqn(3)

1.62 × x = 48,600

⇒ x = 48,600/1.62 = 30,000

∴ Money in option 1 is Rs. 30,000 and in option 2 is Rs. 50,000

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